Heat transfer engineering an international journal, tập 31, số 3, 2010

In the quest for improved heat removal rates, in general, pool boiling is considered to be more efficient higher heat transfer coefficient than single-phase liquid flow, while flow boili

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Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

Mechanical Engineering Department, Rochester Institute of Technology, Rochester, New York, USA

Recent literature indicates that under certain conditions the heat transfer coefficient during flow boiling in microchannels

is quite similar to that under pool boiling conditions This is rather unexpected, as microchannels are believed to provide

significant heat transfer enhancement under single-phase as well as flow boiling conditions This article explores the

underlying heat transfer mechanisms and illustrates the similarities and differences between the two processes Formation

of elongated bubbles and their passage over the microchannel walls have similarities to the bubble ebullition cycle in pool

boiling During the passage of elongated bubbles, the longer duration between two successive liquid slugs leads to wall

dryout and a critical heat flux that may be lower than that under pool boiling conditions A clear understanding of these

phenomena will help in overcoming these limiting factors and in developing strategies for enhancing heat transfer during

flow boiling in microchannels.

INTRODUCTION

The nucleation criterion developed by Hsu [1] has been

suc-cessful in predicting the onset of nucleation in pool boiling as

well as in flow boiling The criterion was also shown to be quite

accurate for flow boiling in microchannels by a number of

in-vestigators, including Zhang et al [2] and Kandlikar et al [3]

The high single-phase heat transfer coefficient value prior to

nu-cleation in flow boiling leads to nunu-cleation cavity diameters that

are smaller than those in pool boiling This link between pool

boiling and flow boiling is an important factor in comparing the

two boiling modes

In the quest for improved heat removal rates, in general, pool

boiling is considered to be more efficient (higher heat transfer

coefficient) than single-phase liquid flow, while flow boiling

provides the highest heat transfer coefficients However, recent

data obtained with enhanced single-phase flow channels and

flow boiling in microchannels indicate that this may not be

nec-essarily true with the current status of these two modes of heat

transfer Following the definition of Kandlikar and Grande [4],

microchannels are defined as channels with hydraulic diameter

Address correspondence to Professor Satish G Kandlikar, Mechanical

En-gineering Department, Rochester Institute of Technology, Rochester, NY 14623,

USA E-mail: sgkeme@rit.edu

(or the smallest flow passage width of a channel) between 10 µmand 200 µm

Table 1 shows a comparison of heat transfer coefficients andheat fluxes for four cases: single-phase flow in plain microchan-nels, single-phase flow in enhanced microchannels, pool boiling,and saturated flow boiling in plain and enhanced (with reentrantcavities) microchannels Due to the pressure drop constraints,the flow in microchannels is generally in laminar flow regime.The single-phase heat transfer coefficients are therefore calcu-lated for laminar flow (including the entrance region effect).The plain microchannels are unable to meet the high heat fluxcooling requirement of 1000 W/cm2 (10 MW/m2) However,the microchannels enhanced with short offset strip fins provide

a very high heat transfer coefficient In a practical system withthis geometry, Colgan et al [5] employed multiple-inlet/-outletregions with a flow length of only 2 mm through the microchan-nels This configuration holds the most promise in meeting thefuture chip cooling challenges Results with single-phase flow[5, 6], pool boiling [7, 8], and flow boiling in microchannelsunder stable and unstable conditions [9, 10] are used in thecomparison presented in Table 1

The pool boiling mode at macroscale offers an efficient mode

of heat transfer The saturated flow boiling heat transfer withplain microchannels [9] and that with reentrant cavities [10]both provide an improvement over plain microchannels, but fallsubstantially below the desired values Although these values

159

Table 1 Comparison of heat transfer coefficients with water under different

modes

Heat transfer mode h, kW/m 2 ◦C q, MW/m2

Single-phase flow in plain 100- to

200-µm square microchannels

10–15 0.1–0.2 Single-phase flow in enhanced

microchannels, 48 µm × 256 µm,

offset strip fins, 500 µm, Colgan et al.

[5], Steinke and Kandlikar [6]

>500 5–10

Pool boiling, flat surface, fully developed

boiling, Nukiyama [7], microdrilled

surface, Das et al [8]

∼30–300 1.2–4.8

Saturated flow boiling in D h∼ 207 µm

rectangular microchannels, Steinke

and Kandlikar [9], with reentrant

cavities, Kuo and Peles [10]

are higher than those under pool boiling, the increase is not

significant In fact, employing enhanced pool boiling surfaces

can improve the performance by a factor of 2–4, e.g., by

mi-crodrilling the heater surface with holes at 5–10 mm pitch as

reported by Das et al [8]

In comparison, a set of parallel microchannels with or

with-out reentrant cavities yields much lower performance as

com-pared to single-phase flow in enhanced microchannels or pool

boiling on enhanced surfaces This has been a major concern in

developing flow boiling systems to meet the needs in electronic

cooling applications

There have been a number of papers published exploring the

effect of diameter on flow boiling heat transfer A comparison

of two data sets obtained by Kenning and Cooper [11] for a

9.6 mm diameter circular tube and by Steinke and Kandlikar [9]

for a 207 µm hydraulic diameter rectangular channel is shown

in Figure 1 Both data sets are obtained at close to atmospheric

pressure and the Boiling numbers are around 1.5 × 10−4 in

both cases The effect of diameter on the ratio of two-phase

to liquid-only single-phase heat transfer coefficients is depicted

Figure 1 Effect of channel hydraulic diameter on the ratio h T P / h LOfor Bo

≈ 1.5 × 10 4 during flow boiling of water near atmospheric pressure.

in Figure 1 It is seen that this ratio is reduced considerablyfrom a value of 9.5 for the 9.6 mm-diameter tube to 4 for

the 207 µm channel Further, considering the fact that h LO

in the microchannel corresponds to laminar flow conditions, acompelling argument can be made for the dramatic reduction inheat transfer coefficient for the smaller diameter tube

It has been suggested by a number of authors, includingLazarek and Black [12], that flow boiling in narrow channelscan be predicted reasonably well with a pool boiling correla-tion Kew and Cornwell [13] compared the flow boiling data innarrow channels with an established pool boiling correlation byCooper [14] with some degree of success The other correlationsthat were similarly successful had heat flux as the primary vari-able This realization, brought about by the success of the poolboiling correlations in predicting the flow boiling in microchan-nels, is really the precursor to the present article This similarity

is further explored using the available literature on experimentaldata and theoretical models The discussion is focused on water

as the working fluid, but by no means is this study intended to berestrictive in this regard The broad availability of experimentaldata with water makes it possible to present a more compre-hensive comparison between the pool boiling and microchannelflow boiling

NUCLEATE BOILING AND CONVECTIVE BOILING CONTRIBUTIONS

The contributions from nucleate boiling and convective ing during flow boiling are well recognized The nucleate boilingcontribution is dependent on the heat flux, in a manner similar tothe pool boiling with an exponent of around 0.7 The convectiveboiling component is independent of the heat flux and varieswith the mass flux For the conventional large diameter tubes,the mass flux dependence was identified with an exponent of0.8, which is in agreement with the turbulent single-phase flowrelationship A flow boiling map proposed by Kandlikar [15]showed these contributions with Boiling number Bo and den-sity ratio, ρL /ρ G, as parameters The map was developed with

boil-h T P / h LO versus x using the Kandlikar [16] correlation The

map was instrumental in explaining the different dependenciesobserved in the two-phase heat transfer data as a function ofquality The nucleate boiling component is adversely affectedwith an increase in quality, while the convective boiling termincreases with quality due to the higher specific volume of vaporbeing produced The relative contributions from these compo-nents are governed by Bo and ρL /ρ G A higher density ratiocauses a larger increase in the overall flow velocity upon va-porization, leading to a greater increase in the heat transfercoefficient, while a low value of density ratio causes the con-vective contribution to increase only moderately A combination

of low Bo and high ρL /ρ Gcauses hT P/hLOto increase with an

increase in x, while a combination of high Bo and low ρ L /ρ G

causes hT P/hLO to decrease with an increase in x.

heat transfer engineering vol 31 no 3 2010

Table 2 Comparison of two-phase flow structures in the two boiling modes

Bubble inception as the nucleation

criterion is met for specific

cavities under single-phase liquid

flow.

Bubble inception as the nucleation criterion is met for specific cavities under natural convection with liquid.

Elongated bubble covering the

channel walls.

Growing bubbles covering the heater surface.

Liquid slug being pushed between

the two consecutive elongated

bubbles.

Liquid circulation around the nucleating bubbles as a result of the individual bubble ebullition cycles.

Liquid slugs are intensely mixed

with vapor in a churn flow.

Liquid surrounding bubbles (undergoing ebullition cycles) is intensely mixed with vapor at high heat fluxes under fully developed boiling conditions.

These trends, as described by Kandlikar [15], are further

affected by laminar flow occurring in small-diameter channels

Depending on the single-phase liquid Reynolds number, the

flow may be in the laminar region, where the single-phase liquid

heat transfer coefficient under fully developed flow conditions

is independent of the mass flux This is one of the reasons why

the two-phase heat transfer coefficient is dramatically altered in

microscale channels

Another effect of the small channel dimensions arises due

to the changes occurring in the flow patterns The nucleating

vapor bubbles are confined in the small channels and grow as

elongated bubbles, forming alternate liquid slugs and elongated

bubbles The two-phase flow structures during flow boiling

re-semble the respective pool boiling characteristics as shown in

Table 2

The single-phase heat transfer in microchannels is generally

under laminar flow conditions due to the pressure drop

limita-tions and the small channel dimensions As pointed out earlier,

the convective contribution from the single-phase liquid flow

needs to be considered using the laminar flow equation The

de-pendence of the convective contribution is thus altered from the

conventional channel trends since the Nusselt number in laminar

flow is independent of the flow rate These effects are accounted

for in the flow boiling correlation proposed by Kandlikar and

Balasubramanian [17] The correlation is rewritten in terms of

the density ratio and Boiling number as follows:

3000, a linear interpolation is recommended

For the low Reynolds number range 100≤ ReLO <400, theheat transfer coefficient is found to be always nucleate boilingdominant (NBD) Thus:

h T P

h LO = 1058.0Bo 0.7(1− x) 0.8 F F l (5)Equations (1)–(5) are used to generate a flow boiling mapfor microchannels Three values of density ratio, 10, 100, and

1000, and two values of Bo∗, 10−4 and 10−3, are used to erate the plots The modified Boiling number Bo∗is defined asfollows:

Figures 2–4 show the plots generated for different Re ranges

Figure 2 shows the variation of the ratio h T P / h LO with x

with different values of Bo for 400 ≤ ReLO ≤ 1600 Thisplot is same as the one for large-diameter tubes, but the actualheat transfer coefficient will be different since the single-phase

Figure 2 Flow boiling map for microchannels in the range 400 ≤ ReLO ≤

1600, Bo∗= Bo × (F F l)1/0.7.heat transfer engineering vol 31 no 3 2010

Figure 3 Flow boiling map for microchannels in the range 100 ≤ ReLO <

400, Bo∗= Bo × (F F l)1/0.7.

coefficient h LO will be derived from the laminar flow

equations

Figure 3 shows the flow boiling map for 100≤ ReLO <400

Here the nucleate boiling component begins to play a major

role as seen by the continuous decrease in h with x throughout

the range In other words, the increased flow velocity at higher

x does not provide the expected benefits in terms of improved

convective heat transfer

Figure 4 shows the flow boiling map for very low values of

ReLO <100 The convective component is completely blocked

off; the density ratio has no effect on h Here the suppression

effects are overriding and the heat transfer exhibits similar

char-acteristics as in nucleate boiling with the increased suppression

effects at higher qualities

Figure 4 Flow boiling map for microchannels in the range ReLO <100,

ReLO is reduced, it is seen that the nucleate boiling becomes

the dominant mode, with its decreasing trend in h versus x.

Further decreases in Reynolds number cause the heat transfer todeteriorate, with the elimination of the convective contributionterm in Eq (5)

The boiling instabilities experienced in microchannels areanother major cause for heat transfer reduction These instabil-ities occur at lower mass fluxes as the inertia of the incomingliquid is insufficient to prevent the liquid from rushing back.The reasons for instabilities and methods for preventing themhave been discussed in a number of publications, including Ser-izawa et al [19], Steinke and Kandlikar [9], Hetsroni et al [20],Kandlikar et al [3], and Kuo and Peles [21] As a result of theinstabilities, the walls of the microchannels remain exposed tothe expanding vapor bubble, creating local dry patches on thewall and causing heat transfer deterioration

Another method to avoid the instabilities is to change theoperating conditions with increased mass fluxes Dong et al.[22] conducted experiments with R-141b in 60 µm× 200 µmparallel rectangular microchannels for mass fluxes of 400 to

980 kg/m2-s Boiling was initiated within the channels withsubcooled liquid inlet Pressure drop oscillations were not ob-served and stable boiling was attained The stable results ob-tained under such conditions were shown to agree quite well withthe Kandlikar and Balasubramanian [17] correlation, whereasthe unstable data observed in the Steinke and Kandlikar cor-relation showed a marked deterioration with increasing qual-ity as shown in Figure 5 The results of Dong et al [22] areshown in Figure 6 Although a higher mass flux is beneficial forheat transfer, the resulting pressure drop could be prohibitivelylarge

Similarities Between Pool Boiling and Microchannel Flow Boiling Mechanisms

Some of the recent publications provide an insight into the

reasons for this dramatic reduction in h with x, even under

stable conditions Using the elongated bubble flow pattern scription, Kandlikar [23] pointed out the similarities between themicrochannel flow boiling and pool boiling heat transfer As abubble grows, the downstream interface represents the recedingliquid–vapor interface of a growing nucleating bubble, whereasthe upstream interface of the elongated bubble is similar to theadvancing liquid–vapor interface of a nucleating bubble as itsbase shrinks and the bubble begins to depart from the heatedheat transfer engineering vol 31 no 3 2010

de-Figure 5 Flow boiling results from Steinke and Kandlikar [9] for water,

showing dramatic reduction in heat transfer performance at increased qualities

due to instabilities; qis heat flux, W/m2

surface in pool boiling Figure 7a depicts the respective

inter-faces as elongated bubbles are formed in a microchannel These

two interfaces were experimentally studied in a moving

menis-cus on a heated surface by Kandlikar et al [24] and numerically

by Mukherjee and Kandlikar [25] Their studies showed the

important roles played by transient conduction as the liquid

in-terface advances over the heater surface The microconvection

caused by the liquid flow behind the advancing liquid interface

for a moving meniscus is shown in Figure 7b, and during a

nu-cleate boiling bubble ebullition cycle is shown in Figure 7c The

receding interface provides a phase change surface where the

liquid superheat is dissipated and cooled liquid becomes

avail-Figure 6 Experimental data for flow boiling of R-141b by Dong et al [22]

and predictions from Kandlikar and Balasubramanian [17] at G = 500 kg/m 2 s

under stable operation, FF l = 1.8, Bo* = [q/(Ghf g)] × FF l = 1.2 × 10 −3

(lower line) and 1.6 × 10 −3(upper line).

