Heat transfer engineering an international journal, tập 32, số 1, 2011

5 c concentration of depositing reacting material, kg/m3 E activation energy, J/mol kR Reaction rate constant, m4/kg-s Rf ∗ asymptotic fouling resistance, m2-K/W Rwall thermal resistance

Copyright
C Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457632.2010.505127

Heat Transfer Fouling: 50 Years

After the Kern and Seaton Model

Technische Universit¨at Dresden, Dresden, Germany

Fouling of heat exchangers is a chronic problem in processing industries In addition to the appropriate selection of

operating conditions and exchanger geometry, there are numerous chemical and mechanical methods to mitigate fouling

and to remove deposits from the heat transfer surfaces However, all methods to reduce fouling require some understanding

of the mechanisms of the deposition process and of the structure and adhesion of deposits on the heat transfer surfaces.

Almost exactly 50 years ago, D Q Kern and his co-author, R E Seaton, published a paper attempting to describe the

growth of fouling deposits in terms of an unsteady-state heat and mass balance for the heat transfer surface More or less

at the same time, the TEMA fouling resistances were published based on operational and anecdotal evidence of fouling for

a range of heat exchanger applications These two approaches have since formed the basis for most heat transfer fouling

models and heat exchanger designs Increased costs of energy, raw materials, and production downtime have contributed

to the growing interest in heat transfer fouling More recently, environmental legislation has put additional pressure on

fouling-related CO 2 emissions and disposal of cleaning chemicals Despite these efforts, fouling of heat exchangers is still

far from been understood in its whole complexity The present paper documents the 2009 D Q Kern Award Lecture in

which some selected aspects of fouling research to date have been presented and areas have been identified where significant

research and development activities are still required.

INTRODUCTION

In most industrial processes, heat-exchanging fluids contain

certain amounts of dissolved or suspended material or provide

conditions favorable for the growth of biological organisms

Design and operation of heat exchangers are still to a major

extent determined by the process-related formation of deposits

on the heat transfer surfaces, i.e., fouling A typical example of a

fouled heat exchanger is shown in Figure 1 for the water side of

a gas cooler Since the thermal conductivity of such deposits is

low, their resistance to heat transfer may well exceed that of the

process fluids, resulting in significantly reduced heat exchanger

performance [1] As a result, substantial safety margins in the

design, pretreatment of hot/cold fluids, and regular cleaning of

equipment are usually required

Several surveys [2–4] have reported that more than 90% of

in-dustrial heat exchangers suffer from fouling problems and must

be designed with some allowance for the resulting reduction in

thermal and hydraulic performance This is also indicated in

Fig-ure 2, which shows the percentage of operating heat exchangers

Address correspondence to Dr Hans M¨uller-Steinhagen, Technische

Uni-versit¨at Dresden, 01062, Dresden, Germany E-mail: rektor@tu-dresden.de

confronted with fouling problems, as found in a detailed studyfor New Zealand [2]

To date, the formation of deposits on heat transfer faces is the least understood problem in the design of heatexchangers Well-proven codes and correlations are now avail-able for standard heat exchanger design, and computationalfluid dynamics simulation can be performed for complexsingle-phase flow conditions However, all these sophisticatedcalculations are offset by the current practice of using constant,crudely estimated, experience- or imagination-based foulingresistances or safety margins Even worse is the situationfor the prediction of pressure drop While more heat exchangersare taken out of operation due to excessive, fouling-relatedincrease in flow restriction [5], there is virtually no informationabout the potential effects of deposits on pressure drop.Considering the fact that heat exchangers are the workhorse

sur-of most chemical, petrochemical, food processing, and powergenerating processes, this situation is most unsatisfactory.The costs of heat exchanger fouling due to oversizing ofequipment, maintenance, fluid treatment, additional hardware,additional fuel consumption, and loss of production have beenestimated as about 0.25% of the gross domestic product (GDP)

of industrialized countries in several studies from the 1980s andearly 1990s [2–4] Even today, where “a billion dollars” seems1

2 H M ¨ULLER-STEINHAGEN

Figure 1 Fouled heat exchanger Courtesy of Hong Kong Towngas.

to become a common order of magnitude in terms of public

expenditure or debts, the costs due to fouling are an excessive

burden on industry and economy

For a long time, fouling was treated as an incomprehensible

and unavoidable curse of any heat exchanger operation

Em-pirical knowledge was developed with respect to the beneficial

aspects of additives and operating conditions, but no systematic

approaches have been developed to understand the mechanisms

of fouling and to affect these mechanisms in a beneficial way

Typical examples for this were the addition of potatoes or

saw-dust to the boiler feedwater to mitigate fouling in early steam

generators

The present paper documents the 2009 D Q Kern Award

Lecture in which some selected aspects of fouling research to

date have been presented and areas have been identified where

significant research and development activities are still required

It has deliberately been focused on fouling during heat transfer

to single-phase, liquid fluids, as this represents the majority

of investigations to date, and in order to limit the paper to an

acceptable number of pages

STANDARD DESIGN PROCEDURE FOR FOULING

The possibility of deposition on heat transfer surfaces is

gen-erally considered in the design of heat exchangers by using

Figure 2 Fouling problems in various heat exchanger types [2].

so-called fouling resistances in the calculation of the overallheat transfer coefficient U

1

U=

1

of the separating wall It is obvious that the frequently usedexpression “fouling factor” is incorrect, as the effect of fouling is

to create an additional thermal resistance The fouling resistancereduces the overall heat transfer coefficient U, and hence leads

to the reduction of the heat duty of an existing heat exchanger

or to additional surface requirements in the design of new heatexchangers The results of this procedure are heat exchangerswith excess heat transfer surface that may (or may not) allowplant operation for an acceptable period of time

In the early 1950s the first compilation of fouling tances was published in the Standards of the Tubular ExchangersManufacturers Association (TEMA), based on operational andanecdotal evidence of fouling for a range of heat exchanger ap-plications Even though additional proprietary data are availablewithin specialist companies, the TEMA values still form the ba-sis for the design of most heat exchangers, worldwide

resis-However, there are several problems with respect to the critical use of the TEMA fouling resistances, such as:

un-1 Their origin and operating conditions are not known

2 The majority of values are for flow of water or hydrocarbons

3 They apply for shell and tube heat exchangers only

4 They do not provide any information on the effect on thedeposition rate of operating parameters such as flow velocity,fluid temperature, heat flux, and fluid composition

5 They do not indicate after which operating time the givenfouling resistances are reached

6 They do not provide for time-dependent management of ing resistance

foul-In 1990 Chenoweth and co-workers [6] critically reviewedthe original TEMA fouling resistances However, only minormodifications have been included in the later editions of theTEMA Standards, mainly due to the lack of suitable industrialdata

THE KERN AND SEATON MODEL

While several attempts were made before the 1950s to late the fouling-related reduction of heat transfer, none of theseequations was based on first principles The decisive change withrespect to the analysis of fouling came with the model developed

corre-by D Q Kern and his co-author R E Seaton Almost exactly

50 years ago, they published a paper attempting to describe thegrowth of fouling deposits in terms of an unsteady-state heat andmass balance for the heat transfer surface [7] Together with theheat transfer engineering vol 32 no 1 2011

H M ¨ULLER-STEINHAGEN 3

Figure 3 Typical fouling resistance versus time curves.

TEMA fouling resistances, this approach formed for the next

20 years the basis for most heat transfer fouling models and

practical heat exchanger designs

Having observed that fouling in industrial heat exchangers

often followed a decreasing or even asymptotic trend, as

de-picted in Figure 3, Kern and Seaton suggested modeling the

fouling processes as a balance between opposing transport

pro-cesses to and from the heat transfer surface, namely, deposition

and removal [7], as shown in Figure 4

Therefore, the accumulation of the deposited mass of fouling

material with time was written as

dm

dt = ˙md− ˙mr= dRf

assuming that the thermal conductivityλd and the densityρd

of the deposit remain constant with time and deposit thickness

The deposition rate was modeled with a simplified mass transfer

correlation as being proportional to the bulk flow velocity and

the foulant concentration:

˙

Modeling of the removal of already deposited material due to

shear forces from the bulk flow was significantly more difficult,

and it was assumed that this may be proportional to the wall

shear stress and to the thickness of the deposit, which may be a

measure for the presence of structural weaknesses in the deposit

Figure 4 Deposition and removal of deposit.

Figure 5 Predicted fouling resistance as a function of time and the parameter

b in Eq (5), according to the Kern and Seaton model [8].

Combining Eqs (3) and (4) and integrating with respect totime leads to Eq (5):

Rf(t)= K3C V

λdK4τw

(1− e−K 4 τ w t)= R∗

f(1− e−bt) (5)

which includes the so-called asymptotic fouling resistance Rf ∗,

a value that will be obtained after some period of operation

if the removal rate becomes equal to the deposition rate, i.e.,the deposit is not very hard and adherent While the value ofthis asymptotic fouling resistance is approximately inverselyproportional to the flow velocity for turbulent flow, the rate atwhich it is approached increases strongly with flow velocity asshown in Figure 5

THE DEVELOPING YEARS OF FOULING RESEARCH

While the Kern and Seaton model was a significant step ward and provided a physically meaningful description of theeffects of velocity on deposition and removal, and an equation

for-to model the increase of fouling resistance with time, it theless included two parameters that had to be fitted to the actualfouling problem (i.e., required real operational data) No infor-mation was available on how these two parameters may depend

never-on the materials of fouling and their cnever-oncentratinever-on, the structure

of the deposit, and operating conditions such as surface perature and flow conditions Furthermore, the Kern and Seatonmodel has obvious deficiencies in that it does not include thechemical reactions that are the basis of most fouling processessuch as scale formation, crude oil fouling, or food fouling.heat transfer engineering vol 32 no 1 2011

tem-4 H M ¨ULLER-STEINHAGEN

It was, therefore, not surprising that little use was made of the

Kern and Seaton model in terms of actual heat exchanger design

The majority of heat exchangers continued to be designed using

the TEMA or proprietary fouling resistances for tubular heat

exchangers For compact heat exchangers, the use of the TEMA

values would lead to excessive overdesign, making them

inef-fective and uneconomic Compact heat exchangers are hence

generally designed with 15–25% excess surface, to

accommo-date the fouling-related drop in heat transfer capacity [1]

Frequently, design engineers try to compensate for their lack

of accurate physical properties of the heat-exchanging fluids or

the limited reliability of correlations for the clean heat transfer

coefficients (for example, for multiphase and/or

multicompo-nent applications) by arbitrarily increasing the fouling

resis-tance or by multiplying the calculated overall heat transfer

co-efficients with a “safety factor,” which also increases the fouling

resistance It has been reported [4] that the practice of

specify-ing foulspecify-ing resistances increases the heat transfer surface

cal-culated for clean conditions by 20–300% These findings have

been confirmed by a study from Heat Transfer Research, Inc

(HTRI), plotting the fouling-related excess area of 2000 recently

designed heat exchangers (see Figure 6)

In addition to increased equipment cost, oversizing of heat

exchangers may even accelerate the rate of deposit formation if

it results in low flow velocities or high surface temperatures

This unsatisfactory procedure would probably have

contin-ued if Taborek et al [9] had not reminded the heat transfer

community in 1972 that fouling is the major unresolved

prob-lem This important paper triggered a range of investigations,

most notably the systematic investigations on cooling water

fouling by HTRI together with J Knudsen from Oregon State

University, by N Epstein and A P Watkinson at the University

of British Columbia, by T R Bott at Birmingham University,

and by M Bohnet at the University of Braunschweig In this

work, typical fouling processes such as scale formation,

par-ticulate deposition, and the growth of biological matter have

been investigated using synthetic model fluids under controlled

conditions Significant differences have been found with respect

Figure 6 Impact of fouling resistance on the design of 2000 shell-and-tube

heat exchangers Courtesy of HTRI.