Figure 7 Elongated bubbles in microchannels presenting advancing and ceding interfaces in (a) that are similar to interface movements of a moving meniscus (b) and a nucleating bubble during a bubble ebullition cycle in pool boiling shown in (c).

able for the transient conduction process The advancing and ceding interfaces seen around an elongated bubble are shown inFigure 7a

re-In the model proposed by Jacobi and Thome [26], theheat transfer in the liquid slug region is assumed to be bylaminar steady-state convection, and its contribution is quitesmall compared to that from microlayer evaporation However,the numerical simulation and the results from transient con-duction model described by Mukherjee and Kandlikar [25]and Kandlikar et al [24] indicate that transient conductionand microconvection modes contribute significantly in theevaporating meniscus geometry Mukherjee and Kandlikar [27]simulated the bubble growth and elongated flow pattern devel-opment in microchannels and concluded that the transient con-duction and the subsequent convection behind theevaporatingliquid–vapor interface were the major contributors to the to-tal heat transfer process in microchannel flow boiling aswell

heat transfer engineering vol 31 no 3 2010

Role of Microlayer Evaporation during Elongated Bubble

Flow Pattern

Comparing pool boiling and the microchannel flow boiling

processes, the three distinct modes of heat transfer that can be

identified in both cases are:

1 Transient conduction heat transfer resulting from the motion

of the liquid–vapor interface over the heated surface The heat

transfer is enhanced due to the cooler liquid being brought

in contact with the heater surface as a result of interface

movement

2 Microconvection heat transfer resulting from the increased

convection from the interface movement It is combined with

the transient conduction contribution effect described above,

since it is difficult to identify and isolate their individual

effects

3 Microlayer evaporation resulting from the evaporation of a

thin layer of liquid left on the heater by the receding liquid–

vapor interface

Relative contributions from these three mechanisms have

been a topic of intense research in pool boiling Myers et al

[28] used silicon chips with heaters and sensors to determine

the localized heat fluxes and surface temperatures around

nu-cleating bubbles Figure 8 shows the relative contributions from

these three mechanisms for water It can be seen that the

tran-sient conduction/microlayer convection together are the largest

contributor to the total heat flux during a bubble ebullition cycle

The microlayer contribution was seen to be quite small, around

20% These results are in agreement with the numerical work

by Son et al [29] Recent work by Moghaddam and Kiger [30]

showed similar results for FC-72

The microlayer contribution has received considerable

at-tention in recent flow boiling studies in microchannels It is

Figure 8 Relative contributions from different mechanisms during pool

boil-ing Redrawn using data from Myers et al [28].

Figure 9 Equivalent convective coefficient for films under a steady-state duction model.

con-very difficult to measure the microlayer thickness in the crochannel flows Calculating from the experimental data, afilm thickness on the order of 10–20 µm has been estimated byJacobi and Thome [26] from a parametric study The initial film

mi-Table 3 Similarities and differences between pool boiling and microchannel flow boiling processes

Nucleation The same nucleation criterion by Hsu [1]

is applicable for both processes.

Nucleation cavities and bubble departure

sizes are larger The low h in single-phase

flow prior to nucleation allows nucleation

at lower wall superheats.

Nucleation cavities and bubble departure

sizes are smaller The high h value during

single-phase liquid flow prior to nucleation introduces large wall superheat Bubble growth Transient conduction and

microconvention heat transfer processes are similar in the liquid slug.

At higher flow rates, the two-phase flow characteristics of large-diameter tubes appear and the microchannel flow boiling becomes distinctly different from pool boiling.

The bulk liquid is not highly superheated prior to onset of nucleation, causing the bubbles to grow predominantly near the heater surface.

Bulk liquid also reaches a high degree of superheat causing explosive bubble growth following nucleation.

Microlayer Role of microlayer evaporation is

relatively limited in both cases, accounting for only 20–25% of the total heat transfer.

The microlayer thickness is on the order of 1–3 µm, Koffman and Plesset [34] The high frequency in the bubble ebullition cycle limits the occurrence, extent, and duration of dry patches from microlayer depletion from evaporation at high heat fluxes.

The microlayer under bubbles in flow boiling are thicker and impede heat transfer The lower frequency of elongated bubble passage allows longer time for microchannel wall dryout.

Critical heat flux

(CHF)

CHF condition results from the inability

of the advancing liquid front to rewet the dry patches.

Smaller bubbles coalesce prior to CHF as the liquid interface retracts away.

The dry patches formed during long duration

of elongated bubble flow are heated to a high temperature before the arrival of the liquid front, leading to the CHF condition Heat transfer

enhancement

Altering nucleation characteristics will provide significant heat transfer enhancements in both cases.

Providing early nucleation by introducing cavities of right sizes and geometries is successfully implemented in pool boiling.

New ideas need to be developed.

Microbubble generation to avoid or delay formation of large elongated bubbles may lead to higher heat transfer rates Local heating elements driven by pulsed currents, vibrations, or dissolved gases may be used to generate the microbubbles.

Comparison Between the Pool Boiling and Microchannel

Flow Boiling Processes

The underlying heat transfer mechanisms in the two

pro-cesses have many similarities, with transient conduction,

mi-croconvection, and microlayer evaporation playing similar roles

in both The essential differences between the two processes

emerge from the presence of strong inertia forces in the bulk

flow and the large shear stress present at the wall These forces

affect the nucleation and other flow characteristics directly Heat

transfer processes are also affected

Table 3 summarizes the main features that are common

be-tween the two processes The role of gravity is critical in pool

boiling, but this effect is negligible in microchannels, where the

interface motion is mainly governed by evaporation momentum

and inertia forces Although the forces are different, the

result-ing interface movement leads to similarities in the underlyresult-ing

heat transfer mechanisms in the two cases The effect on critical

heat flux is also described, and some enhancement strategies are

outlined Avoiding microlayer dryout and avoiding or delaying

the elongated bubble formation are seen as ways to improve the

heat transfer and CHF in microchannels Microbubbles seem to

have great promise in improving the heat transfer They may be

generated in microchannels by using localized heating elements

that are supplied with pulsed electric supply Introducing tions using piezoelectric elements is also seen as a promisingtechnique to generate microbubbles Although dissolved gaseswill also lead to generation of microbubbles, their overall effect

vibra-on the interfacial heat transfer and system performance needs to

be investigated Experimental results from Steinke and likar [36] indicate an increase in the subcooled flow boiling heattransfer at the nucleation, but the heat transfer was reduced asthe bubbles formed a thin insulating layer Effective removal

Kand-of bubbles is important Further research on these topics iswarranted

CONCLUSIONS

The similarities between the pool boiling and microchannelflow boiling processes are discussed The roles of transientconduction, microconvection, and microlayer evaporationduring elongated bubble flow patterns in microchannel flowboiling are similar to those in pool boiling Avoiding liquidfilm dryout, and delaying the formation of elongated bubbleflow pattern by introducing microbubbles are proposed as some

of the ways to enhance the heat transfer and critical heat flux(CHF) As the flow velocity increases, the microchannel flowheat transfer engineering vol 31 no 3 2010

boiling is expected to resemble the flow boiling in minichannels

and conventional-sized channels (>3 mm) with the presence of

churn flow pattern The resulting high pressure drop needs to

be considered while operating under such high flow conditions

Shorter flow lengths and improved header arrangements are

needed to alleviate the pressure drop limitations Microbubbles

are seen as an effective way to improve heat transfer by avoiding

or delaying the formation of elongated bubble flow pattern

NOMENCLATURE

Bo Boiling number= q/(Gh f g), dimensionless

Bo* modified Boiling number, defined by Eq (6),

dimension-less

D h hydraulic diameter, m

FF l fluid surface parameter, dimensionless

G mass velocity, kg/m2-s

h Heat transfer coefficient, W/m2-K

h f g latent heat of vaporization, J/kg

q heat flux, W/m2

Re Reynolds number, dimensionless

x vapor quality, dimensionless

LO entire flow as liquid

NBD nucleate boiling dominant

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Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903304343

Performance of Counterflow

Microchannel Heat Exchangers

Subjected to External Heat Transfer

BOBBY MATHEW and HISHAM HEGAB

Mechanical Engineering Program, Louisiana Tech University, Ruston, Louisiana, USA

This article analyzes the effect of external heat transfer on the thermal performance of counterflow microchannel heat

exchangers Equations for predicting the axial temperature and the effectiveness of both fluids as well as the heat transferred

between the fluids, while operating under external heating or cooling conditions, are provided in this article External

heating may decrease and increase the effectiveness of the hot and cold fluids, respectively External cooling may improve

and degrade the effectiveness of the hot and cold fluids, respectively For unbalanced flows, the thermal performance of

the microchannel heat exchanger subjected to external heat transfer depends on the fluid with the lowest heat capacity At

a particular number of transfer units (NTU), the effectiveness of both the fluids increased with decrease in heat capacity

ratio when the hot fluid had the lowest heat capacity When the cold fluid had the lowest heat capacity, the effectiveness of

both fluids increased with decrease in heat capacity ratio at low values of NTU but at high values of NTU the effectiveness

increased with increase in heat capacity ratio A term called the “performance factor” has been introduced in this article to

assess the relative change in effectiveness due to external heat transfer.

INTRODUCTION

The conventional ε-NTU (number of transfer units)

equa-tions are based on several assumpequa-tions [1] One among them

is that the thermal interaction in a two-fluid heat exchanger is

limited to that between the fluids This is a valid assumption

as long as the heat exchangers are reasonably insulated from

their surroundings However, thermal insulation of

microchan-nel heat exchangers (MCHXs) by packaging them in materials

of low thermal conductivity or vacuum can significantly affect

their size and prevent them from being integrated with other

micro devices [2, 3] The lack of proper insulation can cause the

fluids in a MCHX to thermally interact with their surroundings

due to reasons such as:

1 Low thermal resistance between the ambient and the

individ-ual fluids due to small wall thickness and high heat transfer

coefficient in the channels,

2 Proximity between the MCHX and other thermal

microelec-tromechanical systems (MEMS) devices placed on the same

substrate,

Address correspondence to Professor Hisham Hegab, Mechanical

Engineer-ing Program, Louisiana Tech University, P.O Box 10348, Ruston, LA 71272,

USA E-mail: hhegab@latech.edu

3 High temperature differences between the ambient and thefluids, as in microchannel heat exchanger reactors, micro-miniature refrigerators, and microcombustors [2–5].The need for thermal isolation can be further understood byanalyzing the microchannel heat exchanger that was recentlydeveloped by Hill et al [6] for conducting chemical reactions.Chemical reactions occurred in one set of channels while thecoolant was pumped through the other set of channels Thismicrodevice interacted with the ambient, as it was not providedwith proper thermal isolation Hill et al [6] observed that 10 W

of heat was transferred to the coolant from the ambient whileoperating this microdevice The effect of external heat transferwas not taken into consideration during the design stage, and due

to this the outlet temperature of the chemicals could be higherthan that estimated during designing Based on these reasons

it is important to consider the effect of external heat transferwhile designing a MCHX Thus, there is need for extending theconventional ε–NTU relationship to account for the effect of ex-ternal heat transfer on the effectiveness of a MCHX Heat trans-fer between the fluids and the external heat source is referred

to as external heat transfer in this study External heat transferconsidered in this article is the result of subjecting the fluids

of a MCHX to uniform axial heat flux Therefore the external

168

heat transfer is constant over the entire length of the MCHX A

counterflow microchannel heat exchanger (MCHXCF) has the

best performance, compared with other types of heat

exchang-ers, for a specific value of NTU and thus it is often preferred over

other flow arrangements Consequently, it is examined in this

article

There are a few articles that have examined the effect of

external heat transfer on the thermal performance of heat

ex-changers Hurd [7] developed an analytical expression for the

mean temperature difference between the fluid in the annular

section of a bayonet tube heat exchanger and the external fluid

Bayonet tube heat exchangers are commonly used for

recover-ing heat from the surroundrecover-ings and thus their interaction with

the environment is necessary and is not considered a drawback

Hurd [7] concluded that best recovery of heat (external heat

transfer) occurs when the external fluid and that in the

annu-lar section flow in opposite directions Barron [8] formulated

equations for predicting the performance of counterflow heat

exchangers subjected to heat transfer between the ambient and

the individual fluids He considered two cases; in each of these

cases only one of the fluids was externally heated/cooled by the

ambient For both cases, he considered the effectiveness of the

hot fluid alone He provided formulas for determining the axial

temperatures of the fluids, as well as the heat transferred

be-tween the fluids and the ambient From both models, Barron [8]

observed that the hot fluid effectiveness degraded whenever the

ambient temperature was greater than the inlet temperature of

the fluids Under extreme conditions of external heating, the

ef-fectiveness of the hot fluid became negative Barron [8] defined

the heat capacity ratio with respect to the fluid that was being

heated/cooled; thus his models can only be used for balanced

flow or whenever the heated/cooled fluid has the lowest heat

capacity

Chowdhury and Sarangi [9] developed analytical equations

for predicting the axial temperature of the fluids in a double pipe

counterflow heat exchanger subjected to external heat transfer

In this model the fluid in the inner tube was free from external

heat transfer They developed analytical equations for

determin-ing the axial temperature of the fluids in such a heat exchanger

However, only the effectiveness of the fluid in the outer tube was

considered by them They introduced the concept of effective

NTU, which is determined from the actual effectiveness If the

external heat transfer causes degradation of effectiveness, then

the effective NTU would be lower than the NTU at which the

heat exchanger was originally designed to operate In the

ab-sence of external heat transfer the effective NTU becomes same

as the NTU at which the heat exchanger was originally designed

Comparison of both the NTUs can provide information about

the reduction in heat transfer surface area that occurs due to

external heating However, the concept of effective NTU is

use-ful only as long as the effectiveness is between zero and unity

Chowdhury and Sarangi [9] used this model to analyze a case

where the hot and cold fluids were pumped through the inner and

outer tubes, respectively, of a heat exchanger subjected to

exter-nal heating They observed that the presence of exterexter-nal heating

brought about considerable reduction in the effectiveness of thehot fluid

Ameel and Hewavithrana [10] developed a model for dicting the thermal performance of counterflow heat exchang-ers subjected to heat transfer with the ambient Their model wasvery similar to that of Barron [8] except that in their modelboth fluids could be simultaneously subjected to external heattransfer They provided equations for estimating the tempera-ture profile of the fluids and the heat exchanged between eachfluid and the ambient; however, they considered only the hotfluid effectiveness According to their model, the hot fluid ef-fectiveness decreased whenever heat was transferred from theambient to the fluids The degree of degradation of the hot fluideffectiveness depended on the amount of heat transferred fromthe ambient to the fluids Moreover, they stressed the importance

pre-of temperature cross in the design pre-of heat exchangers subjected

to external heat transfer They noticed that no improvement, for

a specific amount of heating and capacity ratio, in the tiveness of the heat exchanger could be achieved by increasingits heat transfer surface area once temperature cross had oc-curred In their model the heat capacity ratio was defined withrespect to the cold fluid and thus their model is only relevantfor balanced flow or when the cold fluid has the minimum heatcapacity

effec-Peterson and Vanderhoff [11] computationally analyzed anMCHXCFthat experienced performance degradation due to radi-ation heat loss and axial heat conduction This kind of situationusually exists in an MCHXCF that is used in devices such asmicrocombustors and microminiature refrigerators The ends ofthe wall separating the coolants were not insulated Radiationheat loss occurring between the ambient and the outer surface

of the MCHXCF was considered in their study The axial heatconduction through the entire MCHXCFstructure was taken intoaccount in this model Radiation heat transfer was accounted for

by using the concept of radiation heat transfer coefficient Theauthors presented their results in terms of heat loss (due to axialheat conduction, radiation, and finite heat transfer surface area)rather than in terms of effectiveness or fluid temperatures Heatloss between the MCHXCFand its surroundings was found todecrease with initial increase in NTU, but it increased as NTUwas further raised Peterson and Vanderhoff [11] suggested fab-ricating a MCHXCFusing materials of low thermal conductivity

in order to reduce the effect of radiation heat loss and axial heatconduction on its thermal performance

Seetharamu et al [12] applied the concept of a three-fluidheat exchanger for predicting the thermal performance of atwo-fluid parallel-flow double-pipe heat exchanger subjected toheating/cooling from the ambient The fluid in the outermosttube was considered to be ambient, and thus only the fluid inthe intermediate tube interacted with the ambient Seetharamu

et al [12] numerically analyzed this particular three-fluid heatexchanger, and their predictions, for fluid temperature and effec-tiveness, were found to be in good agreement with the solutionsprovided by earlier researchers [8] They observed that when theinlet temperatures of both fluids are above that of the ambient,heat transfer engineering vol 31 no 3 2010

reduction in the thermal resistance between the ambient and the

fluid in the intermediate tube improved and degraded the hot

and cold effectiveness, respectively

Nellis and Pfotenhauer [13] theoretically analyzed a

coun-terflow heat exchanger in which the fluids were subjected to

uniform external heat flux They considered the effectiveness of

both fluids in their model Using the model they observed that

the external heating of either of the fluids by the application

of uniform heat flux always decreased the hot fluid

effective-ness [13] Nellis and Pfotenhauer [13] defined the external heat

transfer with respect to the product of thermal conductance and

inlet temperature difference (UA(Thi−Tci)) This term does not

have any physical significance with respect to the design and

operation of heat exchangers Moreover, Nellis and Pfotenhauer

[13] defined heat capacity ratio with respect to the hot fluid

Thus, the NTU defined in their work will become the same as

the conventional NTU only for balanced flow or when the hot

fluid has the lowest heat capacity

Mathew and Hegab [14] recently conducted experimental

studies on the thermal performance of a MCHXCFsubjected to

uniform external heat flux To the knowledge of the authors this

is the only article that has reported experimental studies on the

performance degradation of MCHXCFdue to external uniform

heat flux heating In their experiments both fluids were equally

heated by the external heat source The NTU was varied between

0.35 and 1.4 and the corresponding hot fluid effectiveness, with

no external heating, ranged from 0.26 to 0.58 [14] The hot fluid

effectiveness corresponding to 15% and 25% external heating

range from 0.23 to 0.5 and 0.21 to 0.44, respectively [14]

These experimental data show a drastic reduction in the hot

fluid effectiveness and provide further proof for the need for

extending the conventional ε-NTU relationship An in depth

analysis of the many articstudies that have dealt with similar

topics can be found elsewhere [15]

A thermal model of an MCHXCFwhose fluids are subjected

to external heat transfer has been developed in this article In

this model the cause of external heat transfer is the uniform heat

flux that is applied to the fluids of the MCHXCF The concept put

forward in this study is simpler than the ones already existing, as

the input parameters such as NTU and heat capacity ratio have

been defined in a conventional way The external heat transfer

has been defined with respect to the maximum heat transfer

(qmax) thermodynamically possible in a heat exchanger without

external heat transfer, i.e., qmax = Cmin(Th,i – Tc,i), and thus

its impact on the thermal performance of an MCHXCF can be

easily understood The theory provided in this study can be used

irrespective of the fluid that is being externally heated/cooled

The same cannot be said about the analytical equations provided

by Barron [8], Ameel and Hewavithrana [10], and Nellis and

Pfotenhauer [13], as has been explained previously In addition,

formulas for determining the axial temperature of the fluids have

also been provided in this article Toward the end of this article

the authors have introduced a term, the “performance factor,”

to analyze the relative change in effectiveness of an MCHXCF

when subjected to external heat transfer

THEORETICAL MODEL

The following assumptions were made to develop a modelfor the MCHXCFsubjected to external heat transfer:

1 MCHXCFoperates under steady-state conditions

2 The temperatures of the fluids vary only in the axial direction

3 No-slip boundary condition is assumed in the microchannels

(Kn < 0.001).

4 There is no phase change in either of the fluid streams

5 Effects of longitudinal heat conduction in the fluid, viscousdissipation and flow maldistribution are neglected

6 Axial heat conduction through the wall separating the fluids

is neglected

7 The thermophysical properties of the fluids are assumed to

be constant over the length of the MCHXCF

8 The ends of the wall separating the fluids are considered to

be insulated

Figure 1 represents a differential element of the MCHXCF

considered in this study Equations (1) and (2) can be obtained

by applying the first law of thermodynamics to the individualfluids

These equations are rearranged and dq ex has been replaced

by UP(T h – T c ) dx to obtain the governing equations:

dθ h

dZ + C Rh N T U(θh− θc)− Q h C Rh= 0 (5)

dθ c

dZ + C Rc N T U(θh− θc)+ Q c C Rc= 0 (6)

Figure 1 Schematic representation of a differential element of the MCHX CF

studied in this article.

heat transfer engineering vol 31 no 3 2010

The boundary conditions, in nondimensional form, are:

Under the balanced flow condition, CRhand CRc would be

the same and numerically equal to unity While operating the

MCHXCF under unbalanced flow condition, CRh and CRc

de-pend on the heat capacities of the fluids If the cold fluid has the

lowest heat capacity then CRc would be unity and CRhwould

represent the conventional heat capacity ratio (CR) Likewise,

when the hot fluid has the lowest heat capacity then CRh and

CRcwould be numerically equal to unity and the conventional

heat capacity ratio, respectively Q is the nondimensional

exter-nal heat transfer It can be noticed from Eqs (5) and (6) that the

external heat transfer (qA) and the heat exchanged between the

fluids (q ex ) are defined with respect to qmax Both Qhand Qcare

positive if the fluids are externally heated and negative if they

are being externally cooled

The mathematical procedure for solving these equations has

been provided by Wylie [16] For balanced flow condition, Eqs

(9) and (10) represent the hot and cold fluid temperature,

a1 = 1,

a2 = −NT U + Q h + NT U · (Q h + Q c)(1+ 0.5NT U)

1+ NT U

Equations (11) and (12) represent the nondimensional axial

temperature of the fluids for unbalanced flow conditions

k1= NT U · (C Rh − C Rc ), k2= C Rh C Rc N T U · (Q h + Q c)The effectiveness of an MCHXCF, for all values of nondi-mensional external heat transfer parameters, is defined in thesame way as conventional effectiveness, i.e., as the ratio of ac-

tual heat transfer (q act) to the maximum heat transfer possible

between the fluids (qmax) [1] In order to determine the actualand maximum heat transfer, the heat capacities as well as theinlet and outlet temperatures of the fluids are required Thenondimensional outlet temperatures can be determined fromEqs (9)–(12) The equations for determining the effectiveness

of the fluids for both balanced and unbalanced flow conditionsare shown in Table 1

Equations (9)–(12) cannot be directly used when NTU is zero

or infinite In order to obtain the effectiveness when NTU is zero

or infinite, L’Hospital’s rule is applied to these equations Theeffectiveness of the fluids thus obtained is provided in Table 2 AMCHXCFmay never be operated at the extreme values of NTU;however, these equations have been presented here to provide acomplete discussion of their thermal performance

Equations (9)–(12) can be used for predicting the temperature

as well as effectiveness of the fluids even when there is noexternal heating/cooling The temperature or effectiveness ofthe fluids for such a situation can be obtained by substitutingzero for Qhand Qcin the appropriate equations provided earlier.Equations (13) and (14) represent the temperature of the hot andcold fluid under balanced flow condition The temperature of thehot and cold fluid for unbalanced flow conditions is presented

in Eqs (16) and (17), respectively The effectiveness of the hotand cold fluid is the same when external heat transfer to either

of the fluids is absent Equation (15) represents the effectivenessfor balanced flow, while Eq (18) represents that for unbalancedflow Equation (15) can be obtained from either Eq (13) or (14).Similarly, Eq (18) can be derived from either Eq (16) or (17)

θh= 1+ (1 − Z)NT U

Table 1 Hot and cold fluid effectiveness for balanced and unbalanced flows

Effectiveness Fluids C min = C Rc C min = C h C min = C c

Table 2 ε-NTU relationships when NTU = 0 and NTU = ∞

Effectiveness

Shah and Sekulic [1] had developed equations for

determin-ing the axial temperature of the fluids in a counterflow heat

exchanger free of external heating/cooling; however, the flow

paths of the fluids in their heat exchanger were in a direction

opposite to that assumed in this work Therefore, for the purpose

of comparison the nondimensional axial distance parameter in

the preceding equations was replaced by 1 – Z Equations (13),

(14), (16), and (17) were then validated to be exactly same as

those formulated by Shah and Sekulic [1]

The heat exchanged between the fluids can be determined

from the equations that define their axial temperature The

gen-eral form for calculating the nondimensional heat transferred

between the fluids is given in Eq (19)

The heat transferred between the fluids has been

nondimen-sionalized with respect to the maximum heat transfer (qmax)

possible in a MCHXCFwithout external heat transfer Equations

(20) and (21) represent the heat transferred, in dimensionless

form, between the fluids for both balanced and unbalanced flow

of viscous dissipation is to raise the temperature of the fluids

in the microchannels in a manner similar to that of subjectingthe fluids to a uniform external heat flux [17–19] Thus thesolution developed here can be used for determining the thermalperformance of a MCHXCF with viscous dissipation as well,even though it was not explicitly included in the governingequations [19]

RESULTS AND DISCUSSION

For this section the thermal performance of a MCHXCFjected to external heat transfer has been analyzed using theequations already derived These equations can be used for de-termining the hot and cold fluid effectiveness irrespective of theamount of external heat transfer For illustrative purposes, inthis article the case when both fluids are subjected to the equalamounts of external heat transfer (Qh= Qc= 0, 0.25, 0.5, 0.75,1) is analyzed Toward the end of this article the authors haveintroduced a term called the “performance factor” for assessingthe relative change in effectiveness of the fluids of a MCHXCF

sub-due to external heat transfer

The variation of hot and cold fluid effectiveness with respect

to NTU for balanced flow has been shown in Figure 2 The solidline in this figure represents the effectiveness of both fluids whenexternal heating is absent As seen from Figure 2, the effective-ness of the hot fluid decreased, for a particular value of NTU,with increase in external heating This is an expected trend;with increase in the amount of external heating there occurs anincrease in the outlet temperature of the hot fluid and thus an ob-served reduction in its effectiveness Further, the effectivenessheat transfer engineering vol 31 no 3 2010

Figure 2 ε–NTU relationship of a balanced flow MCHX CF (CRh= CRc).

of the hot fluid increased with increasing NTU for all levels of

external heating This may be explained by the fact that raising

the NTU by decreasing the flow rate, for a specific Qhand Qc,

is accompanied by a decrease in the heat flux that is applied

to fluids if the geometry of the MCHXCFis kept constant This

can be understood from the equation defining Q Thus there is

a decrease in the external heat transfer (q ext) to the individual

fluids Moreover, in this scenario, there is an increase in the heat

transfer surface area per unit volume of the fluid These two

effects combined lead to an improvement in the effectiveness of

the hot fluid as seen in Figure 2 The NTU can also be raised

by increasing the heat transfer surface area of the MCHXCF

Even for this scenario the external heat flux to the individual

fluids decreases due to changes in the geometry of the channels

However, the external heat transfer (q ext) remained the same as

Q was kept constant Thus the hot fluid effectiveness improved

with increase in heat transfer surface as shown in Figure 2 It

can be noticed from Figure 2 that when NTU is zero, the hot

fluid effectiveness is numerically equal to the negative of the

nondimensional external heat transfer parameter (Qh) This is

due to the fact that when NTU is zero there is no heat transfer

between the fluids, and consequently the heat supplied to the

hot fluid from the external source raises its outlet temperature

At infinite NTU, it can be noticed from Table 2 that the

effec-tiveness reaches a finite value The effeceffec-tiveness of the fluids in

an MCHXCFoperating at infinite NTU and free from external

heating is unity Whenever the fluids in an MCHXCFthat is

op-erating at very large NTU are externally heated, the externally

supplied heat is equally shared between the two fluids since

the thermal resistance between the hot and cold fluid is very

low Therefore, the application of external heat degrades the hot

fluid effectiveness from unity to 1 – 0.5(Qh+ Qc) Moreover,

the addition of external heat to the hot fluid will cause the outlet

temperature to be higher than the inlet temperature of the cold

fluid and vice versa

In Figure 2 the effectiveness of the cold fluid increased, for

a specific value of NTU, with increase in the external heating

External heating raised the outlet temperature of the cold fluid

and thereby its effectiveness Raising the NTU raised the

ef-fectiveness for a particular value of Qhand Qc When NTU is

zero, the effectiveness of the cold fluid is numerically equal to

Figure 3 ε-NTU relationship of an unbalanced flow MCHX CF (C min = Ch,

CRh= 1.0, CRc= 0.5).

the nondimensional external heat added to it If the MCHXCFisoperated at infinite NTU, then the effectiveness increases to avalue presented in Table 2 The reasons for these behaviors aresimilar to those already explained for the hot fluid

With regard to unbalanced flow an MCHXCFcan be operated

in two ways, with either of the fluids as the one with the lowestheat capacity Under conditions of zero external heating thethermal performance of an MCHXCFdepends only on the heatcapacity ratio (Cmin/Cmax) and NTU; it does not depend on thefluid that has the minimum heat capacity [1] However, when theMCHXCFis subjected to external heat transfer this is not the case

as investigated in this section Thus two cases are investigated:(1) Ch = Cmin and Cc = Cmax, and (2) Cc = Cmin and Ch =

Cmax However, the heat capacity ratio (Cr) for both these cases

is kept at 0.5 for the results presented in this article

The effectiveness of a MCHXCFfor the first case, i.e., whenthe hot fluid has the lowest heat capacity (CRh= 1.0 and CRc=0.5), is shown in Figure 3 When the MCHXCFis free of exter-nal heating, the effectiveness of the fluids is shown by the solidline in this figure As seen from this figure, the effectiveness

of the fluids increased with NTU for a specific amount of ternal heating When this MCHXCFwas operated at zero NTU,the effectiveness of the hot fluid was numerically equal to thenegative of the nondimensional external heat transfer parameter(Qh) Thus, the effectiveness of the fluids in a balanced flow andthe effectiveness in an unbalanced flow heat exchanger were

ex-Figure 4 Temperature profile of an unbalanced flow MCHX CF (C min = Ch,

CRh= 1, CRc= 0.5, Qh= Qc= 0.5).

heat transfer engineering vol 31 no 3 2010

Figure 5 ε-NTU relationship for an unbalanced flow MCHX CF (C min = Cc,

CRh= 0.5, CRc= 1.0).