Figure 7 Effect of (a) flow velocity and(b) surface temperature on water fouling.

cooling-to the effect of the main operational parameters flow velocityand surface temperature on the fouling behavior of the differenttypes of fouling, as exemplified in Figure 7

In 1985 Epstein summarized findings to-date in his famous 5

× 5 matrix [10], which has been adopted to plot Figure 8 Here,for the first time, the different mechanisms of fouling and thedifferent steps in the net deposition process have been broughttogether and analyzed This has led to a much more systematicand focused approach to the investigation and mitigation of heattransfer fouling, for both practical and fundamental problems.For example, fouling is now generally modeled as a consec-utive process made up from transport, reaction/attachment, andremoval The transport rate is determined according to Eq (6)

Figure 8 Epstein’s 5 × 5 matrix: perceived level of understanding (increasing from 0 to 5) versus fouling mechanism and type of fouling [10].

heat transfer engineering vol 32 no 1 2011

H M ¨ULLER-STEINHAGEN 5with the mass transfer coefficientβ obtained from the appropri-

ate Sh-Re-Sc relationships:

˙

The subsequent attachment or reaction rate is obtained from

Eq (7), with the reaction rate constant kR and the reaction

For a second-order reaction such as the formation of CaSO4

and assuming that the reaction rate must be equal to the transport

rate, Bohnet and co-workers derived Eq (9) [11]:

14

⎤

⎦(9)

which subsequently has been applied in many investigations

[e.g., 12, 13]

Research and development efforts during these years have

shed considerable light into the most common fouling

mecha-nisms, such as crystallization, particulate, biological, corrosion,

and chemical reaction fouling Numerous models for fouling

during convective heat transfer have been derived based on these

approaches, to correlate available data

It is not the aim of this paper to summarize in detail the vast

area of heat transfer fouling research, or to provide a historical

treatise of it The latter has already been done in a laudable

way for the period up to 1990 by Somerscales [14] Significant

progress has been made in this period of time by following

several approaches in parallel, such as:

• Detailed investigation of fouling mechanisms, increasingly

also for gas-side fouling and for fouling during boiling

• Empirical development of mechanical and chemical on-line

fouling mitigation techniques, such as sponge ball systems,

wire brush systems, and chemical additives [15]

• Development of advanced mechanical and chemical cleaning

systems and procedures for heat exchangers [15]

• Development of heat exchanger types with reduced fouling

rates, for example, the fluidized bed heat exchanger [16]

• Development of guidelines for heat exchanger design, e.g., by

HTRI

It is, however, noteworthy that most of the investigations

published during this period have been obtained for ideal (or

“model”) fluids, and not many research results, and hardly any

of the numerous deposition models, have found their way into

practical heat exchanger design and operation

FOULING BECOMES AN INTERNATIONALLY ACCEPTED RESEARCH TOPIC

Following up on the increasing academic interest in heatexchanger fouling, the first conferences targeted specifically

at this topic were organized in Guildford (1979) [17], Troy(1981) [18], and Alvor (1987) [19] These pioneering meetingscontributed much to the formation of a “fouling researchcommunity” with significant coherence and interaction.Consequently, United Engineering Foundation Conferences(now Engineering Conferences International) decided toinitiate a series of international meetings on fundamental andtechnological aspects of heat exchanger fouling Seven highlysuccessful meetings have been held in San Luis Obispo, CA(United States, 1994), Castelvecchio Pascoli (Italy, 1997),Banff (Canada, 1999), Davos (Switzerland, 2001) [20], Santa

Fe, NM (United States, 2003), Kloster Irsee (Germany, 2005),and Tomar (Portugal, 2007) These conferences attracted anincreasing number of participants from industry, research or-ganizations, and universities Papers presented at each of theseconferences have been published in the respective conferenceproceedings and probably provide the most comprehensiveoverview of the state of the art of this complex subject The fullproceedings of the 2003–2007 meetings can be downloadedfrom http://services.bepress.com/eci/heatexchanger

For organizational reasons, the ECI fouling conference serieswas continued from 2009 onward as the EUROTHERM Sem-inar Series, starting with the 2009 conference in Schladming(Austria) Proceedings of and information about this confer-ence can be found at http://www.heatexchanger-fouling.com.The next conference in this series will be held in Crete (Greece,June 2011); see the website just given

For engineers working in the area of food processing, an cellent series of bi-annual conferences at Cambridge University(England), organized by Wilson, Fryer, and Hastings, providescurrent developments in fouling and cleaning in that industry

ex-FOULING RESEARCH REACHES MATURITY

Increasing costs of energy, raw materials, and productiondowntime have contributed to the growing interest in heat trans-fer fouling More recently, environmental legislation has putadditional pressure on fouling-related CO2 emissions and dis-posal of cleaning chemicals [21]

For immediate benefits, fouling task forces includingrepresentatives from major international process engineeringcompanies, heat exchanger design and construction companies,and suppliers of chemical and mechanical fouling mitigationmeasures have been established by ESDU and HTRI to compilebest practice guides for heat exchanger design and operation

To date, very detailed reports have been prepared for crude oil[22], seawater [23], and freshwater [24]

Based on almost 50 years of experience, HTRI has developed

a design methodology that yields smaller, more cost-effectiveheat transfer engineering vol 32 no 1 2011

6 H M ¨ULLER-STEINHAGEN

shell-and-tube heat exchangers with extended run times between

cleanings [1, 25] While this methodology has, so far, only been

validated for crude oil processing, its rigorous approach can be

taken as an example for other fluids and heat exchangers types

Using this methodology, only a small design margin may be

added to the design to address design uncertainties Rarely is

this margin in excess of 30%

These experience-based approaches are extremely useful for

appropriate design and operational mitigation of standard

foul-ing problems However, they cannot be extrapolated to

individ-ual fouling problems or lead to a general solution for the

reduc-tion or even eliminareduc-tion of fouling For this, more fundamental

research and development are required Some of these efforts

are described in the following It is obvious that the general

approach to improved understanding of deposition mechanisms

has been moving from macro-scale to micro-scale to molecular

level, and that advanced computational tools are increasingly

finding their way into fouling analyses

Whole Plant Modeling

Heat exchangers are rarely stand-alone units unaffected by

upstream and downstream processes Hence, the conditions

leading to and resulting from fouling are the result of

com-plex interactions within a range of equipment, including, e.g.,

heat exchangers, settling tanks, reactors, mixers, and

evapora-tors In many bulk material processes, addition of chemicals to

mitigate fouling is not possible due to product requirements, and

significant changes to the existing hardware cannot be afforded

However, it may still be possible to reduce the formation of

deposits or improve the economy of the process, if appropriate

operating conditions and/or operating schedules are selected

This requires understanding of both the local fouling

condi-tions and the overall plant operation Ideally the optimization

processes should include the following steps:

1 Analysis of plant operating data

2 Analysis of deposits and of foulant solubility behavior

3 Laboratory experiments to determine the effect of

operat-ing conditions (concentration flow velocity, bulk and heat

transfer surface temperature)

4 Laboratory experiments to determine possible fouling

mit-igation methods (e.g., seeding, turbulence promoters,

flu-idized bed)

5 Modeling of fouling process

6 Limited number of plant measurements on a slipstream to

confirm the validity of the laboratory data and of the fouling

model for actual plant operating conditions

7 Heat exchanger model to predict local and overall

temper-atures and fouling rates

8 Comparison of heat exchanger model with plant operating

data

9 Overall plant model with/without fouling related

deteriora-tion of heat transfer

10 Use of model to determine optimum operating tions/procedures and to investigate the effects of plant mod-ifications to maximize throughput or minimize operatingcosts This model can also be used for model-based processcontrol and environmental impact studies

condi-An effective approach to provide the information requiredfor optimizing plant operation and plant layout requires a com-bination of fundamental and industrial studies It is unlikely thatall the information just specified can be collected, due to finan-cial and/or time constraints The important criterion is, however,that some plant verification for the developed fouling/operatingmodel is available This general approach has been applied suc-cessfully in several comprehensive studies:

• Kraft black liquor in the pulp and paper industry [26, 27]

• Bayer liquor in bauxite refineries [28, 29]

• Phosphoric acid plants for fertilizer production [30, 31]

• Sulfuric acid recovery plant in a titanium oxide extractionprocess [32]

• Crude oil preheat train [33, 34]

In the processes just listed, heat exchangers generally sufferfrom severe fouling problems, leading to significant limitation

in plant operation and high additional costs The investigationshave been performed in close collaboration with industry andresulted in significant gain in knowledge and industrial bene-fits Results of these investigations have been implemented intodesign and operation of the investigated plants, or are furtherinvestigated in pilot-plant studies Actual and potential futuresavings are in the order of many millions of dollars, providing asignificant payback on the investments for the detailed studies

A typical example is shown in Figure 9, indicating the predictedextension of operating time of a sulfuric acid concentration unit

if operated at higher temperatures and with variable flow locity [32] The dashed line shows the original operation with

ve-a constve-ant ve-acid flow velocity of 2.5 m/s ve-and increve-asing heve-atingsteam temperature to overcome the effects of fouling The solidline shows the suggested operation with constant maximumsteam temperature of 200◦C and variable flow velocity from

1 m/s to 2.5 m/s With the second option, the run time could beincreased from 150 hours to 275 hours, with only minor plantmodifications

Neural Networks

Despite increased attention during the past decades, lations recommended for heat exchanger fouling can only beapplied to a limited number of idealized deposition processes,while they lead to massive uncertainties and inaccuracies forindustrial fluids These drawbacks may be the result of:

corre-• Nonlinearity of the fouling process

• The character of the fouling process, which is unsteady-statewith potentially high fluctuation

heat transfer engineering vol 32 no 1 2011

Figure 9 Operational time before shut-down for cleaning of a sulfuric acid

evaporator, operating either with constant flow velocity (dotted line) or constant

steam temperature (solid line).

• The large number of variables and different mechanisms

• The lack of rigorous understanding of the underlying

mecha-nisms

• The inherent inadequacy of conventional regression methods

to correlate experimental data with an ill-distributed

parame-ter variation

The use of artificial neural networks is a pragmatic alternative

to address many industrial fouling problems with significantly

better accuracy than conventional parametric regression models

This can be done by using neural networks as an interpolation

tool within a range of experimental results (black-box approach)

[35], or as a hybrid approach where the neural network is used in

combination with prior knowledge (PK) of the process [36, 37],

as shown in Figure 10 This “prior knowledge” may, for

exam-ple, be the experience that the fouling rate generally increases

with surface temperature and/or decreases with flow velocity

The results of the second method are found to be more reliable

than those provided by the first method

The following promising results have been found in the very

limited number of investigations that have been published to

Figure 10 Hybrid neural network (PK = prior knowledge).