the same when the MCHXCF was operated at zero NTU The

reasons for these observed trends are similar to those already

mentioned for the balanced flow condition When the MCHXCF

is operated at infinite NTU the effectiveness of the fluids reaches

a constant value, as mentioned in Table 2 Figure 4 is a graphical

representation of the temperature profile of the fluids for various

values of NTU with the nondimensional external heat transfer

parameters maintained at 0.5 From this figure it can be seen

that the hot fluid temperature is always greater than the cold

fluid temperature for all values of NTU Thus, the heat transfer

is always from the hot to the cold fluid, irrespective of the NTU

Therefore, when the MCHXCFis operated at infinite NTU the

hot fluid transfers heat, i.e., qmax+ q ext,h, to the cold fluid until

its outlet temperature becomes equal to the inlet temperature of

the cold fluid Thus, the hot fluid effectiveness becomes equal

to unity On the other hand, the cold fluid acts as the sink and

receives all the heat, qmax+ q ext,h + q ext,c Therefore, the cold

fluid effectiveness becomes equal to 1+ Qh+ Qc The

temper-ature profile of the fluids is the same when NTU is infinite, as

seen in the figure

In the second mode of operation associated with unbalanced

flow, the cold fluid has the lowest heat capacity among the fluids

in the MCHXCF(CRh= 0.5 and CRc = 1.0) Figure 5 represents

the ε-NTU relationship of the MCHXCFwith respect to the hot

and cold fluid The effectiveness of the fluids in a MCHXCF

without external heating is represented by the solid line of

Figure 5 Careful examination of Figures 3 and 5 show that

the ε-NTU relationship is dependent on the fluid that has the

lowest heat capacity The only similarity in the ε-NTU

relation-ship of the fluids occurs when NTU is zero As NTU was raised

there was an initial increase in the hot and cold fluid

effective-ness However, it soon peaked and then started to decline with

further increase in NTU This behavior can be understood from

the temperature profile of the fluids Figure 6 represents the

tem-perature profile of the fluids in the MCHXCFfor NTU values of

1, 5, 10, 20, and∞ The external heat transfer parameters of the

MCHXCFshown in Figure 6 are 0.5

When NTU is 1, the hot fluid temperature is always higher

than that of the cold fluid Thus, the hot fluid heats the cold fluid

throughout the length of the MCHXCF Due to this the curve

Figure 6 Temperature profile of an unbalanced flow MCHX CF (C min = Cc,

CRh= 0.5, CRc= 1.0, Qh= Qc= 0.5).

representing the effectiveness has a positive slope at this NTU.When the NTU is raised to 5, temperature cross is observed.Between the inlet of the cold fluid and the location of tempera-ture cross the hot fluid heats the cold fluid and beyond that pointthe cold fluid heats the hot fluid However, it can be seen fromFigure 5 that the effectiveness of the fluids has a positive slope atthis particular NTU This means that the net heat transfer fromthe hot fluid stream remained positive On further increasing theNTU, the point of temperature cross moved closer to the coldfluid inlet This behavior can be confirmed by comparing thetemperature profile of the fluids at NTU of 5, 10, and 20 Fromthe point of temperature cross to the inlet of the hot fluid, thehot fluid gets heated by the cold fluid for certain values of NTUthat are shown in Figure 5 Between the location of temperaturecross and the inlet of the hot fluid the cold fluid takes the role

of the hot fluid and vice versa As NTU is raised, the hot fluidgets heated over a greater length of the MCHXCF Thus, withincrease in NTU there was reduction in the net heat transferredfrom the hot fluid, and this explains the negative slope in theeffectiveness of the fluids as observed in Figure 5 The changefrom positive slope to negative slope just described can also beobserved in the curves representing the effectiveness when Qh=

Qc = 0.5, 0.75, and 1 The peak in the effectiveness occurredwhen the net heat transfer from the hot fluid was the maximum.The NTU at which the maximum effectiveness occurs is calledthe critical NTU (NTUcritical)

When NTU is raised to extremely high values, the tiveness of the fluids reaches a constant value At infinite NTUtemperature cross occurs in the immediate vicinity of the inlet

effec-of the cold fluid due to the effect effec-of temperature cross Thus, thehot fluid is heated by the cold fluid throughout the entire length

of the MCHXCF, except in a very small section near the coldfluid inlet where the cold fluid is heated by the hot fluid The exittemperature of the hot fluid at infinite NTU has been marked inFigure 6 Irrespective of the amount of heat transferred from thehot to the cold fluid near the inlet of the cold fluid, all the heatfrom the cold fluid is transferred to the hot fluid by the time thecold fluid reaches its exit as the MCHXCFis operating at infiniteNTU Thus, the effectiveness of the cold fluid becomes unityand that of hot fluid become 1 – Qh– Qc

heat transfer engineering vol 31 no 3 2010

Figure 7 Effect of heat capacity ratio on the effectiveness of fluids (Cmin=

Ch, CRh= 1, Qh= Qc= 0.25).

Figures 7 and 8 represent the effect of heat capacity ratio on

the effectiveness of the fluids in an MCHXCFin which the hot

fluid has the lowest heat capacity In this figure CRc represents

Cr In Figure 8 Cr is same as CRhas this figure contains the

ε-NTU relationship of a MCHXCF, in which the cold fluid has

the lowest heat capacity For these figures both the

nondimen-sional external heat transfer parameters (Qhand Qc) were kept

at 0.25 In Figure 7 with decrease in heat capacity ratio the

effectiveness of both fluids increased This trend is similar to

that observed in an MCHXCFfree of external heating In this

figure, the hot fluid effectiveness converges to a common value

when NTU is zero This is because, as explained earlier, when

NTU is zero the hot fluid effectiveness is equal to –Qhwhich is

–0.25 for the cases presented in Figure 7 On the other hand, for

unbalanced flows, when NTU is infinite the effectiveness of the

hot fluid, irrespective of CRc, becomes equal to unity Under the

balanced flow condition, the effectiveness of the hot fluid will

be 0.75 at infinite NTU With regard to cold fluid effectiveness,

while operating under unbalanced flow conditions the curves in

Figure 7 converge to 0.25 and 1.5 when NTU is zero and

infinite, respectively For balanced flow the cold fluid

effec-tiveness is 1.25 when NTU= ∞ The reasons for these have

been already mentioned The values of effectiveness, i.e., when

NTU= 0 or ∞, just mentioned were determined from Table 2

Figure 8 represents the effectiveness of the fluids for several

values of CRh For a particular CRhthe effectiveness of the hot

Figure 8 Effect of heat capacity ratio on the effectiveness of fluids (Cmin=

Cc, CRc= 1, Qh= Qc= 0.25).

and cold fluid initially increased, reached a maximum, and thendecreased with increase in NTU This behavior is in contrast tothat observed in a MCHXCFwithout external heating/cooling.The reversal in effectiveness with increase in NTU is due to thetemperature cross that occurs when the cold fluid has the lowestheat capacity in an externally heated MCHXCF As in Figure 7,the effectiveness of the hot and cold fluid when NTU is zerowas –0.25 and 0.25, respectively From Figure 8 it can also benoticed that at high values of NTU the effectiveness of the hotand cold fluid in an unbalanced flow MCHXCFconverges to-ward 1 and 0.5, respectively These values of effectiveness werealso calculated from Table 2

Equations (9)–(12) can also be used when the fluids are ternally cooled or when one of the fluids is heated and the other

ex-is cooled using an external source As mentioned earlier, Qhand

Qcare positive when the fluids are externally heated, and theyare negative when the fluids are externally cooled

A performance factor is used to define the relative change

in the effectiveness of a MCHXCFsubjected to external ing/cooling with respect to its effectiveness under zero externalheat transfer Mathematically it can be represented by Eqs (22)and (23) Equations (22) and (23) represent the performance fac-tors of the hot and cold fluids, respectively Positive and negativevalues of performance factor represent relative improvement anddegradation, respectively

to the cold fluid improves while that with respect to the hot fluiddegrades An opposite situation would occur when the fluids arecooled by an external source A performance factor can be used

to define both the relative improvement and the degradation inthe effectiveness of an MCHXCF Moreover, the performancefactor is presented here as a function of the NTU and nondi-mensional external heat transfer parameters The authors of thisarticle feel that the main purpose of the performance factorwould be to simultaneously analyze several operating param-eters One purpose of such an analysis would be to determinethe best range of NTU values of an MCHXCF that may expe-rience significant external heating and/or cooling Conversely,performance factors could also be used for determining the lev-els of external heating/cooling that may significantly impact theperformance of a given MCHXCF(known NTU)

heat transfer engineering vol 31 no 3 2010

Figure 9 Performance factor of a balanced flow MCHX CF (CRc = CRh,

Qh= Qc): (a) hot fluid, (b) cold fluid.

The performance factor of the hot and cold fluids, for

bal-anced flow, is shown in Figure 9a and b, respectively For the

particular case analyzed here (external heating) the performance

factor of the hot fluid has negative values which represent

dete-rioration in its effectiveness It can be seen from Figure 9a that

at low values of NTU the degradation in thermal performance is

more than that at moderate and high values of NTU This is

at-tributed to the fact that the thermal performance of an MCHXCF

is low at small values of NTU because the heat transferred

be-tween the fluids is not significant Therefore, the addition of heat

from an external source brings about greater deterioration in its

thermal performance and thus the observed trend in the

perfor-mance factor It should be noted that even as the NTU is raised

the deterioration in hot fluid performance still exists However,

it is not as severe as it was at low values of NTU This is the

result of the improvement in the heat transfer between the fluids

at high values of NTU, as explained previously From Figure

9a it can be noticed that the lines separating the regions are not

smooth, in contrast to the curves in previous figures This trend

is due to the fact the points (performance factors) lying on each

Figure 10 Performance factor of an unbalanced flow MCHX CF (C min = Ch,

CRh= 1, CRc= 0.5, Qh= Qc): (a) hot fluid, (b) cold fluid.

of these lines do not belong to a specific Qhand Qc This can

be better understood by analyzing the points laying on the lineseparating the 0 to –1 and –1 to –2 regions The performancefactor corresponding to NTU of 1 on this line is when Qhand

Qc are equal to ≈0.5 Similarly, at NTU of 3 the maximumperformance factor occurs when Qhand Qcare equal to≈0.75.Similar conclusions can be drawn about all the points lying onthis line and thus the lack of smoothness of the line

For the cold fluid as shown in Figure 9b, the performancefactor is positive, which represents improvement in its effec-tiveness At a specific value of NTU, with increase in exter-nal heating the outlet temperature of the cold fluid increasesfurther, resulting in an increase in the performance factor of thecold fluid Further, the performance factor had high values atlow NTU The lines separating the regions of this figure are alsonot smooth The reasons for these trends are similar to thosealready explained for the hot fluid performance factor

When the hot fluid has the lowest heat capacity then theperformance factor of the fluids are represented in Figure 10aheat transfer engineering vol 31 no 3 2010

Figure 11 Performance factor of an unbalanced flow MCHX CF (Cmin= Cc,

CRh= 0.5, CRc= 1, Qh= Qc): (a) hot fluid, (b) cold fluid.

and b Similar to the case of balanced flow, the performance

factor of the hot fluid was the lowest at low values of NTU

Even for the cold fluid, the performance factor was the highest

at low values of NTU The reasons for these trends are the same

as those already mentioned for balanced flow

The performance factor of an MCHXCF under unbalanced

flow with the cold fluid having the minimum heat capacity

con-ditions is shown in Figure 11a and b The behavior of the fluids

is similar to that observed in earlier cases

CONCLUSIONS

From the analysis provided it is clear that the performance of

an externally heated/cooled MCHXCFmay significantly deviate

from what is predicted by the conventional ε-NTU equations

that do not consider this effect When subjected to external

heating the effectiveness of the hot flui always degraded while

that of the cold fluid improved This trend in the effectivenessreversed when the fluids were cooled by the external heat source.For an unbalanced flow MCHXCFthe effectiveness of the fluidsdepended on the fluid with the lowest heat capacity Wheneverthe hot fluid has the lowest heat capacity in an MCHXCF, theeffectiveness of the fluids always increases with increase inNTU, irrespective of the degree of external heating On theother hand, the effectiveness of the fluids initially increases andthen decreases with increase in NTU if the cold fluid has thelowest heat capacity in a MCHXCF An additional advantage ofthis theory would be in the design of na MCHXCFwith viscousheating This is because the effect of viscous heating is similar

to that of subjecting the fluids to uniform heat flux A parametercalled a performance factor was introduced to aid designers inanalyzing the effect of external heat transfer on the thermalperformance of MCHXs Designers may graphically analyzeseveral operating parameters simultaneously using the concept

of the performance factor

NOMENCLATURE

A heat transfer surface area (m2)

a1, a2 constants used in Eqs (9), (10), and (20)

C heat capacity of individual fluid (W/K)

CR ratio of minimum heat capacity to the heat capacity

of the individual fluid, C R =Cmin

Cmin(T h,i −T c,i)

Q∗ nondimensional heat transfer, Q∗ = q/qmax =

q/Cmin(T h,i − T c,i)

T temperature of the fluid (◦C)

U overall heat transfer coefficient (W/K-m2)

[1] Shah, R K., and Sekulic, D P., Fundamentals of Heat Exchanger

Design, John Wiley and Sons, Hoboken, NJ, pp 100–101, 2003.

[2] Paugh, R L., New Class of Microminiature Joule–Thompson

Refrigerator and Vacuum Package, Cryogenics, vol 30, no 12,

pp 1079–1088, 1990

[3] Peterson, R B., High Temperature Microscale Reactor Analysis

Using a Counterflow Heat Exchanger Model, Microscale

Ther-mophysical Engineering, vol 3, no 1, pp 17–30, 1999.

[4] Little, W A., Microminiature Refirgerator, Review of Scientific

Instruments, vol 55, no 5, pp 661–680, 1984.

[5] Ronney, P D., Analysis of Non Adiabatic Heat Recirculating

Combustors, Combustion and Flame, vol 135, no 4, pp 421–

439, 2003

[6] Hill, T F., Velasquez-Garcia, L F., Wilhite, B A., Rawlins, W T.,

Lee, S., Davis, S J., Jensen, K F., Epstein, A H., and Livermore,

C., A MEMS Singlet Oxygen Generator—Part II:

Experimen-tal Exploration of the Performance Space, Journal of

Microelec-tromechanical Systems, vol 16, no 6, pp 1492–1505, 2007.

[7] Hurd, B L., Mean Temperature Difference in the Field or Bayonet

Tube, Industrial and Engineering Chemistry, vol 38, no 12, pp.

1266–1271, 1946

[8] Barron, R., Effect of Heat Transfer from Ambient on Cryogenic

Heat Exchanger Performance, Advances in Cryogenics, vol 38,

pp 265–272, 1984

[9] Chowdhury, K., and Sarangi, S., Performance of Cryogenic Heat

Exchangers with Heat Leak From the Surroundings, Advances in

Cryogenics, vol 38, pp 273–280, 1984.

[10] Ameel, T A., and Hewavithrana, L., Countercurrent Heat

Ex-changers with Both Fluids Subjected to External Heating, Heat

Transfer Engineering, vol 20, no 3, pp 37–44, 1999.

[11] Peterson, R B., and Vanderhoff, J A., Analysis of a

Bayonet-Type Heat Counterflow Heat Exchanger With Axial Conduction

and Radiative Heat Loss, Numerical Heat Transfer, Part A, vol.

40, no 3, pp 203–219, 2001

[12] Seetharamu, K N., Quadir, G A., Zainal, Z A., and Krishnan,

G M., FEM Analysis of Multifluid Heat Exchangers,

Interna-tional Journal of Numerical Methods for Heat & Fluid Flow, vol.

nel Heat Exchanger, Proc 2006 ASME International Mechanical

Engineering Congress and Exposition, Chicago, 2006.

[15] Mathew, B., Performance Evaluation of Microchannel Heat changer Subjected to External Heat Flux, M.S Thesis, LouisianaTech University, Ruston, LA, pp 39–97, 2007

Ex-[16] Wiley, C R., Advanced Engineering Mathematics, McGraw-Hill,

New York, pp 66–71, 1965

[17] Sahin, A Z., Thermodynamic Design Optimization of a Heat

Re-cuperator, International Communication in Heat and Mass

Trans-fer, vol 24, no 7, pp 1029–1038, 1997.

[18] Murakami, Y., and Mikic, B B., Parametric Investigation of cous Dissipation Effects on Optimized Air Cooling Microchan-

Vis-neled Heat Sinks, Heat Transfer Engineering, vol 24, no.1, pp.