5 6 7 8 9 10 11 12

5 6 7 8 9 10 11 12

Figure 11 Measured versus fitted asymptotic fouling resistances, using a mechanistic model (left, mean average error 38%) and a neural network (right, mean average error 15%).

date:

• Experimental data could be correlated significantly better with

a suitable neural network than with the models recommended

by the original authors This is clearly demonstrated inFigure 11 for cooling water fouling data

• Satisfactory capability of the network for those areas (i.e.,induction period and high surface temperature) where notenough information about the underlying phenomena and/orinsufficient experimental data are available

• The reliability of the resulting networks was confirmed whenthey were applied to those data that had not been used before

• Once converged, the resulting network is a simple and smallprogram that even inexperienced users can apply or that can

be embedded into any heat exchanger design software.Despite these promising results, several questions still remainunanswered, which will have to be addressed if such techniquesare to be pursued for industrial applications:

• Validation for process fluids where the number of input ables is large, and with poorer understanding of the basicphenomena which govern the fouling process A typical ex-ample for this could be crude oil fouling

vari-• Application to cases where the dominant mechanisms changewith operating conditions and/or time One such example iscrystallization fouling, which is diffusion-controlled at verylow velocities and reaction-controlled at higher velocities

• The predictability of the network may severely deteriorate ifdata bases are ill-distributed and much weight of the data isconcentrated only in specific domains

• Poor extrapolation of the resulting network beyond the range

of learning data

• Inclusion of discrete variables such as heat exchanger tries into neural network modeling

geome-CFD Modeling

Fouling in industrial heat exchangers is strongly dependent

on local concentrations, temperatures, and shear rates This isexemplified in Figure 12, which shows the inlet zone of a gasheat transfer engineering vol 32 no 1 2011

8 H M ¨ULLER-STEINHAGEN

Figure 12 Negative effect of excessive inlet baffle spacing on deposit formation.

cooler with cooling water flowing on the shell side Very severe

deposit formation was found in the area between the last

baf-fle and the tube sheet; further away, fouling was significantly

less Looking at the pictures on the left side of Figure 12, one

recognizes the large spacing between tube sheet and first

baf-fle, as compared to the subsequent baffle–baffle spacing The

large gap leads to a significant reduction in flow velocity and to

significant flow maldistribution, both reducing local shear rates

and increasing local wall temperatures, even to the extent that

undesirable local nucleate boiling may have occurred, which

significantly increases the deposition rate [38] It is obvious

that the relatively simple analytical models developed for heat

exchanger design and fouling do not provide the required

infor-mation about local conditions However, numerical simulation

of flow and temperature distribution using commercial

com-putational fluid dynamics (CFD) software has now reached a

quality where it is possible to identify critical areas in industrial

heat exchangers in terms of hot spots or low velocity zones

De-tailed modeling of shell-side flow of large shell-and-tube heat

exchangers has been performed, including leakage streams

be-tween baffles, tubes, and shell [39] This is an area of work with

tremendous potential, not only for shell-and-tube heat

exchang-ers, but also for compact heat exchanger types [40]

First attempts have been undertaken to model the local growth

of deposits in addition to the local temperatures and shear rates

[41] The inclusion of additional mass transfer mechanisms and

reaction kinetics increases the computational effort enormously,but this will be resolved with the advent of increasingly powerfulmicroprocessors More importantly, such modeling approachesdepend on the quality of models for the local deposit formation,which are still under investigation

Heat Transfer Surface–Deposit Interaction

Numerous methods have been developed to remove forming constituents from heat exchanging fluids, to increasetheir solubility in these fluids, or to clean heat transfer surfacesonce they have fouled While the first are highly specific to thecomposition/chemistry of the fluids, the last of these only dealswith a problem after it has occurred From a technical point ofview, it would be much more desirable if heat transfer surfacescould be developed on which deposits do not stick at all Ingeneral, maximum adhesion occurs in interacting systems thatundergo a maximum decrease in surface energy, and poorestfouling adhesion should occur on materials that have low sur-face energies Surface coatings with organic polymers such aspolytetrafluoroethylene (PTFE) and Saekaphen have a very lowsurface energy, but they are mainly used to avoid corrosion asthe coatings themselves provide a significant additional resis-tance to heat transfer While the durability of the coatings in-creases with thickness, this has the inverse effect on heat transfer.heat transfer engineering vol 32 no 1 2011

deposit-H M ¨ULLER-STEINHAGEN 9Therefore, the coating thickness should be kept as thin as possi-

ble These conditions can be met with modern surface-coating

techniques such as ion beam implantation, magnetron

sputter-ing, and autocatalytic Ni–P–PTFE coatings

However, results obtained with a wide range of surface

coat-ings have been contradictory [42], indicating increased or

de-creased deposit formation on surfaces with low surface energy,

as compared with standard stainless steel Hence, there is a lack

of understanding of the principal interacting forces between

depositing material and metallic substrate Since the effect of

gravitational forces on deposition is usually negligible, these

forces consist of a Lifshitz–van der Waals (LW) interaction

component, electrostatic double-layer component (EL), Lewis

acid–base component (AB), and Brownian motion component

(Br) Equations to predict these interactions energies may be

found in [43] The total interaction energy
ETOTbetween a

deposit and a metal surface can be written as the sum of the

respective interaction terms:

ETOT=
ELW+
EEL+
EAB+
EBr (10)

It has been suggested, e.g., by Visser [44] that the balance

between all possible interactions between a deposit and a metal

surface determines whether a system will foul or not; i.e.,

adhe-sion/fouling will take place when
ETOTis negative

However, experimental evidence has shown that under

cer-tain conditions some systems may foul, even though the total

in-teraction energy
E 132 TOTbetween deposit (1) and metal surface

(2) in fluid (3) is positive—for example, if the initial
E 132 TOT

is positive (i.e., repulsive), but the substantial cohesive energy

E 131 TOTbetween the foulant particles leads to coagulation into

larger particles It is also not necessarily correct that the system

will foul if the total interaction energy
E 132 TOTis negative For

example, if the cohesive energy
E 131 TOTexactly equals the

ad-sorption energy
E 132 TOT, the energy characteristics of the heat

transfer surface will be the same as that of the foulant particles

This means that the colloidal particles in the wall-near boundary

layer may not attach to the surface or coagulate to each other,

but remain suspended in the solution in some sort of dynamic

equilibrium Therefore, the cohesive energy
E 131 TOTwill have

to be taken into account in the investigation of fouling behavior,

and particularly during the fouling induction period Based on

these findings, the following criterion to determine whether a

system will foul or not has been suggested in [45]:

If the Lifshitz–van der Waals forces are dominant, the surface

free energyγs,minat which fouling is minimal can be calculated

= 28 mN/m should have minimum fouling This is confirmed

by comparison with the experimental data by F¨orster et al [46]shown in Figure 13 The location of the fouling minimum co-incides with the experimental findings for the DLC-F sputteredsurface, for which also a surface free energy of 28 mN/m wasmeasured

Similar agreement between predicted minimum fouling faces and measurements has also been found for deposition ofmilk and microbes While the findings just described are promis-ing, they are nevertheless only a first step forward There isexperimental evidence that other effects, such as surface rough-ness, aging, and temperature, will also have significant effects

sur-on depositisur-on rate and asymptotic fouling resistance

Molecular Modeling

While the modeling of surface–deposit interaction may vide some information about the sticking propensity of variousdeposits on various surfaces, it still depends on the measurement

pro-of lumped parameters taking into account several molecular fects happening on the interface between surface and deposit.The weakness of this approach is evidenced by the poor correla-tion of surface energy and fouling rate or fouling delay time, asreported in [42] Here it was found that stainless-steel surfacesimplanted with hydrogen ions suffered considerably more fromfouling than the original steel surfaces, which in turn fouledsignificantly faster than stainless-steel surfaces implanted withfluorine ions In both cases, the surface energies of the im-planted surfaces as well as their polar components are almostidentical This phenomenon has been analyzed by Rizzo et al.[47], who found that the induction period of the nucleation pro-cess of CaSO4 crystallization fouling could not be correlatedwith results from surface energy measurements Instead, a lin-ear relation between the slope of the ln(induction period) versus

ef-ln–2(supersaturation ratio) plots and the electronegativity of theimplanted ions was observed, as shown in Figure 14

This empirical result sheds some light on the tory results reported in [42]; it nevertheless does not allowheat transfer engineering vol 32 no 1 2011

contradic-10 H M ¨ULLER-STEINHAGEN

Figure 14 Slope of nucleation curves versus electronegativity E ea for

stainless-steel surfaces implanted with fluorine, oxygen, hydrogen, and neon ions [47].

extrapolation to other surfaces and fouling fluids Therefore,

molecular modeling has been applied by Puhakka and

co-workers [48–50] in order to obtain explanations for interaction

mechanisms (chemical or physical nature of bonding) between

heat transfer surfaces and deposits In particular, there has been

investigation of whether there is any physicochemical

explana-tion at molecular level for the effects of surface material (e.g.,

stainless steel), surface oxidation, or surface coating (such as

SiOx, TiCN, DLC) on inorganic fouling For this, the total

elec-tronic energy and the elecelec-tronic energy density distribution were

solved to define the energetically stable structures for chemical

compounds and reaction intermediates

Investigations by Puhakka et al [48–50] indicated that

molec-ular modeling is capable of distinguishing different fouling

mechanisms on heat transfer surfaces and to estimate the

sig-nificance of the chemical effects of the process fluid on the

uppermost layer structure of the heat transfer surface, which is

responsible for the initial period of fouling Water can adsorb

onto solid surfaces as a molecule, or it can dissociate forming

partially or fully hydroxylated surfaces The existence of

hy-droxyl groups on the surfaces has an effect on the initial stage

of deposition formation When the surface hydroxyl groups

exist, fouling can take place via condensation reactions with

species containing hydroxyl groups On surfaces without

hy-droxyl groups, fouling takes place preferably via adsorption of

ions Following the modeling of water adsorption, the

subse-quent adsorption of calcium (Ca2+) and carbonate (CO3 −) ions

onto surfaces and the formation mechanism of CaCO3deposits

were determined Fouling was found to happen via hydrogen

carbonate intermediates, and the final deposit structure varied

for the different surface materials As an example, the formation

of deposits from pure Ti(OH)4and Ti(OH)4/Si(OH)4solutions

on TiO2(rutile) surfaces has been simulated, as shown in Figure

15 [49]

Unquestionably, molecular modeling is a powerful tool that

will make a significant contribution to the improved

under-standing of deposit formation and fouling mitigation This may

include the adsorption of antifoulants on clean heat transfer

surfaces, and the effects of surface modifications and of trace

Figure 15 Predicted formation of titania and silica deposits on a rutile substrate [49].

additives to the fluids However, this fundamental approach tothe understanding of deposit formation is still in its infancy and

is associated with many assumptions and a significant tational effort It is, nevertheless, an excellent example for thepathway that fouling research has to follow in order to developfrom “art” to “science.”