[20] Chiou, J P., The Effect of Longitudinal Heat Conduction on

Cross-flow Heat Exchanger, Journal of Heat Transfer, vol 100, no 2,

pp 346–351, 1978

[21] Gupta, P., and Atrey, M D., Performance Evaluation of CounterFlow Heat Exchangers Considering the Effect of Heat In Leakand Longitudinal Conduction for Low-Temperature Applications,

Cryogenics, vol 40, no 12, pp 469–474, 2000.

Bobby Mathew is a Ph.D student in Engineering at

Louisiana Tech University In May 2007 he received his M.S degree in engineering at Louisiana Tech University His current research interests include mi- crochannel heat exchangers, micro loop heat pipes and microscale heat transfer and fluid mechanics.

Hisham Hegab is an associate professor of

mechan-ical engineering at Louisiana Tech University and serves as the program chair of Microsystems and Nanosystems Engineering within the College of En- gineering and Science He received his Ph.D in me- chanical engineering in 1994 from the Georgia In- stitute of Technology His current research interests are in microscale heat transfer, microfluidic systems, micro heat exchangers, and micro-/nanotechnology education.

heat transfer engineering vol 31 no 3 2010

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903304350

Heat Transfer and Pressure Drop

Under Dry and Humid Conditions

in Flat-Tube Heat Exchangers With

Plain Fins

CAROLINE HAGLUND STIGNOR,1BENGT SUND ´ EN,2PER FAHL ´ EN,3

and SOFIA STENSSON1

1SP Technical Research Institute of Sweden, Energy Technology, Bor˚as, Sweden

2Lund University, Lund Institute of Technology, Heat Transfer, Lund, Sweden

3Chalmers University of Technology, Building Services Engineering, G¨oteborg, Sweden

Flat-tube heat exchangers could be an interesting alternative to make indirect cooling of display cabinets more

energy-efficient This application involves low air velocities in combination with condensation of water vapor on the air side, so

plain fins could be suitable Two different heat exchangers having flat tubes and plain fins on the air side were evaluated

experimentally One of the heat exchangers had continuous plate fins, and the other had serpentine fins The performances

during dry and wet test conditions were compared and related to theoretical predictions for different assumptions The

influence of air velocity, air humidity, and inclination angle was investigated The results show that, in most cases, the heat

transfer performance is somewhat reduced under wet conditions in comparison with dry test conditions, and that wet heat

transfer surfaces lead to an increased pressure drop At the lower air velocity range that was investigated, the heat exchanger

having continuous plate fins drained better than the one with serpentine fins.

INTRODUCTION

Flat-Tube Heat Exchangers in Heating, Ventilation,

Air-Conditioning, and Refrigeration Applications

Flat-tube heat exchangers (FTHE), predominately with

lou-vered fins, have been used for a long time in applications where

compactness and performance are important, such as in

auto-motive applications For heating, ventilation, air-conditioning,

and refrigeration (HVAC&R) applications, heat exchangers with

round tubes are still most frequently used in stationary

appli-cations According to Webb [1], the flat-tube configuration has

some advantages over the round-tube heat exchangers For

ex-ample, it has better fin efficiency and a smaller wake region

behind the flat tubes A limited range of operating conditions

Financial and material support from the Swedish Energy Agency, Hydro

Alunova, Grundfos, and Wilo is kindly acknowledged.

Address correspondence to Caroline Haglund Stignor, SP Technical

Re-search Institute of Sweden, Energy Technology, PO Box 857, SE-501 15 Bor˚as,

Sweden E-mail: caroline.haglund.stignor@sp.se

had been studied earlier, but in recent years the studied ing ranges have been widened to include HVAC&R applications,i.e., operating conditions involving wet and frosted surfaces onthe air side Jacobi and coworkers have performed extensivestudies of flat-tube heat exchangers with flat, wavy, strip, andlouvered fins under dry, wet, and frosting conditions The stud-ies involve literature studies, calculations, and experiments, andthey present their results in two reports [2, 3] According tothe authors, the research presented in those reports constitutedprobably the most comprehensive studies of flat-tube heat ex-changers in HVAC&R applications at that date

operat-Indirectly Cooled Display Cabinets

In recent decades, the use of indirect cooling by means of

a secondary refrigerant (coolant) has become very frequent insupermarkets, especially in some of the Nordic countries Thissystem arrangement has recently attracted more attention, and

is getting more and more common in other parts of the world

as well [4, 5] Traditionally, different kinds of tube coils with

179

aluminum fins on expanded copper tubes have been used as

cooling coils in display cabinets The liquid flow regime is often

laminar with low heat transfer coefficients as a consequence, due

to the high viscosity of many secondary refrigerants However,

good energy efficiency can be obtained even under laminar flow

conditions, if the geometry of the heat exchanger is adapted

to this kind of flow, e.g., with smaller hydraulic diameters on

the liquid side For this reason, flat-tube heat exchangers are an

interesting alternative

The display cabinet application is different from many other

heat exchanger and HVAC&R applications, since it involves low

air velocities (down to 0.3 m/s) in combination with

conden-sation of water vapor and sometimes even frosting However,

it should be possible to operate an energy-efficient indirectly

cooled cooling coil in a medium-temperature display cabinet

without frosting The question is how to design the liquid and

air sides of the cooling coil/heat exchanger to achieve the best

performance and avoid frosting In earlier research work, the

authors of the present article investigated heat transfer on the

liquid side of multiport extruded aluminum tubes [6] They also

developed a preliminary model to predict the performance of

a flat-tube heat exchanger in a display cabinet application in a

parameter study, and found promising results for some designs

[7] However, the air-side performance when condensation of

water vapor occurs on the fins had to be verified experimentally

for these results to be reliable When fouling takes place on a

heat transfer surface, i.e., the surface is coated with deposits

originating from the flow systems, the heat transfer resistance

is found to increase At the same time, the area available for

flow is decreased, which results in higher fluid velocity This,

in combination with a rougher surface, leads to increased

pres-sure drop [8] Condensation of water vapor on a heat exchanger

surface might have a similar effect However, since the

con-densate drains continuously, the influence of the concon-densate on

heat transfer and pressure drop depends on how much

conden-sate is accumulated in the heat exchanger before steady state is

reached

Selection of Appropriate Fin Design

A louvered fin geometry is often reported as superior to the

plain fins [2, 3] Davenport [9] compared test results from

lou-vered samples with results from samples with plain fins It was

found that both the Colburn j factor and the friction factor, f ,

for the louvered samples were between 2 and 3.5 times greater

than for the plain samples, depending on louver geometry The

results by Davenport [9] also illustrated the irrelevance of

hy-draulic diameter for the performance of louvered surfaces but

that the hydraulic diameter was relevant for the samples with

plain fins For louvered surfaces, louver-pitch-based Re was

rec-ommended as given by the equation (Re L p = (µ · ρ · L p )/µ).

Colburn j factors were presented down to Re Lp = 100, but not

for lower values of Re The reason was that the curves flattened

at low velocities, which was thought to be caused by boundary

layer thickening on the louver surface that in turn changed the air

flow pattern through the fins of the heat exchanger Therefore, j

curves should not be extrapolated to lower Re values since thiswill almost certainly result in an overestimation Achaichia andCowell [10] presented performance data for a range of plate andflat tube and louver fin geometries Their resulting Stanton num-ber (St) curve demonstrated characteristics that were consistentwith the earlier findings by, for example, Davenport [9] that athigh Re the fluid flow is predominately parallel to the louvers,but as Re is reduced the flow direction becomes increasinglydetermined by the plate fins and the St-curves flattened

In a display cabinet application, for which frosting can occur,the fin pitch is often equal to or greater than 5 mm in order tohave long operating periods between the defrosts However, iffrosting could be minimized or avoided the fin pitch could bedecreased Nevertheless, due to the low air velocities and oc-currence of dust and condensate, it is not desirable to have toosmall fin pitches in the heat exchangers A fin pitch of around

4 mm has therefore been the focus of investigations for thisstudy In a source database presented by Jacobi et al [3] thelouver pitch for most specimens ranges from 1 to 2.3 mm Forsuch small dimensions, the flow in a display cabinet applicationwill most certainly be duct-orientated even if the fins are lou-vered, due to the low air velocities In such a case, there is a risk

of the louver resulting only in an additional pressure drop overthe heat exchanger In addition, condensed water might alsopartially clog the louver gaps, which contributes to making theflow duct-directed Under such circumstances heat exchangerswith flat tubes and plain (flat) fins will be preferable

Jacobi et al [2] performed experiments with a flat-tube heatexchanger with plain fins under dry, dehumidifying and frost-ing conditions The heat exchanger had dimensions similar butnot identical to those of the MPET heat exchanger evaluated

in the present study (see Table 1), but the plain fins were tinuous plate fins (no serpentine fins) The researchers foundthat for dry test conditions the heat transfer and friction factorperformance could be predicted simply by duct-flow modeling.They compared the performance of this heat exchanger with asimilar heat exchanger with wavy fins in a Reynolds number

con-region of 300 < Re dh < 2100 They found the Colburn j factor

to be higher or similar for the plain fins in the lower Reynoldsnumber region (Re≤ 1000) compared to the wavy fins underboth dry and wet conditions, while the opposite was true forhigher Reynolds number Almost the same relations were found

for the friction factor, f The Colburn j factor was not much

affected by the condensation of water vapor for either the plain

or the wavy fin geometry, while the friction factor was found toincrease by a factor of 2.2 to 2.8 Jacobi et al [2] also carriedout experiments with a heat exchanger with louvered fins hav-ing a fin pitch of 5.08 mm and a louver pitch of 1.14 mm andcompared its performance for dry and wet conditions The dif-ference in performance was found to be very small which provesthat the flow is duct-oriented as was expected for such large finpitch No heat transfer enhancement was therefore obtained byboundary-layer restarting for either of the test conditions.heat transfer engineering vol 31 no 3 2010

Table 1 Dimensions of the evaluated heat exchangers

Tube pitch, transversal T p.t mm 10.0 23.1

Tube pitch, longitudinal T p,l mm 19.0 73.0

Hydraulic diameter (air side) d h,a mm 4.8 6.3

Tube depth (outer width) T d mm 13.6 45.0

Tube inner width T w,i mm 13.0 44.2 (total),

1.42 (duct) Tube wall thickness δt ube mm 0.2 0.4

Hydraulic diameter (tube side) d h,b mm 3.32 2.06

Outer perimeter of tube P t ube,o mm 31.8 94.6

Number of tubes, transversal to

Number of parallel vertical tube

rows in each pass

N t ube,p (—) 2 1 tube (with 25

parallel channels)

Purpose of Study

On the basis of the results found in the literature, and from

earlier research by the authors presented earlier, flat-tube heat

exchangers with plain fins could be an interesting alternative for

indirect cooling of the air in display cabinets and other

applica-tions where dehumidifying condiapplica-tions are combined with low

air velocities However, it is of interest to study the performance

under dehumidifying conditions and even lower air velocities

than has been done in earlier investigations, with particular

em-phasis on investigating whether condensed water drains well

from serpentine plain fins or from continuous plate fins, and

whether and to what extent the humidity of the incoming air

influences the sensible heat transfer coefficient and the pressure

drop Two different flat tube heat exchangers with plain fins

of the different types and horizontal flat tubes with different

depths have therefore been investigated experimentally Their

geometrical data are presented in Table 1

EXPERIMENTS

Description of Tested Objects

Two different heat exchangers having flat tubes and plain

(flat) fins on the air side were evaluated experimentally The

dimensions of the heat exchangers are presented in Table 1

Figure 1 Schematic drawing and nomenclature of the “flat-fin-core” heat exchanger, denoted FFC: (a) side view of cross section, (b) cross section of staggered tube layout, (c) plate fin geometry.

(see Figures 1 and 2 for description of nomenclature), whileFigure 3 shows the media flow arrangements of the heat ex-changers One of the heat exchanger is called “Flat-Fin-Core”

by its manufacturer and is therefore denoted FFC It consistsheat transfer engineering vol 31 no 3 2010

Figure 2 Schematic drawing and nomenclature of the multiport extruded

tube heat exchanger, denoted MPET-HE: (a) side view of cross section, (b)

serpentine fin geometry, (c) cross section of MPE tube.

of plain continuous plate fins on a tube bundle The tube

con-figuration of the FFC heat exchanger is between an in-line and

a staggered configuration, as can be seen in Figure 1 The flat

tubes are plain and empty As can be seen, the liquid circuit is

arranged in such way that the heat exchanger consists of four

cross-flow heat exchangers connected in series, with an overall

counter(current) flow The fins are made of copper and the tubes

are made of brass The fins are connected to the tubes by soft

Figure 3 Liquid circuitry of the FFC and the MPET-HE heat exchanger.

soldering (tin) When punching the tube holes out of the platefins, a collar is left Before the soldering, the tubes are coatedwith tin The heat exchanger is then put into an oven and in-clined in such way that the melted tin fills the gap between thetube and fin material and creates good thermal contact betweenthe tubes and the fins The FFC type heat exchanger is normallyused in forest and agricultural machinery

The other heat exchanger investigated in this work consists ofMULTIPort extruded tubes (MPE tubes) and folded serpentineflat (plain) fins on the air side It is denoted here as MPET-HE(multiport extruded tube heat exchanger) As Figure 3b shows,

it consists of two cross-flow heat exchangers connected in ries with an overall counter (current) flow The cross section ofthe MPE tubes of the heat exchanger can be seen in Figure 2c.Both the fins and the tubes are of aluminum and the heat ex-changer is put together by a controlled-atmosphere brazing pro-cess using a cladding material (AlSi) Due to the design of theheat exchanger, with serpentine fins between flat tubes, it is pos-sible to apply external pressure on the heat exchanger during thebrazing process, to ensure good thermal contact between the finsand the tubes This heat exchanger was uniquely constructed forthis research study

se-As far as the air sides of the heat exchangers are concerned,the main difference is that the FFC heat exchanger has contin-uous plain fins, while the MPET heat exchanger has serpentinefins folded between the flat tubes In addition, the tube depth(or outer width)—i.e., the length of the air-side channels—ismuch greater for the MPET heat exchanger than for the FFCheat exchanger

heat transfer engineering vol 31 no 3 2010

Figure 4 Schematic drawing of the experimental setup, including measuring

points (not according to scale).