compu-CONCLUSIONS

Fifty years after Kern’s pioneering work, fouling is still themajor problem in the design and operation of industrial heat ex-changers This may lead to the conclusion that fouling researchactivities to date have not been particularly successful—which

is not at all correct The increased awareness of fouling and theimproved qualitative understanding of the effects of flow ve-locity, surface temperature, and surface topography on foulingrates already have had a major impact on the way heat exchangerdesign is approached and on the way existing exchangers areoperated

Numerous chemical additives have been developed that, inmany cases, can reduce the deposition rates of selected foulingproblems considerably However, these chemicals add to theplant operating costs, and their application may be restricted

by environmental legislation or by product specifications Thestrategic long-term goal must therefore be to avoid fouling al-together by appropriate design of heat exchangers and selection

of suitable plant operating parameters

Several designs of self-cleaning heat exchangers have beenintroduced into the market with considerable success, e.g., asponge ball system for power plant condensers, wire brushsystems for medium-size cooling-water applications, and thefluidized-bed heat exchanger for severely fouling process liq-uids The application of these concepts may, with appropriatemodifications, be extended to other fouling problems and oper-ating conditions

In the near to medium term, tangible progress in the gation of heat exchanger fouling can only be achieved by closecooperation between industry and research institutions, becauseimproved understanding of the process of deposit formationwill always be a prerequisite However, this progress will comewith a substantial price tag It requires considerable initialheat transfer engineering vol 32 no 1 2011

miti-H M ¨ULLER-STEINHAGEN 11investment for appropriately sized and well-instrumented

equipment, as well as a longer term funding strategy, which

extends beyond that of typical doctoral programs Companies

need to assess the true costs caused by their fouling problems

and initiate research projects for better design of the next

generation of heat exchangers or for improved plant operation

Rather than spending time and efforts on uncoordinated

research and development, a number of relatively generic

high-priority fouling problems (e.g., crude-oil fouling,

cooling-water fouling, milk fouling, etc.) may be identified, which

will then be investigated by (virtual?) research centers with

industrial input Startup funds should be provided by industry

with matching contributions from governmental programs

There must also be a willingness from all involved partners

to share know-how and benefits to a significantly larger extent

than is common practice today Encouraging examples for

such an approach are several projects funded by the European

Commission, the HTRI Crude Oil Fouling Task Force, and the

ESDU Best Practice Data Items on crude-oil fouling, seawater

fouling, and cooling-water fouling, which have been produced

with substantial contributions from industrial working parties

These application-oriented attempts must be accompanied

and extended by increased fundamental research related to the

mechanisms of deposit formation and adhesion As has been

demonstrated in the preceding discussion, innovative scientific

and computational approaches have a significant potential The

interactive forces between deposits and surfaces are not at all

well understood, even though they are the key to understanding

the initiation of deposit adhesion The application of

fundamen-tal models such as the DLVO theory or molecular dynamics

modeling may already provide useful information about the

re-lationship between surface characteristics and deposition rates

for simple aqueous systems, but cannot yet deliver conclusive

recommendations for most industrial fouling problems

Ulti-mately, nanotechnology may allow the development of

nonfoul-ing surfaces, as amply demonstrated by nature with the leaves

of flowers or the scales of fish

Despite all efforts to reduce the formation of deposit on heat

transfer surfaces, we will never be able to avoid it altogether

and in all applications Cleaning of heat exchangers will still be

required, even though—hopefully—in less frequent intervals

There is still a significant potential to improve the efficiency of

existing cleaning processes and to develop new cleaning

con-cepts The mechanisms of cleaning are even less understood

than deposit formation itself, even though significant practical

experience is available

NOMENCLATURE

A heat transfer surface area, m2

b lumped parameter in Eq (5)

c concentration of depositing reacting material, kg/m3

E activation energy, J/mol

kR Reaction rate constant, m4/kg-s

Rf ∗ asymptotic fouling resistance, m2-K/W

Rwall thermal resistance of wall separating heat exchangingfluids, m2-K/W

α film heat transfer coefficient, W/m2-K

β mass transfer coefficient, m/s

EL electrical double layer

LW Lifshitz–van der WaalsTOT total

∗ at saturation

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A P Watkinson, Engineering Conferences tional, Kloster Irsee, Germany, pp 316–326, 2005,http://services.bepress.com/eci/heatexchanger2005/46.[48] Puhakka, E., Riihim¨aki, M., and Keiski, R L., MolecularModelling Approach on Fouling of the Plate Heat Ex-changer: Titanium Hydroxyls, Silanols, and Sulphates onTiO2 Surfaces, Heat Transfer Engineering, vol 28, pp.

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nium Carbide Surfaces, Heat Transfer Engineering, 2011

(in press)

Hans M ¨uller-Steinhagen is the Rector of the

Tech-nical University of Dresden, Germany Previously, he has been Director of the Institute of Technical Ther- modynamics of the German Aerospace Centre (DLR) and of the Institute of Thermodynamics and Thermal Engineering of the University of Stuttgart His re- search work covers a wide range of topics related to heat and mass transfer, multiphase flow, fuel cells, solar technologies and process thermodynamics He

is the author of more than 600 articles and has ceived numerous international awards, including the 2009 AIChE D.Q Award Professor M¨uller-Steinhagen is a fellow of the Royal Academy of Engineering, past-President of EUROTHERM, member of the Executive Boards of EUREC and ICHMT, of the Innovation Council of the State of Baden-W¨urttemberg, and associate editor of Heat Transfer Engineering He is also chairman of the Advisory Board of the Desertec Industrial Initiative.

re-heat transfer engineering vol 32 no 1 2011

Copyright
C Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457631003732805

Heat Transfer Enhancement of

Square-Pitch Shell-and-Tube Spray

Evaporator Using Interior Spray

Nozzles

TONG-BOU CHANG, JUN-CHENG LI, and CHIH-CHANG LIANG

Department of Mechanical Engineering, Southern Taiwan University, Tainan, Taiwan

This study proposes a new nozzle/heater arrangement for enhancing the heat transfer coefficient of a square-pitch

shell-and-tube spray evaporator In the proposed approach, the nozzle shell-and-tubes are positioned within the shell-and-tube bundle in such a way that the

surface of each heater tube is sprayed simultaneously by four cooling sprays As a result, the dry-out phenomenon on the lower

surface of the heater tubes is prevented The experimental results reveal that the shell-side heat transfer coefficient obtained

using the proposed spray technique is significantly higher than that achieved in a conventional flooded-type evaporator.

Moreover, it is shown that the heat transfer performance increases as the saturation temperature decreases and the spray

film flow rate increases.

INTRODUCTION

Spray evaporation systems, in which cooling liquid droplets

are sprayed directly onto the heated surface, are widely applied

in the winery and poultry industries Compared to conventional

flooded-type evaporators, spray evaporators improve the heat

transfer performance and reduce the chiller refrigerant inventory

by around 20–90%, depending on the system design

Spray cooling heat transfer was first examined

experimen-tally by Hodgson and Sutherland [1] in 1968 In their

experi-ments, the temperature of the heated surface was higher than

the Leidenfrost temperature, and thus film boiling conditions

were observed The findings of Hodgson and Sutherland [1]

prompted many other researchers to investigate the complex

mechanisms associated with spray heat transfer For example,

Choi and Yao [2] investigated the heat transfer mechanisms of

horizontal impacting sprays and found that film boiling heat

transfer is controlled primarily by the liquid mass flux Pais

et al [3] conducted a series of spray cooling tests and showed

that the impact of the refrigerant droplets caused a breakup of

This study was supported by the National Science Council of Taiwan (NSC

96–2221–E–218–034).

Address correspondence to Professor Tong-Bou Chang, Department of

Me-chanical Engineering, Southern Taiwan University, 1, Nan-Tai Street, YungKang

City, Tainan County, Taiwan E-mail: tbchang@mail.stut.edu.tw

the liquid film on the solid heated surface, and therefore allowedthe vapor bubbles to be more easily released

In a refrigeration cycle, an expansion process is required toreduce the refrigerant pressure to a level at which evaporationcan take place In practice, the resulting pressure drop can beused to drive a liquid spray However, even though spray evap-oration is known to have a high heat transfer performance, it isseldom used in compact heat exchangers with tube bundles sincethe conventional sprays (i.e., overhead sprays) used in such sys-tems generally fail to reach the lower tubes in the bundle (Figure1) Moeykens and Pate [4] performed overhead spray evapora-tion tests on a horizontal plain tube using R134-a as the coolant.The results showed that when the tube had a high surface heatflux, a dry-out phenomenon occurred on the lower surface, andthus the heat transfer performance of the spray evaporator modewas lower than that of the pool boiling mode In an attempt toresolve this problem, Moeykens and co-workers [5, 6] and Chyuand co-workers [7–9] investigated the effects of many differentspray parameters (e.g., the nozzle height, the nozzle orifice di-ameter, the spray mass flow rate, and the spray angle) on the heattransfer performance of overhead shell-and-tube spray evapora-tor systems with triangular-pitch or square-pitch tube bundles.The experimental results showed that the heat transfer perfor-mance obtained in the uppermost row of tubes was significantlyhigher than that obtained in any of the other rows within thebundle Ribatski and Jacobi [10] presented a comprehensive14

review of the experimental parameters affecting the heat

trans-fer performance of spray and falling-film evaporation in tube

bundles Chang and Chiou [11] performed overhead spray

cool-ing tests on a tube bundle and found that a dry-out phenomenon

occurred on the lower tubes In order to eliminate the dry-out

phenomenon in triangular-pitch tube bundles, Chang and

co-workers [12, 13] attached liquid collectors to the underside of

each tube in the bundle The collectors were designed in such a

way as to collect the liquid film flowing over the surface of the

tubes and to guide the overfill liquid such that it impacted a tube

located in the row below The experimental results showed that

the heat transfer performance of the enhanced spray evaporator

system was superior to that of a pool boiling system under both

low and high heat flux conditions

However, the liquid collectors proposed in [12] and [13]

are ineffective in square-pitch shell-and-tube spray evaporators

since the liquid film distribution differs from that in

triangular-pitch tube bundles In a recent study, Chang et al [14] showed

that the dry-out problem can be prevented in compact

triangular-pitch shell-and-tube evaporators by introducing liquid sprays

within the bundle interior In the present study, the same concept

is applied to resolve the dry-out problem in square-pitch

shell-and-tube spray evaporators The experimental results show that

the deployment of nozzle sprays within the evaporator system

results in a significantly improved heat transfer performance

compared to that obtained in a conventional pool boiling system

S

R

P R T

T

1 2

Relief valve

RTD Flow meter Side glass

Condenser

heater

Test section

Storage tank

Chiller

Strainer Pump

Figure 2 Schematic illustration of experimental system.