Experimental Setup

The experimental setup, including the measuring points, is

shown schematically in Figure 4 An air-conditioning plant

con-trolled temperature, humidity, and flow on the air side To gain

a homogeneous air flow when reaching the heat exchanger, air

duct sections were mounted upstream and downstream of the

evaluated heat exchangers and a perforated plate was mounted

at the inlet of the first duct section The air flow was

deter-mined by measuring the pressure difference over a Pitot tube

by a micro-pressure gauge In front of the heat exchanger, the

air temperature was measured by one Pt-100 temperature

sen-sor and five thermocouples distributed in the cross section The

thermocouples were used to determine the spatial and temporal

temperature variations over the cross section of the air flow

After the heat exchanger one Pt-100 sensor and nine

thermo-couples measured the air temperature The Pt-100 sensors were

shielded from radiation The relative humidity of the air was

measured by capacitive relative humidity meters before and

af-ter the heat exchanger The air-side pressure drop was measured

by a micro-pressure gauge There were two cross sections for

pressure measurement: one before and one after the heat

ex-changer, having four taps each The atmospheric pressure was

measured by a pressure gauge Temperature and flow of the

sec-ondary refrigerant was controlled via a liquid loop The liquid

flow was measured by a Coriolis mass flow meter The liquid

temperatures into and out of the heat exchanger were measured

by Pt-100 temperature sensors The pressure drop on the

liq-uid side of the heat exchanger was measured by a differential

pressure transmitter

Measurement Plan

The main focus of this experimental study was to

inves-tigate the air side performance of the heat exchangers in the

laminar flow range—on the air as well as on the liquid side.The air side heat transfer was studied under dry conditionsand under conditions where condensation of water vapor tookplace—“wet conditions.” The display cabinet application wascentral for these investigations However, such an applicationinvolves relatively small temperature differences: In order toobtain an acceptable uncertainty of measurement in the experi-ments, larger temperature differences than those encountered inthe display cabinet applications were used Propylene glycol at

a concentration of 39% by weight (a freezing point of−20◦C)

was used as the heat transfer medium on the tube side of the heatexchangers

The air-side heat transfer and pressure drop were measured

at four different air flow rates, resulting in the following frontalair velocities (range given after the± sign): 0.23 m/s (only onetest), 0.28± 0.01 m/s, 0.70 ± 0.03 m/s and 1.20 ± 0.04 m/s.The experiments were performed with four different climates,one dry and three wet Wet implies that the dewpoint temper-ature of the air into the heat exchanger was higher than thetemperature of the liquid (or secondary refrigerant) into theheat exchanger The dewpoint temperatures of the three wet cli-mates were 9± 1◦C (wet 1), 16± 1◦C (wet 2), and 22± 1◦C

(wet 3)

Most of the tests were performed at a liquid mass flow rate

of 200 kg/h For the FFC heat exchanger, this mass flow rateresulted in a liquid velocity and Reynolds number of 0.045 m/sand 19, respectively For the MPET heat exchanger, this massflow rate resulted in a liquid velocity and Reynolds number

of 0.046 m/s and 15, respectively However, in order to verifythe separation of the heat transfer resistance on the air and theliquid side of the heat exchanger, the heat exchangers were alsoevaluated at other mass flow rates

Since the flat tubes had a horizontal orientation and the airvelocities were low, it was of interest to investigate whetherthe air-side heat transfer and pressure drop were affected byincreasing the inclination angle of the heat exchanger Forthe majority of the test points, the heat exchanger had a 1◦inclination angle, but for a number of test points the an-gle was increased to 10◦ in order to see whether this in-creased forward inclination facilitated the drainage of thecondensate

Finally, the pressure drop on the liquid side was measuredunder isothermal conditions (no heat flux) For the MPET heatexchanger, the liquid-side pressure drop was measured over onlyone tube with the same cross-sectional dimension as the tubes

of the complete heat exchanger The experimental setup for thelatter is described in reference [6]

The most important measured values for the various testpoints are listed in reference [11] All heat transfer test pointswere recorded during at least 35 min with at least three measure-ments per minute, resulting in a minimum of 100 measurements.The measuring period was preceded by a stable period of atleast 30 min During the test points for isothermal pressure dropmeasurements, data were recorded every fifth second for at least

9 min, resulting in a minimum of 100 measurements

heat transfer engineering vol 31 no 3 2010

Table 2 Estimated expanded measurement uncertainty of the parameters,

tabulated values, calculated dimensions, and energy balances in the

performed experiments

Air

Air volume flow rate, ˙V a ±3 ±3 %

Air temperature in, t a,in ±0.3 ±0.3 K

Air temperature out, t a,out ±0.3 ±0.4 K

Relative humidity, out ±3 ±3 % (units)

Specific heat capacity,a c p,a ±0.5 ±0.5 %

Atmospheric pressure ±0.05 ±0.05 kPa

Air side heat transfer area, A a,t ot 1.0 2.3 %

Air side cross-sectional area, A c,a 1.4 2.5 %

Energy balances (uncertainty of)

aUncertainty for tabulated values taking the uncertainty regarding the

temper-ature into account.

bValid for the two highest values of the measured pressure drop.

Uncertainty of Measurement

The uncertainty of measurement has been evaluated

accord-ing to the Guide to the Expression of Uncertainty in

Measure-ment [12] and EAL-R2 [13] Details of the estimated expanded

uncertainties for the measurands, the tabulated values and the

dimensions used in the experiments can be found in Table 2

These values are based on long-time experience of the different

measurement devices and installations One of the authors of

this article has presented detailed uncertainty budgets for

ca-pacity measurements on brine-cooled air coils [14] The total

(summarized) estimated uncertainty values for the measurement

results are shown in the graphs where these results are presented

and, as is often the case in heat transfer measurements, these

values are not negligible even though the uncertainty of each

measurands, etc., is relatively small

DATA REDUCTION

Reduction of the measured data for the heat exchangers

was performed according to Eqs (1)–(28) This data reduction

method is valid for dry air-side test conditions and for when

condensation of water vapor takes place on the air side (wet

air-side test conditions) However, the data reduction method has

been adapted to wet conditions by multiplication by the totalheat flow to sensible heat flow ratio, ˙Q b / ˙ Q a,s, in appropriateplaces, i.e., in Eq (4) and in Eq (25) For the dry test pointsthis ratio is unity (if there is no deviation in the energy balance)

As described by the equations that follow, the data reduction isbased on a mean temperature difference method in combinationwith the P-NTU method described by Shah and Sekulic¸ [15].The reason for basing the data reduction on a temperature driv-ing potential instead of an enthalpy driving potential is that theformer has better prospects for resulting in accurate results, es-pecially for tests with partially wet surfaces, which was shown

by Jacobi et al [3], who compared the result from the mic mean temperature difference method with the logarithmicmean enthalpy difference method with numerical simulation re-sults (The same results are also presented by Jacobi and Xia[16].) The reason for using the P-NTU-method (which is verysimilar to the better known ε-NTU method) is that this methodoffers an expression for heat exchangers connected in series

(9)

P 1,p = [(1− R1· P1)/(1 − P1)]1/n− 1[(1− R1· P1)/(1 − P1)1/n − R1

(10)

where n is the number of identical heat exchangers connected

in series, such that for the FFC heat exchanger n= 4, and for

the MPET heat exchanger n= 2

For Eqs (9) and (10) to be valid, both fluids are consideredperfectly mixed between exchangers or passes This might bealmost true for the liquid side, since all the tubes are connectedheat transfer engineering vol 31 no 3 2010

to joint manifolds on the heat exchanger sides, but not for the air

side, and especially not for the FFC heat exchanger However,

according to Shah and Sekulic¸ [15] the relationship of Eqs

(9) and (10) should be adequate for the design and analysis of

most two- and three-pass industrial exchangers, even though

one of the fluids is not mixed between the passes in an overall

cross-counterflow heat exchanger It should be appropriate for

a four-pass exchanger as well, since the temperature gradient of

the air between the passes will be lower for a larger number of

where N T U pis solved by iteration

The expression in Eq (13) is taken from Incropera and

DeWitt [17] and is valid for a single-pass cross-flow heat

ex-changer with both fluids unmixed According to Shah and

Se-culic [15], the flow on either side of the heat exchanger should

be divided into at least four parallel channels in order to be

considered as unmixed; otherwise, it is considered as partially

mixed However, since the heat exchangers were evaluated in

the lower laminar flow regime on the liquid side, the mixing in

the transversal liquid flow direction has been considered

negli-gible even for the FFC heat exchanger, despite there being only

two parallel tubes, and therefore an expression for both fluids

unmixed would lead to a good approximation also for this heat

exchanger

The expression in Eq (13) is exact only for C r= 1 However,

according to Incropera and DeWitt [17], it can be used as an

excellent approximation for 0 < C r <1 Shah and Sekulic¸

[15] presented an expression for ε= f(C r ,NTU) for a cross-flow

heat exchanger with both fluids unmixed that was not limited to

C r = 1, which can be found in Eqs (14) and (15) They also

presented a graphic illustration of ε= f(C r ,NTU) The values

of ε resulting from analyzing the test data using Eq (13) were

compared with the corresponding ε values given by the graphic

illustration of Eqs (14) and (15) In the range with which we

are here concerned, 0.12 < C r < 0.98 and 0.42 < NTU Ai <

1.31, no visible difference between the two relationships could

be observed Equation (13) was therefore selected for the data

reduction, since this relation is much easier to handle when a

parameter is to be solved by iteration

the applied operating range 0.15 < x b∗<0.25

was measured only over one tube, with the same cross section

as the tubes of the MPET heat exchanger The resulting

fric-tion factor from the pressure drop measurements was calculated

from Eq (28) Equation (28) is somewhat simplified in

compar-ison to Eq (27), due to the fact that pressure drop measurements

were performed only under isothermal test conditions and hence

there are no density variations Values for K c and K ewere taken

from Kays and London [20]

b − K e,b)· ρb,in

ρb,out

(27)

taken from Melinder [21] Thermophysical data for air were

taken from handbooks [22–25] For the heat exchanger

materi-als, heat conduction data were taken from reference [26] Unless

otherwise indicated, the thermophysical properties are taken at

the mean temperature of the liquid

RESULTS AND DISCUSSION

Heat Transfer Performance

For each measurement point, an energy balance was

calcu-lated using measured flow rates, temperatures, relative humidity

(dehumidifying test points) and tabulated data For all dry test

points, the energy balance differed from 1.00 by less than 4%

For the dehumidifying test points, 87% of the test points showed

a deviation of less than 5% from 1.00, and the remaining test

points deviated by less than 7% For all test points the deviation

of the energy balance from 1.00 was less than or equal to the

estimated uncertainty of the energy balances given in Table 2,

which indicates that the uncertainty estimations are reasonable

However, as can be seen in the data reduction procedure

de-scribed earlier, only the sensible heat flow rate on the air side,

˙

Q a,s, and the heat flow rate on the liquid side, ˙Q b, were used

in the calculation of the sensible Nusselt number, Nua,s The

somewhat larger deviation of the energy balance for the

de-humidifying test points is therefore of less importance for the

results

For all the test points the major fraction of the heat

trans-fer resistance was on the air side For the FFC heat exchanger

the heat transfer resistance on the liquid side ranged between 7

and 17% of the total heat transfer resistance The

correspond-ing figure for the MPET heat exchanger was 7% to 15% For

the wet test points, the total-to-sensible heat ratio, ˙Q b / ˙ Q a,s,

0 1 2 3 4 5 6 7 8 9 10

Dimensionless length, x a *=T d /(d h,a *Re dh,a *Pr a )

Nua,s_dry Nua,s_calc,fd Nua,s_calc,sd

Figure 5 Experimentally determined sensible Nusselt number for the FFC heat exchanger compared to theoretical predictions Dry test conditions.

ranged from 1.08 to 2.20 The heat transfer resistance throughthe tube wall was negligible The expanded surface efficiency,

η 0, was calculated to be between 0.98 and 0.99 for the FFCheat exchanger and between 0.95 and 0.97 for the MPET heatexchanger (the applied relations for fin and extended surfaceefficiency takes the total to sensible heat ratio into account andcan be found in the reference by Haglund Stignor [11]).The graphs that follow show the experimentally determinedsensible mean Nusselt number on the air side, Nua,s (Nua,s =

Nu0,a,s·η0) for different test conditions, i.e., Nua,s resultingfrom measured values and with data reduction according toEqs (1)–(26) Figure 5 shows experimentally determined Nus-selt numbers (Nua,s = Nua,s dry) on the air side of the FFCheat exchanger versus the dimensionless length of the heat ex-changer during dry test conditions Dry test conditions meansthat the dewpoint temperature of the air is lower than the inletliquid temperature resulting in no condensation of water vapor

In the graph, the experimentally determined Nusselt number iscompared to a Nusselt number predicted by relations for twodifferent assumptions The first assumption is that the air flowbetween the fins and the tubes is fully developed The appliedvalues for Nua,s,calc,f d(= Nua,s calc,fd) are interpolated fromtabulated data for fully developed laminar flow in rectangularducts with constant wall temperature as a boundary conditionpresented by Shah and London [18] and multiplied by the cal-culated efficiency for the extended surface, η 0 according toShah and Sekulic¸ [15] The aspect ratio of the duct betweentwo tubes and two fins has then been used The second assump-tion is that the flow is simultaneously (both hydrodynamicallyand thermodynamically) developing, and that it redevelops bothwhen entering a tube row and when leaving a tube row andentering a passage without tubes In the case of the FFC heatexchanger, different theoretical Nusselt numbers are calculatedfor the part of the heat exchanger where there are tubes andfor the part of the heat exchanger resulting from the distancesbetween the tubes The Nusselt numbers are calculated fromcurve fits for data interpolated from tabulated values for simul-taneously developing flows in rectangular ducts with constantwall temperature as a boundary condition presented by Shahand London [18] (and multiplied by η 0) The overall Nusseltheat transfer engineering vol 31 no 3 2010

Dimensionless length, x a *=T d /(d ha *Re dh,a *Pr a )

Nua,s_dryNua,s_wet1Nua,s_wet2Nua,s_wet3

Figure 6 Experimentally determined sensible Nusselt number for the FFC

heat exchanger for dry and wet test conditions.

number, Nua,s,calc,sd(= Nua,s calc,sd) is then a weighted value

for the areas of the different parts of the heat exchanger The

expressions defining how the theoretical Nusselt numbers have

been calculated can be found in Haglund Stignor [11]

At the lowest air flow rates, i.e., the highest value of the

dimensionless lengths, the experimentally determined Nusselt

number is even lower than the theoretical value assuming fully

developed flow There are two possible explanations for this

First, there might be a wake region behind the tubes at these

low air flow rates, and therefore the whole fin area might not be

used efficiently This is the most probable explanation Second,

the thermal contact between the tubes and the fins might not

be perfect, due to the construction of the heat exchanger and

the production method involving no external or internal

pres-sure However, for the higher air flow rates, i.e., lower values of

the dimensionless length, the experimentally determined

Nus-selt numbers exceed the theoretical ones for the fully developed

flow assumption and get closer and closer to the predicted values

for the simultaneously developed flow assumption For some of

the values of the dimensionless length on the air side, several

measurements with differing liquid flow rates (200–400 kg/h)

were performed to ensure that the liquid-side heat transfer

coef-ficient was predicted correctly by Eq (21) No significant trend

could be seen Therefore, the conclusion can be drawn that the

liquid-side heat transfer is predicted correctly

Figure 6 presents experimentally determined sensible

Nus-selt numbers for test conditions that are dry (= Nua,s dry) and

wet (= Nua,s wet), i.e., where condensation of water vapor

takes place The climate denoted “wet1” involves the lowest

water content of the air, and “wet3” the highest Looking at

the set of test results for x a∗ ≈ 0.034, the conclusion can be

drawn that at this low air velocity, the sensible Nusselt number

is not very much affected by the condensation of water vapor

Here, too, tests were performed at different liquid flow rates

(200–300 kg/h), but this did not much affect the experimentally

determined sensible Nusselt number At higher air flow rates,

i.e., lower values of the dimensionless length, the sensible

Nus-selt number is more affected by the water content of the air

A deterioration of at most 30% was found Varying the liquid

flow rate (200–300 kg/h) also resulted in different values of theexperimentally determined sensible Nusselt number No suchdifference was seen for the dry air test conditions, and therefore

it was concluded that the reason for this must be linked to thewater vapor condensation A likely explanation is that the watercondensate droplets are distributed differently, depending on thediffering temperature distributions in the heat exchanger that thevarious liquid flow rates result in This results in various extent

of nonideal distribution on the air side of the heat exchangeraffecting the performance in a negative way However, since theexperiments were carried out at an elevated temperature level

on the air side, in order to obtain large temperature differencesand thereby good measurement uncertainty, the water content

of the air in all experiments is much higher than it would be

in reality in a display cabinet application This means that theresults for the “wet1” condition are most similar to those thatwould be obtained for a display cabinet climate