a condenser, and the resulting liquid then flowed past an RTDtemperature meter and returned to the storage tank Meanwhile,the non-evaporated liquid refrigerant exited the test section via

an outlet pipe fitted to its lower surface and was returned to thestorage tank via a flow meter and a bypass valve The exper-imental tests were conducted using R141-b refrigerant as theworking fluid R141-b is an HCFC refrigerant and has a boilingtemperature of just 32◦C under atmospheric pressure As a re-sult, the test system could be maintained at a low pressure andwas therefore safer from an experimental point of view.Figure 3 presents a schematic illustration of the heater andnozzle tube arrangement in the square-pitch tube bundle consid-ered in the present study As shown, each nozzle tube is located

in the center of an imaginary square formed by four ing heater tubes The nozzle tubes are designed to spray foursprays at angles of 45◦to the horizontal and vertical axes of thetube Thus, as shown in Figure 4, each heater tube in the bundle

neighbor-is sprayed simultaneously by four neighboring nozzles As aheat transfer engineering vol 32 no 1 2011

16 T.-B CHANG ET AL.

Figure 3 Schematic illustration of proposed heater and nozzle tube

arrange-ment in square-pitch tube bundle.

result, the heater surfaces receive sufficient refrigerant liquid to

prevent the dry-out phenomenon The four holes in each nozzle

have the form of full-cone circular hydraulic nozzles and have

an orifice diameter of 1 mm and a cone angle of 90◦ Note that

due to budget constraints, the tube bundle installed within the

test section comprised just four heater tubes and nine nozzle

tubes (Figure 5)

The test section had the form of a cylindrical stainless-steel

vessel with a length of 40 cm, an internal diameter of 30 cm, and

a thickness of 0.5 cm The heat source within the test section

was provided by four resistor-type copper heater tubes, fastened

at one end of the vertical side plates of the test section Each

heater tube had a diameter of 19.05 mm (3/4 in) and was capable

of generating a maximum heat flux of 220 kW/m2 In order to

prevent axial conductivity heat losses, the outer copper surface

of each tube was fabricated with a thickness of just 0.5 mm

and the unheated section was filled with silica Four

thermocou-ples were embedded in the surface of each heater tube through

within drilled ports, filled with lead–tin solder Importantly, the

port diameter was kept to a minimum in order to ensure that

the temperature of the solder bead closely matched that of the

wall The thermocouple wires were then run through the space

between the outer surface of the cartridge heater and the

in-Figure 4 Schematic illustration of proposed internal spray method.

Figure 5 Schematic illustration of tube bundle used in present experimental tests.

ner surface of the copper tube (see inset in Figure 5) In order

to maintain the cartridge heater in a centerline position withinthe tube, the space between the outside of the cartridge heaterand the inside of the copper tube was filled with a mixture ofmagnesium dioxide powder and highly conductive grease.During the experiments, the thermocouple signals, the RTDoutput signal, the spray film flow rate, and the surface heatflux were monitored continuously by the data acquisition sys-tem Having waited for approximately 30 min for the system

to reach steady-state conditions (as indicated by a variation inthe saturation temperature of less than 0.1◦C/min), each datapoint of interest was obtained by averaging a minimum of 20data-acquisition scans Note that in the tests, the input powerwas immediately turned off if any of the heater temperaturemeasurements suddenly increased (indicating the occurrence ofdry-out) in order to protect the measurement instrumentation

EXPERIMENTAL DATA REDUCTION

In the tests, the film flow rate of the refrigerant was varied

in the range 0.09–0.12 kg/ms, while the heat flux was variedfrom 104W/m2to more than 105W/m2 Finally, the saturationtemperature was set to 20◦C, 24◦C, or 28◦C, respectively

The mean shell-side heat transfer coefficient, h, was

deter-mined in accordance with Newton’s cooling law, i.e.,

T.-B CHANG ET AL 17arithmetic mean of the 16 thermocouple readings, i.e.,

tioned in the four locations shown in Figure 5, while subscripts

1, 2, 3, and 4 denote the four thermocouple positions on the top,

sides, and lower surface of each heater tube, respectively

To ensure the accuracy of the measured data, each

measur-ing device was calibrated prior to use Followmeasur-ing calibration, the

accuracies of the temperature sensors (RTD and TC), power

me-ter, and flow meter were found to be±0.2◦C,±0.1%, and ±0.1

kg/ms, respectively Based upon these calibration results, and

applying the propagation-of-error method presented in [15], the

experimental uncertainty in the average shell-side heat transfer

coefficient was found to be of the order of±6%

RESULTS AND DISCUSSION

Figure 6 illustrates the variation of the overall heat transfer

coefficient (HTC) of the tube bundle with the surface heat flux

as a function of the saturation temperature (i.e., 20◦C, 24◦C,

and 28◦C) and a constant spray film flow rate of ˙m= 0.06

kg/ms The pool boiling data obtained by immersing all four

heater tubes in the refrigerant and specifying a saturation

tem-perature of 20◦C are also plotted for comparison purposes The

results confirm that the proposed interior spray cooling method

achieves a better heat transfer performance than the pool boiling

mode at a saturation temperature of 20◦C It is also observed

that for a constant value of the wall heat flux, the HTC decreases

with an increasing saturation temperature From inspection, the

Figure 6 Variation of heat transfer performance with surface heat flux as a

function of saturation temperature for constant spray film flow rate of ˙ m= 0.06

kg/ms Note that pool boiling data are also presented for comparison purposes.

as the saturation temperature reduces and therefore results in abetter heat transfer performance

Figure 7 illustrates the variation of the mean shell-side HTCwith the wall heat flux for the same saturation temperatures

as those considered in Figure 6, but a higher spray film flowrate of ˙m= 0.12 kg/ms As in Figure 6, it is observed that

the mean shell-side HTC reduces with an increasing saturationtemperature However, comparing the two figures, it is evidentthat for a given saturation temperature and wall heat flux, theshell-side HTC increases with an increasing spray film flow rate.This result can be attributed to the fact that a greater film flow rateincreases the force with which the droplets impact the liquid film

on the heated surface and therefore prevents the liquid film fromdeveloping a thermal insulation layer In addition, the greaterfilm flow rate improves the distribution of the liquid film on theheater tubes, and therefore reduces the size of the dry regions.Figure 8 illustrates the effect of the spray film flow rate onthe mean shell-side HTC for a constant saturation temperature

of 20◦C It is observed that for all values of the surface heatflux, the HTC reduces with a reducing film flow rate Frominspection, it is found that for low values of the heat flux (i.e.,

q= 2×104W/m2), the HTC obtained at a spray film flow rate

of 0.12 kg/ms is 12% higher than that obtained at a film flow rate

of 0.09 kg/ms, which in turn is 29% higher than that obtained

at a film flow rate of 0.06 kg/ms However, for higher values ofthe heat flux, i.e., q> 105W/m2, the HTC obtained for a sprayheat transfer engineering vol 32 no 1 2011

Tsat=20 oC

Figure 8 Variation of heat transfer performance with surface heat flux as a

function of spray film flow rate for constant saturation temperature of T sat =

20 ◦C.

film flow rate of 0.12 kg/ms is 35% higher than that obtained at

a film flow rate of 0.09 kg/ms, which in turn is 48% higher than

that obtained at 0.06 kg/ms In other words, the efficacy of a

higher film flow rate in enhancing the heat transfer performance

increases with an increasing surface heat flux Ribatski and

Thome [16] conducted an experimental investigation into the

onset of the local dry-out phenomenon in evaporating falling

films on horizontal plain tubes, and showed that the onset of

dry-out was determined principally by the heat flux and the film

flow rate They also reported that for a constant heat flux, an

increasing film flow rate was found to induce an increase in the

heat transfer coefficient

Figure 9 shows the effect of the spray film flow rate on

the mean shell-side HTC for a constant saturation temperature

of 28◦C As in Figure 8, it can be seen that the efficacy of

a higher spray film flow rate in enhancing the heat transfer

performance increases with an increasing surface heat flux For

low values of the heat flux (i.e., q= 2 × 104W/m2), the HTC

obtained at a spray film flow rate of 0.12 kg/ms is 4% higher

than that obtained at 0.09 kg/ms, while that obtained at 0.09

kg/ms is 16% higher than that obtained at 0.06 kg/ms However,

for higher surface heat fluxes, i.e., q > 105 W/m2, the HTC

obtained at a spray film flow rate of 0.12 kg/ms is 28% higher

than that obtained at 0.09 kg/ms, which in turn is 41% higher

than that obtained at 0.06 kg/ms Significantly, these percentage

improvements are smaller than those observed in Figure 8 for

the lower saturation temperature of 20◦C Thus, it is inferred

that a better liquid distribution is attained at a lower saturation

en-in order to prevent the dry-out phenomenon The tal results have shown that the mean shell-side heat transfercoefficient (HTC) obtained using the proposed technique is sig-nificantly higher than that obtained in a conventional floodedtype evaporator over a wide range of surface heat fluxes andrefrigerant film flow rates In addition, it has been shown that

experimen-a better liquid distribution on the tube surfexperimen-ace reduces the dryregions at lower saturation temperature then the shell-side HTC

is correspondingly improved In addition, it has been suggestedthat a better liquid distribution is achieved on the tube surface atlower saturation temperatures, which reduces the size of the dryregion and therefore prompts a corresponding improvement inthe shell-side HTC Moreover, the results have shown that the ef-ficacy of a higher spray film flow rate in enhancing the heat trans-fer performance increases with an increasing surface heat flux

NOMENCLATURE

h heat transfer coefficient (W/m2-K)HTC heat transfer coefficient

•

m spray film flow rate (kg/ms)

q wall heat flux (W/m2)

T temperature (◦C)

Tsat saturation temperature (◦C)

Tw average wall temperature (◦C)heat transfer engineering vol 32 no 1 2011

T.-B CHANG ET AL 19

REFERENCES

[1] Hodgson, J W., and Sutherland, J E., Heat Transfer from a

Spray Cooled Isothermal Cylinder, Industrial &

Engineer-ing Chemistry, Fundamentals, vol 7, pp 567–571, 1968.

[2] Choi, K J., and Yao, S C., Mechanisms of Film

Boil-ing Heat Transfer of Normally ImpactBoil-ing Spray,

Interna-tional Journal of Heat and Mass Transfer, vol 30, no 2,

pp 311–318, 1987

[3] Pais, M R., Chow, L C., and Mahefkey, E T., Surface

Roughness and Its Effects on Heat Transfer Mechanism in

Spray Cooling, ASME Journal of Heat Transfer, vol 114,

pp 211–219, 1992

[4] Moeykens, S A., and Pate, M B., Spray Evaporation Heat

Transfer of R-134a on Plain Tubes, ASHRAE Transactions,

vol 100, pp 173–184, 1994

[5] Moeykens, S A., Newton, B J., and Pate, M B., Effects of

Surface Enhancement, Film-Feed Supply Rate, and

Bun-dle Geometry on Spray Evaporation Heat Transfer

Per-formance, ASHRAE Transactions, vol 101, pp 408–419,

1995

[6] Moeykens, S A., and Pate, M B., The Effects of Nozzle

Height and Orifice Size on Spray Evaporation Heat

Trans-fer Performance for a Low-Finned, Triangular-Pitch Tube

Bundle with R-134a, ASHRAE Transactions, vol 101,

pp 420–433, 1995

[7] Chyu, M C., Zeng, X., and Ayub, Z H., Nozzle-Sprayed

Flow Rate Distribution on a Horizontal Tube Bundle,

ASHRAE Transactions, vol 101, pp 443–453, 1995.

[8] Zeng, X., Chyu, M C., and Ayub, Z H., Performance

of Nozzle-Sprayed Ammonia Evaporator With

Square-Pitch Plain-Tube Bundle, ASHRAE Transactions, vol 103,

pp 68–81, 1997

[9] Zeng, X., Chyu, M C., and Ayub, Experimental on

Am-monia Spray Evaporator With Triangular-Pitch Plain-Tube

Bundle, Part 1: Tube Bundle Effect, International Journal

of Heat and Mass Transfer, vol 44, pp 2229–2310, 2001.

[10] Ribatski, G., and Jacobi, A M., Falling-Film Evaporation

on Horizontal Tubes—A Critical Review, International

Journal of Refrigeration, vol 28, no 5, pp 635–653, 2005.

[11] Chang, T B., and Chiou, J S., Spray Evaporation Heat

Transfer of R-141b on a Horizontal Tube Bundles,

In-ternational Journal of Heat and Mass Transfer, vol 42,

pp 1467–1478, 1999

[12] Chang, T B., and Chiou, J S., Heat Transfer Enhancement

in a Spray Evaporator, Journal of Enhanced Heat Transfer,

vol 12, no 1, pp 85–100, 2005

[13] Chang, T B., Effects of Nozzle Configurations on a

Shell-and-Tube Spray Evaporator With Liquid Catcher, Applied

Thermal Engineering, vol 26, no 8, pp 814–823, 2006.

[14] Chang, T B., Lu, C C., and Li, J C., Enhancing the HeatTransfer Performance of Triangular-Pitch Shell-and-Tube

Evaporators Using an Interior Spray Technique, Applied

Thermal Engineering, vol 29, pp 2527–2533, 2009.

[15] Holman, J P., Experimental Methods for Engineers, 6th

ed., McGraw-Hill, New York, pp 49–56, 1994

[16] Ribatski, G., and Thome, J R., Experimental Study on theOnset of Local Dryout in an Evaporating Falling Film on

Horizontal Plain Tube, Experimental Thermal and Fluid

Science, vol 31, issue 6, May 2007.

Tong-Bou Chang is a professor in the Department

of Mechanical Engineering, Southern Taiwan versity, Tainan, Taiwan He received his Ph.D de- gree at National Cheng Kung University, Taiwan,

Uni-in 1997 His research Uni-interests Uni-include heat transfer with phase change, energy-system optimization, heat and mass transfer in porous medium, enhancement of heat transfer, and high-performance heat exchangers.

He has co-authored more than 40 papers in archival journals and conference proceedings.He is currently working on two-phase heat transfer using nanofluids.

Jun-Cheng Li was a graduate student in the

Depart-ment of Mechanical Engineering, Southern Taiwan University, Taiwan His research interests include spray heat transfer, enhancement of heat transfer, and high-performance heat exchangers He is currently working at a heat transfer company as an engineer.

Chih-Chang Liang was a graduate student in the

Department of Mechanical Engineering, Southern Taiwan University, Taiwan His research interests in- clude spray heat transfer, enhancement of heat trans- fer, and high-performance heat exchangers He is cur- rently working at the Ministry of National Defense

as an engineer.

heat transfer engineering vol 32 no 1 2011

Copyright
C Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457631003732821

Transient Turbulent Flow and Heat

Transfer Phenomena in Plate-Fin

Type Cross-Flow Heat Exchanger

1Department of Mechanical Engineering, University of Atat¨urk, Erzurum, Turkey

2Department of Electrical-Electronics Engineering, University of Atat¨urk Erzurum, Turkey

3Department of Mechanical Engineering, University of Hitit, Corum, Turkey

4Department of Mechanical Engineering, Gazi University, Ankara, Turkey

In this article, a transient performance of a plate-fin cross-flow heat exchanger with convergent–divergent longitudinal vortex

generators is investigated The effect of flow geometry is taken into account to analyze the transient forced convection heat

transfer in a designed heat exchanger The time-dependent Nusselt number and dissipation energy criterion are experimentally

measured in 4- and 8-kW heater powers for various Reynolds numbers between 42,000 and 60,000 for the hot and cold fluids.

In order to present the quality of the heat exchanger, the general empirical equations of the time-dependent Nusselt number

and friction factor were derived as a function of the Reynolds number corresponding to fin geometry parameters Following

this, the transient behavior of the heat exchanger according to the change in the inlet and outlet temperatures of the hot and

cold fluids was analyzed The results showed that the variations of the time-dependent dissipation energy criterion increase

with the increase in the Reynolds number The appropriate correlations are proposed to predict the heat transfer and friction

characteristics of the transient performance for the presented configuration, which indicates the designed heat exchanger

has good heat conduction.

INTRODUCTION

Unsteady thermal processes are very important in modern

power and dynamic systems, heat exchangers and other

engi-neering applications Heat exchangers are generally designed to

meet certain performance requirements under steady operating

conditions There are several heat exchanger types for different

applications, according to their size, weight, shape, and flow

pattern Based on the flow pattern, one of the important types is

the plate-fin compact heat exchanger During recent years, the

transient behavior of plate-fin compact heat exchangers with

changes in the inlet temperature or flow rate of fluids has been

widely employed in engineering applications, especially in the

automotive industry, power plants, chemical processes and

cryo-genics, aerospace industries, combustion, air conditioning and

refrigerant apparatus, and air/gas heating and cooling systems

This study was supported by Atat¨urk University project BAP-1997/37.

Address correspondence to Dr Isak Kotcioglu, Department of Mechanical

Engineering, Faculty of Engineering, University of Atat¨urk 25240, Erzurum,

Turkey E-mail: ikotcioglu@atauni.edu.tr

The cross-flow heat exchanger with convergent–divergentlongitudinal vortex generators (CDLVG) can serve as an ef-fective tool to augment forced convection heat transfer Theformations of the vortices in these heat exchangers, which areproduced by the winglet elements, have a definite effect on thelocal average velocity and temperature field of the fluid The flowbetween the winglets, which have longitudinal velocity compo-nents, is important in the heat transfer characteristics, secondaryflow, and boundary-layer distribution of the heat exchangers.The winglets strongly disturb the boundary-layer structure due

to the influences of the interacting CDLVGs, which are located

at different intervals in the cross-flow channels In designingsuch heat exchangers, it is necessary to analyze the interactionsbetween the local heat transfer and flow distribution within theplate fins in cross-flow heat exchangers

There are number of studies in the literature that improvedthe heat exchanger design from various perspectives The en-ergy dissipation criterion (ie) was proposed by Sano and Usui

[1] on the basis of correlating the heat transfer coefficient (h).

As an approximate method for the finned-tube cross-flow heat

20

I KOTCIOGLU ET AL 21exchangers, Ataer [2] showed the effect of the transient behavior

of the heat exchangers on overall performance The approaches

and various techniques are developed for the prediction of

tran-sient behavior of cross-flow finned-type heat exchangers These

techniques provide the applicability for other heat exchanger

types For an extensive review of the transient response of heat

exchangers, Shah et al [3] presented a transient response

anal-ysis including problem formulation related to the inlet

tempera-tures and flow rates Spiga and Spiga [4] presented the analytical

solutions for the transient temperature distributions of the core

wall and unmixed gases with arbitrary initial and inlet by using

the threefold Laplace transform for cross-flow heat exchangers

The heat and mass transfer characteristics of heat exchangers

during frost formation process were analyzed numerically by

Seker et al [5] The design and thermal selection of heat

ex-changers have been extensively studied by Kakac and Liu [6]

Dynamic response of the discharge air temperature to changes

in the hot water flow rates has been studied for a commercial

finned serpentine tube water-to-air heat exchanger by Pearson

et al [7] Roetzel and Xuan [8] analyzed the dynamic behavior

of cross-flow heat exchangers extensively for different

arrange-ments such as the various combinations of temperature and flow

transients The transient temperature response of cross-flow heat

exchangers having finite wall capacitance with fluids unmixed

was investigated numerically by Mishra et al [9] They have

examined the heat exchanger according to flow rate of hot and

cold fluids Tandiroglu and Ayhan [10] investigated the effect

of the flow geometry parameters on the transient forced

convec-tion heat transfer for turbulent flow in a circular tube with baffle

inserts Numerical analysis on the flow field and heat transfer

by interaction between a pair of vortices in rectangular channel

flow was reported by Yang et al [11] The fundamental studies

of unsteady convective heat transfer processes in many

indus-trial applications and related calculations have been presented

by Kakac and Yener [12] The flow and heat structures in a

plate-fin heat exchanger were improved by Sohankar [13] Numerical

and experimental analyses were carried out by Leu et al [14] to

study the heat transfer and flow in the plate fin and tube heat

ex-changers with inclined block shape vortex generators mounted

behind the tubes Biswas et al [15] studied the flow structure

of an air stream over winglet pair-type vortex generators They

found that the winglet pair produced a main vortex, a corner

vortex, and an induced vortex, based on the flow structure in

regions between the winglets Ferrouillat et al [16] have

in-vestigated the potential of using delta and rectangular winglet

pairs as a mixer as well as a chemical reactor The relationships

between the effectiveness and number of transfer units of the

cross-flow heat exchanger were determined by Kotcioglu et al

[17] In another study by Kotcioglu and Caliskan [18], the

rela-tionships between the effectiveness and the number of transfer

units of the cross-flow heat exchanger were investigated

In this study, the unsteady convective heat transfer properties

of a compact heat exchanger with CDLVGs for the case of

time-dependent temperature changes were presented The effects of

the CDLVGs for various flow velocities on the cross-flow heat

exchanger were investigated experimentally The correlationsfor the heat transfer coefficients and pressure drop (
P) charac-

teristics were obtained as functions of the Reynolds (Re) numberand Prandtl (Pr) number

The arrangement of winglets can create an original geometryfor a diffuser–nozzle couple that promotes the turbulence levels

As a consequence, suitable correlations are also proposed topredict the heat transfer and friction characteristics, which is

a new type designed for the cross-flow heat exchangers Theconfiguration of the designed heat exchanger core was formedand tested for different hot flow inlet conditions

Further in this study, the dissipation energy criterion, thetime-dependent Nusselt number, pressure drop, and transientforced convection in the designed heat exchanger were eval-uated The transient performance of the system related to theeffect of flow geometry on transient forced convection heattransfer for turbulent flow in a cross-flow heat exchanger withCDLVG was determined

EXPERIMENTAL APPARATUS AND PROCEDURE

A schematic diagram of the experimental apparatus for thedesigned heat exchanger is shown in Figure 1 The apparatusbasically includes a cross-flow compact heat exchanger core, hy-drodynamic entrance section, heating section, cold air channelinlet and outlet, hot air channel inlet and outlet, hot and cold airblower, air filters, clacks, orifice meters, pressure measurement

Figure 1 Experimental setup: 1 and 2 are hot and cold air blower, 3 and 4 are clacks, 5 and 6 are orifice meters, 7, 8, 15, and 16 are U-manometers, 9 is the heat exchanger core, 10 and 11 are cold air channel inlet and outlet, 12 and

13 are hot air channel inlet and outlet, 14 is the heating section, 17 is the data acquisition card, 18 is the computer, and 19–26 are thermocouples.