Since the tubes of the heat exchangers are flat and horizontal,

it was of interest to investigate whether a forward inclination ofthe heat exchanger could result in less deterioration of the heattransfer performance due to water vapor condensation A com-parison was made between the experimentally determined sen-sible Nusselt number at 1◦inclination, which was the standardinclination, used in most of the tests, and the sensible Nusseltnumbers at 10◦ inclination However, no significant differencewas obtained (not shown in the graph in Figure 6)

Similar comparisons as for the FFC heat exchanger werealso made with the MPET heat exchanger and are shown inthe following graphs Figure 7 shows a plot of experimentallydetermined Nusselt numbers on the air side of the MPET heat ex-changer versus the dimensionless length of the heat exchangerduring dry test conditions These experimentally determinedNusselt numbers are compared with theoretical ones for the as-sumption with fully developed flow and for the assumption withsimultaneously developing flow As the graph shows, the ex-perimentally determined Nusselt numbers lie between the onespredicted by the two different assumptions for the largest dimen-sionless length (lowest air flow rate) However, for the smallerdimensionless length (higher air flow rates), the experimentally

0 1 2 3 4 5 6 7 8 9 10

Dimensionless length, x a *=T d /(d h,a *Re dh,a *Pr a )

Nua,s_calc,fd Nua,s_calc,sd

Figure 7 Experimentally determined sensible Nusselt number for the MPET heat exchanger compared to theoretical predictions Dry test conditions.heat transfer engineering vol 31 no 3 2010

Dimensionless length, x a *=T d /(d h,a *Re dh,a *Pr a )

Figure 8 Experimentally determined sensible Nusselt number for the MPET

heat exchanger for dry and wet test conditions.

determined Nusselt numbers exceed the predicted values for

the assumption that the flow is simultaneously developing and

redevelops, between the tube rows However, it must not be

forgotten that the uncertainty of measurement is not negligible,

and the predicted value for simultaneously developing flow is

almost within the span of uncertainty of measurement

Several measurements with differing liquid flow rates were

made for this heat exchanger, too, in order to ensure that the

liquid side heat transfer coefficient was predicted correctly by

Eq (22) No significant differences or trends were seen

Experimentally determined sensible Nusselt numbers for dry

and wet test conditions are shown in Figure 8 Looking at the set

of test results it can be seen that the heat transfer performance

is adversely affected by the condensation of water vapor The

extent of deterioration is similar for all evaluated values of the

dimensionless length (i.e., air flow rates) However, the

maxi-mum deterioration was 18%, which is less than the deterioration

of many louvered-fin heat exchangers reported by Jacobi et al

[3] Here, too, tests were performed at different liquid flow rates,

but the results did not significantly affect the experimentally

de-termined sensible Nusselt number, as opposed to the case for

the FFC heat exchanger

For this heat exchanger as well, it was of interest to

inves-tigate whether the forward inclination could help draining the

condensate water, leading to a less significant deterioration of

the heat transfer performance Results from 1◦inclination were

compared to results from 10◦inclination A small difference in

a positive direction (2–8%) was obtained at all test points but

one (not shown in the graph in Figure 8) However, the

dif-ference was small and not completely consistent, especially in

comparison with the measurement uncertainty

Pressure Drop Performance

For the pressure drop, the measured pressure drop

(
p a,dry = dpa dry etc.) for different test conditions over

the heat exchangers were compared with calculated values

(
p a,dry,calc,f d = dpa calc,fd,
p a,dry,calc,sd= dpa calc,sd)

us-ing theoretical approaches First, it was assumed that the flow is

0 5 10 15 20 25 30

Figure 9 Measured and predicted pressure drop on the air side of the FFC heat exchanger for dry and wet test conditions.

fully developed, and second that the flow redevelops both whenentering a tube row and when leaving a tube row and entering

a passage without tubes in the same way as for the comparison

of experimentally determined and theoretical/calculated selt numbers already described The second approach thereforeinvolves several expansions and contractions of the flow duringits way through the heat exchanger, especially for the FFC heat

Nus-exchanger The applied values for the friction factors, f a,f dand

f a,app,sd, are interpolated from tabulated data for fully oped and developing flow in rectangular ducts as presented by

devel-Shah and London [18] Values for K c and K ewere taken fromKays and London [20] Since the different approaches involvenot only different friction factors, but also different numbers

of contractions and expansions of the flow, measured and oretical pressure drops are presented and compared instead ofdimensionless friction factors for pedagogical reasons The ex-pressions defining how the theoretical pressure drops have beencalculated are listed in Haglund Stignor [11]

the-Figure 9 shows the measured pressure drops over the FFCheat exchanger for dry and different wet test conditions, andcompares them with calculated pressure drops applying differ-ent theoretical approaches It can be seen that, for all Reynoldsnumbers at dry test conditions, the measured pressure drop isconsiderably higher than the predicted value for the fully de-veloped flow approach, but not as high as if the flow had re-developed after and before each tube row These findings are

in agreement with the results for the heat transfer performance(see Figure 5) For dehumidifying (wet) test conditions, the mea-sured pressure drop is increased by a factor of 2 as a maximum.The increase is higher for a higher water content of the incom-ing air Some of the test points were repeated at an inclinationangle of 10◦ The results showed that the forward inclinationangle helped drain the water from the fins, and the measuredpressure drop was somewhat lower (–1 Pa at highest air flowrate) However, the difference was not very large (These resultsare not shown in the graph in Figure 9.)

The experimentally determined friction factor on the liquidside of the heat exchanger was compared with theoretical values,assuming a fully developed velocity profile of the liquid flow inheat transfer engineering vol 31 no 3 2010

Figure 10 Experimentally determined and predicted friction factor on the

liquid side of the FFC heat exchanger under isothermal and non-isothermal test

conditions.

rectangular ducts The theoretical friction factor was calculated

according to Shah and London [18] The pressure drop was

measured under isothermal and non-isothermal test conditions

The friction factor was calculated according to the data

reduc-tion described by Eq (27) The graph in Figure 10 reveals that,

for the isothermal tests, the experimentally determined (f b,iso=

fb, iso) and theoretical fraction factors (f b,iso,theo= fb,iso theo)

agree very well This proves that the applied tube dimensions

are correct and that there is no occurrence of severe nonideal

dis-tribution on the liquid side However, this graph also shows that

under non-isothermal test conditions, the experimentally

deter-mined friction factor (f b,non-iso= fb,non-iso) is actually lower

than the predicted factor in many cases (f b,non-iso,theo=

fb,non-iso theo) This is probably due to the fact that the temperature of

the liquid is higher close to the tube wall compared to the bulk

temperature and therefore the liquid viscosity is lower close to

the wall, which decreases the shear stress

Note that the measurement uncertainty is not shown in the

graph The reason for this is that the major part of the total

uncertainty is that of the uncertainty of the internal tube

dimen-sion, resulting in a total uncertainty of over 16% However, for

the heat transfer measurement the uncertainty of the internal

tube dimension is of minor importance Since the measured and

theoretical values agree well, the conclusion can be drawn that

the applied uncertainties of the tube dimensions are

overesti-mated However, this affects the uncertainty of the heat transfer

performance only marginally

Figure 11 shows the measured and predicted pressure drops

on the air-side of the MPET heat exchanger For dry air test

conditions, the measured value lies between the predicted ones

for the different assumptions—fully developed and developing

duct flow This is valid for all the evaluated Reynolds

num-bers and is in accordance with the findings for the FFC heat

exchanger On the other hand, for the two highest evaluated

Reynolds number regions, the experimentally determined

Nus-selt number actually exceeded the predicted one, assuming a

simultaneously developing flow (see Figure 7) For

dehumidi-fying conditions, the measured pressure drop is almost doubled,

012345678910

dpa_dry dpa_wet1 dpa_wet2 dpa_wet3 dpa_calc,fd dpa_calc,sd

Figure 11 Measured and predicted pressure drop on the air side of the MPET heat exchanger for dry and wet test conditions.

but the internal variation for the different wet test conditions is

in most cases relatively small This pressure drop increment is

in the same order of magnitude as the one found by Jacobi et al.[3] for a similar geometry

In the same way as for the FFC heat exchanger, some of thetest points were repeated with the MPET heat exchanger at aninclination angle of 10◦ It was found that the forward inclinationangle helped drain the water from the fins, and the measuredpressure drop was a maximum of 25% lower (not shown in thegraph in Figure 11) The difference in pressure drop betweenthe two inclination angles was somewhat larger than for the casewith the FFC heat exchanger Even if a forward inclination doesnot result in much improved heat transfer, it helps to reduce thepressure drop for this heat exchanger with plain serpentine fins.The liquid-side pressure drop was measured over the MPETheat exchanger, but since this was a prototype the inlet andoutlet connections of the two separate heat exchangers were not

of ideal dimensions, but relatively small In a real application,the connections should be similar to the ones on the FFC heatexchanger Therefore, most of the pressure drop was not created

by the heat exchanger core, but by changes in the pipework sizes.For this reason, the measured pressure drop is of no interest here.However, in earlier experimental heat transfer investigations onsingle MPE tubes performed by some of the authors of thepresent paper and described in Haglund Stignor et al [6], thepressure drop was also measured over single tubes

The experimentally determined friction factor on the liquidside of one single tube with the same cross-section dimension

as the tubes of the MPET heat exchanger was compared withtheoretical values assuming a fully developed velocity profile

of the liquid flow in rectangular ducts in Figure 12 The oretical friction factor was calculated according to Shah andLondon [18] The pressure drop was measured during isother-mal test conditions The friction factor was calculated according

the-to the data reduction described by Eq (28) The graph revealsthat, for the isothermal tests, the experimentally determined andtheoretical friction factors agree very well

Note again that the measurement uncertainty is not shown inthe graph The reason for this is that the major part of the totalheat transfer engineering vol 31 no 3 2010

Figure 12 Experimentally determined and predicted friction factor on the

liquid side of one tube with the same cross-sectional dimensions as the tubes

of the MPET heat exchanger, but a length of 2.4 m, under isothermal test

conditions.

uncertainty is the uncertainty of the internal tube dimensions,

resulting in a total uncertainty of over 40% However, for the

heat transfer measurement the uncertainty of the internal tube

dimension is of minor importance Since the experimentally

de-termined and theoretical values agree quite well, the conclusion

can be drawn that the applied uncertainties of the tube

dimen-sions are overestimated in this case as well However, this affects

the uncertainty of the heat transfer performance only marginally

CONCLUSIONS

Heat transfer and pressure drop have been evaluated

exper-imentally on the air side of two brazed (or soldered) heat

changers having flat tubes and plain (flat) fins One of the heat

ex-changers had continuous plate fins (FFC heat exchanger), while

the other had serpentine fins between the tube rows (MPET heat

exchanger) The latter heat exchanger had considerably larger

tube depth than the former, 45 mm compared to 13.6 mm The

test conditions were appropriate for a display cabinet

applica-tion and other applicaapplica-tions involving a low air velocity (0.23–

1.2 m/s) in combination with condensation of water vapor in the

air The following conclusions could be drawn:

• The heat exchanger with continuous plate fins might suffer

from wake regions (most probable explanation) or poor

con-tact between the tubes and the fins This degrades the heat

transfer performance somewhat, at least for the lowest air

flow rates However, at these air flow rates its heat transfer

performance is not significantly affected by the occurrence of

condensate water on the fin surfaces, while this is the case for

the higher evaluated air flow rates, where a deterioration of

up to 30% was found The pressure drop was increased by up

to a factor of 2 under wet, as compared to dry, test conditions

• For the plain serpentine fin heat exchanger, the heat

trans-fer can be predicted relatively well by modeling the flow as

simultaneously developing duct flow under dry test

condi-tions However, such modeling overpredicts the pressure drop

for dry air flows For dehumidifying test conditions, the heattransfer performance is degraded by a maximum of 18% atthe evaluated air flow rates The condensed water vapor on thefins resulted in an almost doubled pressure drop compared tothe dry case for some (but not all) of the tests

• Forward inclination helps drain the condensate water out ofthe heat exchangers to some extent—more for the heat ex-changer having serpentine fins than for the one with continu-ous plate fins The inclination results in a decreased pressuredrop, but does not affect the heat transfer performance much

• A heat exchanger with plain continuous plate fins drains densate water better than one with plain serpentine fins—atleast at low air velocities However, the serpentine fin heatexchanger might have a better air surface area utilization.Nevertheless, since deterioration due to dehumidifying con-ditions or the non-perfect area utilization is only moderate,both heat exchangers have the necessary qualities to operatewell in a display cabinet or a similar application

con-NOMENCLATURE

A c cross - sectional area (m2)

C1 heat capacity flow rate on side 1 (W· K−1)

C2 heat capacity flow rate on side 2 (W· K−1)

C r heat capacity flow rate ratio, C r ≤ 1 by definition

(—)

C min heat capacity flow rate on minimum side (W· K−1)

c p specific heat capacity (J· kg−1· K−1)

K c contraction loss coefficient at heat exchanger inlet

K e expansion loss coefficient at heat exchanger outlet

L characteristic length, e.g., in the definition of

Reynolds number, L = d h for a duct flow and L = L p

(louver pitch) in a louvered fin geometry (m)

l tube heated tube length (m)

˙

m mass flow rate (kg· s−1or kg· h−1)

N number of tubes, fins or passesNTU number of heat transfer units, N T U = U · A/Cmin

P1 temperature effectiveness related to side 1 (—)

P 1,p temperature effectiveness per heat exchanger/pass

(—)

Pr Prandtl number, Pr= c p·µ

λ (—)

˙

Q cooling capacity or heat flow rate (W)

R heat transfer resistance (K· W−1)

R1 heat capacity rate ratio, R1= C1

α0 heat transfer coefficient (W· m−2· K−1)

α effective heat transfer coefficient (W· m−2· K−1)

σ ratio of free flow area to frontal area

η0 efficiency of the extended surface

in into heat exchanger, at inlet conditions

l longitudinal (direction of air flow)

non-iso non-isothermal

out out from heat exchanger, at outlet conditions

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kemitekniska tabeller (in Swedish), 6th ed., Liber Utbildning AB,

Stockholm, Sweden, p 77, 1994

[23] VDI-W¨armeatlas—Berechnunsbl¨atter f¨ur den W¨arme¨ubergang

(in German), VDI-Verlag, D¨usseldorf, Germany, 1984

[24] VDI 3786 part 4, Meteorological Measurements Concerning

Questions of Air Pollution—Air Humidity, VDI-Kommission

Reinhaltung der Luft, Sweden, 1985

[25] ASHRAE Hanbook—Fundamentals, American Society of

Heat-ing, Refrigerating and Air Conditioning Engineers, Atlanta, GA,

1997

[26] Hellsten, G., Tabeller och diagram, Energi- och kemiteknik (in

Swedish), Almqvist & Wiksell F¨orlag AB, Falk¨oping, Sweden,

pp 9–11, 1992

Caroline Haglund Stignor received her master

of science degree in chemical engineering from Chalmers University of Technology in Gothenburg, Sweden, in 1999 The same year she started to work

at SP Technical Research Institute of Sweden Since then she has mainly worked with research within the field of heat transfer, heat pumping, and refrigeration technologies She received her degree of licentiate of engineering in heat transfer from Lund Institute of Technology in 2002 Her main focus of research has been investigating the possibilities of making indirect or secondary loop cool-

ing systems in supermarkets more energy efficient Therefore she has performed

theoretical and experimental studies aiming at improving the heat transfer and

pressure drop performance of cooling coils and heat exchangers operated with

different liquid secondary refrigerants.