heat transfer engineering vol 32 no 1 2011

22 I KOTCIOGLU ET AL.

Figure 2 Geometric features of the matrix with placement of fins: (a) whole

heat exchanger; (b) one of the finned plates.

units, and thermocouples The experiments are conducted

mainly in the test section of the apparatus, which is

manu-factured from stainless-steel plates (1.5 mm thick) As shown

in Figure 2, a and b, the heat exchanger is in a cube shape and

its dimensions of the duct are La= 0.2 m (length), Lb= 0.2 m

(height), and Lc = 0.2 m (width) In order to inhibit the heat

loss and obtain a uniform heat flux, the outer surface of the test

section is insulated with a layer of glass wool In order to obtain

a linear velocity distribution in the channels, wire sieves are

placed between the test section and the outlet of the heaters For

the flow and heat transfer tests, the surface temperatures, inlet

and outlet temperatures, and the pressure drop across the test

section were measured

The vortex generator system is configured schematically in

Figure 2b [18] The apparatus under investigation is based on

the transient analysis and not suitable for fluid visualization

Thus we only relied on the correlations regarding the system

This kind of vortex generator system was also discussed

previ-ously in various articles, where exact visualization was provided

[19–21]

The form of winglet permutation is shown on the plate of

cross-flow heat exchanger in Figure 2b For this particular design

of the heat exchanger, the angle of winglet in the flow direction

(inclination angle) for the hot fluid isβh= 30◦and for the cold

fluid isβc= 60◦ The trailing edges of the winglets are located

at a distance of x= 0.005 m from the inlet

As the CDLVGs act as plates in the flowing fluid, each new

edge starts a new boundary layer (which is very thin), and thus

the high heat transfer coefficients can be obtained While the hot

flow is passing from one direction of the channels, the cold flow

is passing from the other direction The flow rate of the hot air

flow was controlled by adjusting the clack valve and measured

by pressure probes with an accuracy of±0.3% of full scale

Ex-perimental results were obtained for different mass flow rates

and different heater powers In order to measure the pressure

losses the pressure taps are mounted across the orifice plates

located at the inlet and outlet ends of the test section Similarly,

the measurements of the cold air flow rates were performed via

flow meters with an accuracy of±0.22% of full scale In order

to determine the effectiveness of the heat exchanger, the

tem-peratures (T) of the fluid in the test section were measured by

mounting the thermocouples at different locations on the surface

of the test section Similarly, the velocity of fluid (u) in the test

section was measured continuously with the pressure taps peratures were measured with 0.25-mm-diameter Teflon coatedT-type copper-constantan thermocouples This procedure pro-vides the measurements being taken at four locations in the samecross-section The accuracy of the thermocouples is ±0.15%.All of the thermocouples and pressure sensors are fully cali-brated with a dry-box temperature calibrator with 0.01◦C preci-sion The flow properties of the heat exchanger were determined

Tem-at average bulk temperTem-ature The effect of thermal radiTem-ation forinternal flow is ignored during the experiments due to low tem-perature differences between the wall and fins All of the mea-surements were collected and processed by a personal computerthrough the data acquisition card and software

The experimental apparatus was operated in the blow-outmode In order to investigate the heat transfer behavior of thesystem under transient conditions the experiments were per-formed for forced convection turbulent flow in the cross-flowheat exchanger with winglets under various mass flow rates anddifferent heater powers In each run, the hot flow rate and temper-atures in the channel inlet and exit were measured We analyzedthe cross-flow heat exchanger by considering the variation ofthe thermal properties of hot flow and cold flow with tempera-ture for heat transfer The hot and cold flow outlet temperatures,which vary with time, were measured until a steady-state condi-tion was reached The pressure drops corresponding to the heattransfer enhancement due to the winglet-type CDLVGs arrange-ments in the square channels were obtained by performing themeasurements Experimental measurements of both heat trans-fer and pressure drop in the cross-flow heat exchanger for atransient heat transfer were presented by evaluating the friction

factor (f ).

DATA REDUCTION

In order to obtain accurate results, the data collection duringthe experiments was carefully monitored The detailed geomet-rical configuration of the cross-flow heat exchanger is given inFigure 2b, whereas the properties and the characteristics of thissetup is tabulated in Table 1 Considering Figure 2b, the total

number of channels (N) of the plate-fin heat exchanger with

winglet-type CDLVGs is given by

N = L − bc+ 2tw

bc+ bh+ 2tw

(1)

where bhand bcare the winglet-type fin height for each channel

of hot and cold fluids (bh= bc= 0.01 m), respectively, L is the channel dimension (L = La= Lc= Lb= 0.2 m), and twis theplate and fin thickness According to the definition given in Eq.(1) the number of channels is calculated as 9 for each of thehot and cold fluid flows separately, which indicates a total of 18

channels The frontal areas both in the hot ( Afr,h = LaLb) and

cold ( Afr,c = LcLb) fluid sides in the heat exchanger are given asheat transfer engineering vol 32 no 1 2011

I KOTCIOGLU ET AL 23

Table 1 Geometrical characteristics of the heat exchanger

Channel dimensions La× Lb× Lc 0.20 × 0.20 × 0.20 m

Length of each winglet (Figure

Distance interval of winglets

(Figure 2b)

Span of winglet (Figure 2b) e c + g

Thickness of plate-fin winglets

(Figure 2b)

The angle of winglet in the flow

direction of hot fluid

The angle of winglet in the flow

direction of cold fluid

0.04 m2 Similarly, the heat transfer volumes between the plates

on the hot fluid and cold fluid sides are given as Vp,h = N LaLbbh

and Vp,c = N LcLbbc, respectively These relations give the heat

transfer volume as 0.0034 m3for both of the fluid sides The

heat transfer areas for hot and cold fluids are given as Ah =

βcompVp,h and Ac= βcompVp,c, respectively, whereβcompis the

compact rate By taking the compact rate asβcomp= 302 m2/m3,

these relations give Ah= Ac= 1.0268 m2 The minimum

free-flow areas for hot and cold fluids calculated from the definition

of the hydraulic diameter are given as Ao,h = DhAh/(4Lb)

and Ao,c = DcAc/(4Lc) The channel hydraulic diameter is

given as Dc = D h = 4bhL

2(bh+ L), which has the same

value of 0.0163 m for the hot and the cold air sides By using

this hydraulic diameter value, the minimum free flow areas is

obtained as Ao,h= Ao,c= 0.021 m2 Note that these calculations

are performed by considering the plate and fin thickness (tw)

In order to determine the time-dependent fluid dissipation

energy criterion (ie), the experimental investigation of the

tran-sient turbulent flow in a cross-flow heat exchanger based on

the geometric properties is required The heat transfer

coeffi-cients (h) can be compared and correlated with the dissipation

energy criterion and the unit mass of the fluid At the different

turbulence levels, the contribution due to mean velocity to the

dissipation energy criterion is very small This is due to the fact

that the majority of the contribution is due to the fluctuating

ve-locity components relating to different length scales structures

The energy dissipation rate per unit mass of the fluid (ε), on

the other hand, is a time-averaged quantity and it is from the

fluctuations only

In this study, in order to investigate the time-dependent

Nus-selt number (Nu) and the dissipation energy criterion for a

cross-flow heat exchanger, the calculation methodology is developed

in terms of the fundamental correlations taken from the

litera-ture [1] In this heat exchanger, the investigation is also related

to the changes in the outlet temperatures for various mass flow

rates and different heater powers The heat transfer coefficients

are correlated by means of energy dissipation rate per unit mass

of fluid in a heat exchanger Then, a simple dissipation energycriterion is used to compare heat transfer coefficients at a con-stant value ofε Using Fanning’s friction factor, the value of ε

in fully developed turbulent flow is expressed by [10]

ε = (
P)u

2 f u3

where L is the channel length, u is the average velocity of the

fluid in the channel,ρ is the density of the fluid For conveniencethe pressure drop (
P) and the friction factor is related as
P

= 2f ρu2 Eq (2a), which is related to the Reynolds number, can

be written in dimensionless form as

εL4

whereν is the kinematic viscosity of the fluid and the term inthe left-hand side of Eq (2b) is dimensionless and representsthe flow conditions by means of energy dissipation criterion,which in turn corresponds to the Reynolds number Similarly,the term (v3/ε)1/4in Eq (2b) is defined as Kolmogorov length

scale (η)

The friction factor and heat transfer coefficient for

augmen-tation technique are represented by fa and ha, respectively Inaddition, for a smooth channel the friction factor and heat trans-

fer coefficient are represented by fs and hs, respectively Forthe same Reynolds number in the plate-fin cross-flow heat ex-changer with winglet-type CDLVGs, the ratios of the frictionfactors (f) and heat transfer coefficients (h) can be expressed

augmen-of a smooth channel atεais given for turbulent flow by [10]

ie=  f

0.27 h

(6)

heat transfer engineering vol 32 no 1 2011

24 I KOTCIOGLU ET AL.

Using the ratio of the dissipation energy criterion together

with friction factor and the Reynolds number, the Nusselt

num-ber correlation equation of heat transfer with arbitrary shape of

the cross-flow heat exchanger may be explained from Eq (2a)

for transient turbulent flow as

Nua= 0.22ie[2 f (Re)3]0.27(Pr)0.4 (7)

The Prandtl number in the preceding equation is given as

Pr = Cpµ
k, where Cpis the specific heat,µ is the dynamic

viscosity, and k is thermal conductivity of the fluid The Prandtl

number is an important parameter affecting the heat transfer of

plate fins inserted on plates in the channel Since air is used as

working fluid, its Prandtl number in the considered temperature

range remains almost constant Note that the time-dependent

variables are Re and Pr numbers throughout the derivation The

density and the viscosity of the fluid change with temperature

and the pressure for these nondimensional numbers

Experimental measurements of both heat transfer and

pres-sure drop in the cross-flow heat exchanger for a transient flow

condition are presented to describe the effects of the flow

condi-tions and geometry parameters Thus, the friction factor is given

where d P /dx is the pressure gradient and Dh is the hydraulic

diameter of the channel In cross-flow compact heat

exchang-ers the heat transfer results are correlated in terms of the

Reynolds number, flow conditions, and geometry parameters

The Reynolds number is defined in terms of the mass velocity

(G), the hydraulic diameter, and the dynamic viscosity as

Re=G D h

As shown schematically in Figure 2a, both surfaces have

a rectangular fin cross-section in the flow direction with

convergent–divergent longitudinal vortex generators Based on

the mass flow rate ( ˙m) of the air flow in channel the mass velocity

is given as

G= m˙

where Afis the flow area for the hot and cold air channels The

heat transfer coefficient (h) is calculated from the convective

heat transfer rate (Qconv) as

h= Qconv

A (Tw− Tm) (11)

where Twis the surface temperature of the heat exchanger core,

Tmis the average bulk temperature, and A is the total heat

trans-fer surface area For all calculations, the values of the physical properties of the hot and cold air are obtained at the

thermo-average bulk mean temperature, which is Tm = (Tin+ Tout)/2,

where Tin corresponds to inlet and Tout corresponds to let temperatures The Nusselt number for the test section incross-flow heat exchanger with winglet-type CDLVGs by heatconvection can be expressed in terms of heat transfer coefficient

out-(h), the hydraulic diameter (Dh), and thermal conductivity (k)

to the sum of the projected area and surface area contributionfrom the pin fin

The friction factors (f ) in terms of the winglet inclination

angle (β) variation of the correlation is given as [17]

f = C0(Re)−m(tanβ)n (13)

where C0is the friction coefficient for the square channel uration The empirical correlations of the convergent–divergentlongitudinal vortex generators and the proposed time-dependentfriction factor correlation model are obtained from Eq (13) Thevalues of the correlation coefficients C0, m and n belonging tothe friction factor are presented in Table 2 As the winglet incli-nation angle is increased, the strength of the longitudinal vortex

config-is intensified

In a previous study [17], the time averaged Nusselt numberfor a square channel with winglet type CDLVG was expressedas