Bengt Sund´en received his M.S and Ph.D from

Chalmers University, G¨oteborg, Sweden He is rently professor of heat transfer and department head

cur-at Lund University, Sweden His main research ests are computational heat transfer, heat exchangers, transport phenomena in fuel cells, gas turbine heat transfer, combustion-related heat transfer, and en- hanced heat transfer He is a fellow of the ASME and

inter-serves as associate editor of Journal of Heat Transfer.

He is an honorary professor of Xi’an Jiatong sity, Xi’an, China.

Univer-Per Fahl´en received his master of science degree in

physics and electrical engineering from the Royal University of Technology in Stockholm, Sweden,

in 1972 At Chalmers University of Technology, in Building Services Engineering, he acquired a licen- tiate degree in 1994, a Ph.D in 1996, and became Dr.Sc./associate prof in 1998 He has worked in in- dustry with R&D of electrical switch-gear (CEWE), nondestructive testing (ABB), and magneto-elastic force transducers (ABB) In 1976 he became head of fundamental metrology of mass, flow and heat measurement at SP Technical Research Institute of Sweden and in 1980 moved to the department of Energy Technology to establish a division of heating and cooling He became head of R&D and quality in 1986 and remained so until he became professor and head

of the department of Building Services Engineering at Chalmers University

of Technology in 2001 His main focus of research has been air conditioning, supermarket refrigeration, heat pump applications, heat recovery systems, ef- ficiency of pump and fan operation, HVAC control systems, thermal comfort, and measuring techniques.

Sofia Stensson received a master of science in

in-dustrial engineering and management at Link¨oping Institute of Technology in Sweden in 2007 and started working the same year at SP Technical Re- search Institute of Sweden She is also a Ph.D stu- dent at Chalmers University of Technology at the department of Building Service Engineering Her field of research is within energy efficiency, super- market refrigeration, and HVAC systems for com- plex buildings She is investigating system solutions for energy efficiency in shopping centers focusing on space heating and cooling.

heat transfer engineering vol 31 no 3 2010

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903304368

The EMTD Method: An Alternative

Effective Mean Temperature

Difference Approach to Heat

Exchanger Analysis

LINDON THOMAS

Thermal Engineering Associates, Knoxville, Tennessee, USA

The objective of this article is to develop a mean temperature difference approach to heat exchanger analysis that follows

naturally from the underlying classical solution relations The analysis gives rise to a basic optional defining relation for

the number of transfer units NTU I that provides the basis for expressing the effective mean temperature difference EMTD

directly in terms of NTU I and the effectiveness P The resulting relations give rise to the EMTD method, which represents

an alternative mean temperature difference approach that does not involve the traditional correction factor F.

INTRODUCTION

recommended for heat exchanger analysis applications

involv-ing nonideal effects that seriously compromise the standard

modeling assumptions, classical methods are commonly relied

upon by engineers for practical performance analysis tasks

in-volving rating, design, and testing The classical approaches for

heat exchanger analysis documented in the literature include

the P-NTU I , ε-NTU, and ψ methods and a mean temperature

difference approach referred to as the F-LMTD or MTD method

[1–17] Although the P-NTU I and ε-NTU methods have been

used in the automotive, aircraft, and air-conditioning industries

since the 1950s, the F-LMTD method has continued to be widely

used since the 1930s in the power, process, and petrochemical

industries.1

In considering the relative merits of the traditional classical

methods, it has been recognized that the F-LMTD method has

the advantage of being simpler to apply than the effectiveness

methods in design and testing of ideal counterflow and

paral-lel flow arrangements However, the F-LMTD method has the

Address correspondence to Dr Lindon Thomas, Thermal

Engineer-ing Associates, 1424 FarrEngineer-ington Dr., Knoxville, TN 37923, USA E-mail:

lthomas@thermalea.com

1 The ψ method is not presently in common use because of the attributes

and popularity of the effectiveness and F-LMTD methods.

disadvantage of being computationally more involved for ing, as well as for design and testing of exchangers other thanideal counterflow and parallel flow arrangements With thesepoints in mind, the classical heat exchanger solution relationsare reconsidered in this article, with the objective of establish-ing a natural link between the primary performance parameters

rat-P , R, and NTU I and the effective mean temperature difference

EMTD, and developing a more straightforward mean

tempera-ture difference approach

stream solution relations for q are expressed in terms of capacity rates C h = ( ˙mc P)h and C c = ( ˙mc P)c and absolute terminal tem- perature differences δT h = T h,i − T h,o and δT c = T c,o − T c,i

by

For purpose of generalization, these bulk-stream solution

relations are expressed in terms of arbitrarily selected reference

193

stream I and secondary stream II by

q = C I δT I q = C II δT II (2a,b)

where δT I = |T I,i − T I,o | and δT II = |T II,i − T II,o|

The primary dimensionless performance parameters that

nat-urally occur in the standard formulation/solution of heat

ex-changers are identified as the number of transfer units NTU I,

effectiveness P , and capacitance ratio R, which are defined in

terms of the effective uniform overall coefficient of heat transfer

U , capacity rates C I and C II , and inlet temperature difference

δT i = T h,i − T c,iby

C I

(3)and

With the reference stream I specified as the fluid with

mini-mum capacity rate, C I is traditionally designated by Cmin, P by

ε, R by C∗ = Cmin/Cmax, and NTU I by NTU = UA s /Cmin

The solutions that appear in the literature are expressed in

terms of P , R, and NTU I by explicit functional solution relations

for standard arrangements of the form2

P = fn (NTU I , R, I, arrangement) (8)

and explicit inverse functional solution relations for a small

group of “classic” arrangements of the form

NTU I = fn−1(P , R, I , arrangement) (9)

The several arrangements for which the solution relations for P

or NTU I are independent of the reference stream I are referred

to as symmetrical exchangers For future reference, the inverse

functional solution relations for NTU I associated with ideal

counterflow and parallel flow arrangements are specified by

2 Extensive listings of classical solution relations for various standard

ar-rangements are available in references 18 to 21.

Logarithmic Mean Temperature Difference

For special cases involving ideal counterflow and parallelflow, the classical solution relation for heat-transfer rate can

also be expressed in terms of UA sby

for counterflow, and

T1= T h,i − T c,i
T2= T h,o − T c,o

for parallel flow

Effective Mean Temperature Difference

Following the standard mean temperature difference

ap-proach, the general classical solution for heat-transfer rate q

that applies to more complex arrangements involving nations of counterflow and parallel flow, as well as crossflow,

combi-is expressed in terms of effective mean temperature difference EMTD by [1–17]

As a practical point relevant to the present study, Eq (19)

pro-vides the basis for identifying the equivalence between q/(UA s)

and EMTD It should also be observed by comparing Eqs (15)

heat transfer engineering vol 31 no 3 2010

and (19) that EMTD corresponds to LMTD for ideal counterflow

and parallel flow arrangements, such that

EMTD cf = LMTD cf EMTD pf = LMTD pf (20, 21)

Following the approach developed by Nagle [22],

Under-wood [23], Fischer [24], and others, Eq (19) has been adapted

to standard heat exchanger arrangements by use of the

correc-tion factor F referenced to ideal counterflow; that is,

EMTD = F LMTD cf q = UA s F LMTD cf (22, 23)

Although F = 1 for counterflow, F is less than unity for

other arrangements, including parallel flow for which F pf =

LMTD pf /LMTD cf The correction factor F is related to the

primary performance parameters P , R, and NTU I by

use of the applicable inverse solution relation for NTU I, which is

explicit for classic arrangements but implicit for other standard

arrangements

Classical Heat Exchanger Analysis Methods

The general application of the classical heat exchanger

anal-ysis methods involves the identification of two of the three

pri-mary performance parameters P , R, and NTU I as independent

variables that can be calculated for specified input parameters,

and use of the applicable functional solution relation of the

form of Eq (8) or Eq (9) to evaluate the unspecified dependent

parameter P (for rating) or NTU I (for design and testing)

The effectiveness methods feature the use of Eq (12) for

heat-transfer rate and are traced back to the report of London

and Seban [25].3 On the other hand, the traditional F-LMTD

method that emerged from the work by Nagle [22], Underwood

[23], Fischer [24], and others and was popularized by Kern [17]

involves the representation of the heat-transfer rate by Eq (23),

with F specified by use of Eq (24) and LMTD cf calculated by

use of Eqs (16) and (17a,b) Referring to Table 1, the

effec-tiveness method provides a straightforward classical approach

to rating, design, and testing Both traditional and alternative

forms of the F-LMTD method offer the advantage of

simplify-ing the analysis for design and testsimplify-ing of ideal counterflow and

parallel-flow arrangements However, the artificial introduction

of F and LMTD cf into the general solution relation for EMTD

results in a method that is more involved than the effectiveness

method for rating, as well as for design and testing of

exchang-ers other than ideal counterflow and parallel flow arrangements

Furthermore, the traditional F-LMTD method involves

unnec-essary iterations on the unspecified terminal temperatures for

rating

3Because of the equivalence of P and ε for C I = Cmin, the P-NTU Iand

ε-NTU methods are both classified as effectiveness methods.

THE EMTD METHOD

To establish a mean temperature difference approach that lows naturally from the classical solution relations, attention is

fol-returned to the standard defining equation for NTU Ispecified by

Eq (3) Following the approach used to transform Eqs (4) and

(5) for P and R into Eqs (6) and (7), Eq (2a) is used to express

Eq (3) for NTU I in terms of the reference terminal temperature

difference δT I and heat-transfer rate q, with the result

NTU I = UA s δT I

This alternative equation for NTU I provides the basis forindependently identifying the effective mean temperature dif-

ference EMTD = q/(UA s) as a relevant heat exchanger

perfor-mance parameter It follows from Eq (25) that NTU I and EMTD

analysis that does not involve the correction factor F and log mean temperature difference LMTD cf With P , R, and NTU I evaluated by the standard approach, the EMTD method features

4 In the context of showing that the classical effectiveness solution relations for ideal counterflow arrangements are consistent with Eq (20), Spalding [26] has shown that Eqs (1a), (1b), and (19) provide the basis for relations of the

form EMTD = (T1,in– T1,out)/NTU1= (T2,out– T2,in)/NTU2, which are alent to Eq (27) Although these two equations are applicable to all standard arrangements, they have not been previously incorporated into classical heat exchanger analysis methodology.

equiv-5 Following the pattern of the steps taken by Spalding [26], Eqs (27) and

(28) also can be obtained by simply eliminating q between Eqs (2a) and (19)

or Eqs (14) and (19) by writing

q = C I δT I = UA s EMTD EMTD = δT I C I / (UA s)= δT I /NTU I = P δT i /NTU I

and

q = P C I δT i = UA s EMTD EMTD = P δT i C I / (UA s)= P δT i /NTU I = δT I /NTU I

heat transfer engineering vol 31 no 3 2010

Table 1 Comparison of P-NTU I , F-LMTD, and EMTD methods: Kays and London pattern [16]

Basic design and testingKays and London12

Specify reference stream;

A s = q/(U EMTD) for design, or

U = q/(As EMTD) for testing, where q is

evaluated from the terminal temperatures andthe appropriate capacity rate

Present study

EMTD method13(May skip to (3b) for ideal arrangements)

Specify reference stream;

1 Calculate P and R;

2 Calculate NTUI;

3 Calculate

a EMTD = δTI /NTUI, or

b EMTD = LMTD for ideal

arrangements;

4 Calculate

A s = q/(U EMTD) for design, or

U = q/(As EMTD) for testing, where q is

evaluated from the terminal temperaturesand the appropriate capacity rate.Standard rating14

Kays and London12

5 Determine q (j ) = UAsEMTD(j )

6 Calculate terminal temperatures to comparewith the assumption of step 2;

7 Repeat until satisfactory agreement is obtained

Present study

EMTD method

Specify reference stream;

1 Calculate NTUI and R;

2 Calculate P ;

3 Calculate EMTD = P δTi /NTUI;

4 Calculate q = UAs EMTD;

5 Calculate outlet temperatures using Eqs.(4a,b)

Alternative F- LMTD Method

Specify reference stream;

1 Calculate NTUI and R;

2 Calculate P ;

3 Calculate

(a) NTUI,cf = (1 – R)–1ln [(1 – PR)/ (1 – P )]

(b) F = NTUt,cf /NTUt;

(c) δTI = P δTi and TI,o = TI,i ± δTI;

(d) δT II = R δTI and T II,o = T II,i ± δT II;

(e)
T1,
T 2, and LMTDcf;

(f) EMTD = F LMTDcf;

4 Calculate

q = UAs EMTD

12Note that P = , R = C∗, and NTU

I = NTU for C I = Cmin

13The F -LMTD and EMTD methods reduce to the LMTD method for ideal counterflow and parallel-flow arrangements, which eliminates the need for calculating

P , R, and NTU Ifor design and testing.

14 Iterate to refine properties if necessary.

the direct calculation of EMTD by use of Eq (27) for design

and testing or Eq (28) for rating, and the use of Eqs (19) and

(2a,b) for closure

The steps associated with use of the EMTD method are listed

in Table 1 In addition to reducing to the elementary LMTD

method for design and testing of ideal counterflow and parallel

flow arrangements, the EMTD method features general steps for

rating, design, and testing that are directly linked and

compa-rable to the P-NTU I method and are more straightforward than

the F-LMTD method.

heat transfer engineering vol 31 no 3 2010

The P-NTU I , EMTD, and F-LMTD methods are illustrated

for design and rating by two examples:

Example 1, basic design, 1-2 E shell-and-tube exchanger

Example 2, standard rating, 1-2 E shell-and-tube exchanger

Details involved in calculation of the tube-side and shell-side

convection coefficients and thermal resistances associated with

the overall coefficient of heat transfer U used in these examples

are given in [9]

Example 1 Basic Design:

1-2 E Shell-and-Tube Exchanger6

Design calculations are developed in this example for the

surface area A s associated with the 1-2 E shell-and-tube heat

exchanger shown in the schematic

Schematic C t = 878 kW/◦C, C

s = 1940 kW/◦C, q

req =

C s δT s = 5430 kW, T t,o = T t,i + qreq/C t = 32.19◦C, and

U = 1250 W/(m2◦C) for reference surface area A

s = A s,oandspecified fouling factors

Classical approach δT i = 21.8◦C Tube-side fluid is selected

6Refer to Example 11-11 (SV) or 11-19 (PV) of reference 9 The fluid

properties in this example are specified at the inlet temperatures The properties

can be readily specified at the average of the inlet and outlet temperatures for

design and testing applications.

7P , R, and NTU I correspond to ε, C*, and NTU for C I = C t = Cmin For

shell-side reference stream: P = 0.128, R = 2.21, NTU I = 0.164, and same

calculations for EMTD and A s.

255 m2

qreq/(U EMTD)= 255 m2

exam-Schematic C t = 878 kW/◦C, C s= 1940 kW/◦C, and U= 1250W/(m2◦C) for reference surface area A s = A s,o = 438 m2andspecified fouling factors

8NTU Imust be calculated by use of the effectiveness solution relation for exchangers other than classic arrangements, which requires iteration.

9Refer to Example 11-8 (SV) or 11-11 (PV) of reference 9 The fluid erties in this example are specified at the inlet temperatures The rating analysis can be refined by specifying the properties at the average of the inlet and outlet temperatures, which requires iteration.

prop-heat transfer engineering vol 31 no 3 2010