Nu= a(Re)b(Pr)c(La/bh)d(w/g)e(tanβ)f (14)where Pr= 0.71, (La/bh) is the test section geometry ratio, (w/g)

is the plate length of winglet to distance interval of wingletsratio, and a, b, c, d, e, and f are the correlation coefficients Theproposed time-dependent Nusselt number correlation model inthe range of 35,000< Re < 60,000 in a CDLVG given in this

study is obtained from Eq (14)

Empirical correlations are obtained for the time averagedNusselt number as a function of steady-state condition Nusseltnumber and Reynolds number for all of the flow conditions The

Table 2 Parameters of the empirical relationships of the friction factor given in Eq (13)

heat transfer engineering vol 32 no 1 2011

I KOTCIOGLU ET AL 25

Table 3 Parameters for the empirical relationships of the time-dependent Nu number given in Eq (14)

values of the correlation coefficients a, b, c, d, e, and f belonging

to the Nusselt number are presented in Table 3 There are various

features that give an idea about the perfection of the design

In this study, all of the relations were derived for the Nusselt

number and friction factor In order to obtain information about

how the geometry of the system affects these two parameters

(Reynolds and Nusselt numbers), geometric features such as

channel width (La) and height (bh), the winglet inclination angle,

and the other geometrical parameters were considered in the

correlation models

EXPERIMENTAL UNCERTAINTIES AND NON LINEAR

REGRESSION ANALYSIS

Before starting the experimental investigation of the heat

ex-changer apparatus, the calibration of the measuring instruments

in steady-state fluid flow was completed In order to obtain

the highest accuracy and reliability on the experimental

mea-surements, the uncertainties associated with the measured and

calculated values of the parameters were determined The

un-certainties of experimental quantities were computed by using

the method presented by Kline and McClintock [22] The

uncer-tainty calculation method involves calculating derivatives of the

desired variable with respect to individual experimental

quan-tities and applying known uncertainties The magnitude of the

uncertainty for a given parameter such as the Reynolds number,

Nusselt number, friction factor, and mass flow rate

measure-ments were estimated with the preceding procedure The

uncer-tainties in the measured parameters are caused by the mass flow

rate, fluid temperature, dimensions of the apparatus, manometer

calibration coefficients, thermal fluid properties, and pressure

drop in the orifice plate

For all of the relations, it is essential to determine the

qual-ity of the correlations In this study, the correlations given in

Tables 2 and 3 were obtained via the OriginPro package

pro-gram [23] In this process, the data is fitted to a given function,

such as in Eq (13) and Eq (14) Because the fitting has a

non-linearity in its nature we provide initial parameters, such as

C0, m, and n in Eq (13) For simplicity, the initial parameters

were taken as 1 and guessed in terms of convergence for the

following iterations Further iterations of the parameters were

preceded in terms of minimizing the error (χ2) In addition, the

quality of the correlations was determined by finding the

cor-relation coefficient (R2), the reduced chi-square (χ2), and the

root-mean-square error analysis (RMSE) The chi-square and

root-mean-square error are given as, respectively [22],

where j is the number of constants, Nois the number of

observa-tions, Ypre, iis the predicted value, and Yexp, iis the experimentalvalue The difference in the settings and measurements of tem-perature, volume flow rate, and the pressure of air in the systemunder laboratory conditions may be considered as the causes ofthe errors in the nonlinear curve fitting for the proposed Nusseltnumber and friction factor correlation models According to thetest results, it is possible to describe the complex behavior of thepresent CDLVGs configuration for both heat transfer and fric-tional characteristics Thus, a multiple regression was carriedout to obtain the appropriate correlation form of friction factorand Nusselt number for the present CDLVGs configuration

RESULTS AND DISCUSSION

The temperature of the flow at the inlet or outlet for thehot and the cold fluids was measured together with the pres-sure drop and mass flow rates in the system The experimentalinvestigation was carried out to predict the dissipation energycriterion in CDLVGs cross-flow heat exchanger based on theenergy dissipation rate It was shown that the Nusselt numbervariation with time was affected appreciably by the variation

of the fluid viscosity with temperature, viscous dissipation, and

pressure drop (d p

d x) between the winglets, as well as the fluid

Prandtl number (Eq (7)) and thermal boundary conditions Themost effective parameters, which affect the flow formation andproviding viscous mixture via the boundary-layer regeneration,are the winglets’ geometry and design This is due to the fact that

in order to minimize the pressure gradient, the total dissipationrates affecting the flow formation must be minimized Whenthe fluid flows over the CDLVGs, the pressure difference acrossthe vortex generator causes flow separation and induces vorticesdownstream Compared to the plain fin geometry, the penalty ofadditional pressure drops of the proposed vortex generators isrelatively insensitive to change of Reynolds number At the end,because the viscosity of the fluid is a function of the temperature,heat transfer engineering vol 32 no 1 2011

26 I KOTCIOGLU ET AL.

the winglet geometry, fluid velocity, friction losses, pressure

drop, and the density and viscous effects of both of the fluids

(hot and cold) with the temperature are used as the parameters

in the calculations

Based on the results of this work, the variations of the Nusselt

number, pressure coefficient, outlet temperatures, and friction

factor with the Reynolds number and the incidence angles were

provided The relation between the velocity and thermal

bound-ary layers, due to secondbound-ary flows and winglet geometry, was

evaluated for all cases The hot air and cold air exit

tempera-tures with time caused by the step change were calculated until

a steady-state condition was reached While the mean

tempera-ture of the hot fluid and plates (wall) start to increase just after

the step change, there is a temperature drop on the winglet and

cold fluid temperature, possibly due to the thermal resistances

In general, mixing the main flow, reducing the flow boundary

layer, raising the turbulent intensity between winglets, and

cre-ating rotcre-ating and secondary flow are the main reasons for the

increase of the heat transfer Vortex generators generate

sec-ondary flow by swirl and destabilize the flow Due to pressure

difference between two sides of CDLVG leg (both surfaces of

the winglets or between the winglets), longitudinal vortex are

generated along two legs of vortex generator, which enhances

the heat transfer There are strong interactions between the

lon-gitudinal vortex and the boundary layer on the walls of the

channel and winglet

Parametric analysis for the designed system is performed for

βh andβc(which are 30◦ and 60◦, as shown in Figure 2b), for

the Reynolds number ranging from 35,000 to 60,000 and for

the two heater powers of 4 and 8 kW In this study, we also

performed experiments for Reynolds numbers different from

those mentioned earlier, which are not included in this article

However, the curves obtained for the different Reynolds number

range also exhibited the same variation as the ones presented in

this study, so we restricted the data

The experimental analysis was started with considering the

Nusselt number variation with time, obtained from Eq (7)

Figure 3 shows the variation of the time-dependent Nusselt

at the Reynolds number of 42,000 and 60,000 for the hot fluid

In order to present clear data in this figure the Nusselt numbervariation was plotted for only these two mentioned Reynoldsnumbers Only 50% of the data points and two Reynolds num-bers were indicated in the graphs so that one can recognizewhich symbol represents which data The complete data ac-tually include the Reynolds number values of 42,000, 48,000,52,000, 56,000, and 60,000, which show a similar trend for all.This procedure of omitting 50% of the data was applied for all

of the figures throughout the article Similarly, the variation ofthe Nusselt number in terms of time, obtained from Eq (7), wasplotted in Figure 4 for the cold fluid for the same heater pow-ers and Reynolds numbers given for the hot fluid in Figure 3

As shown in both Figures 3 and 4, the time-dependent Nusseltnumber decreases continuously with time up to a certain limit

It is clearly seen from these two figures that the Nusselt numberfor 8 kW heater power is higher than that of 4 kW for the sameReynolds number for both hot and cold fluids It is also noticedfrom the data that the time-dependent Nusselt number decreases

as the Reynolds number increases When comparing the graphs

in these two figures, it can be noticed that the thermal and flowcharacteristics are similar Thus, it is easy to evaluate the behav-ior of the Nusselt number when each graph is divided into three

regions of the time We describe the first region from t= 0 s to

t = 10 s, the second region from t = 10 s to t = 100 s, and the third region from t = 100 s to t = 1000 s In the first region,

the time-dependent Nusselt number starts from a certain valueand continues nearly with a constant value The nearly constantvalue of the time-dependent Nusselt number in the first regioncan be attributed to the particular Reynolds number, which isdependent on the heat capacity of the winglets of the designedheat exchanger Eventually, about 10 s after the start the Nusseltnumber starts to decrease However, the decrease in the Nusseltnumber in the second and third regions is higher compared tothat of the first region Finally, the system reaches a steady stateafter 1000 s

heat transfer engineering vol 32 no 1 2011

I KOTCIOGLU ET AL 27

As can be seen in Figure 3, for hot fluid at 4 and 8 kW heater

powers and same Reynolds numbers, as the Reynolds number

increases the value of the variation interval in Nusselt number

also increases However, the variation trend is different for the

same Reynolds numbers At 8 kW heater power compared to

4 kW, this trend shows a sharp decrease in the second region

and even more in the third region This behavior for the hot

fluid is also the same for all Reynolds numbers Similarly, as

shown in Figure 4 for the cold fluid at 4 and 8 kW heater

pow-ers and the same Reynolds numbpow-ers, as the Reynolds number

increases the interval of the Nusselt number variation also

in-creases However, although the variation trend is different for

the same Reynolds numbers, this trend at 4 and 8 kW heater

powers shows similar decrease from the second region and little

bit more in the third region compared to the second region This

behavior for the cold fluid is also the same for all Reynolds

numbers When comparing the graphs in Figures 3 and 4, for

the same heater powers and Reynolds numbers for the hot and

cold fluids, the decreasing trend in the Nusselt number is sharp

in the second and third regions for the hot fluid The maximum

variation is determined at 8 kW heater power and Re= 60,000

for the hot fluid

The Reynolds number is proportional with the flow rate;

as the Reynolds number increases, the heat transfer to/from the

fluid will be even more This means that more heat from the heat

exchanger will be absorbed For very low Reynolds numbers

the effect of Reynolds number as a function of time can be

ignored This can be proven by performing the experiments and

calculations The Prandtl number is also an important parameter

affecting the heat transfer of plate fins inserted on plates in the

channel

The particular geometrical design of the system requires

se-lection of the Reynolds number range Because the winglets

are not positioned in only one channel we do not work in a

low Reynolds number range In addition, the chosen range of

Reynolds number is due to placing many channels (N= 18) and

winglets (Nw= 64) within the volume of 0.2 m × 0.2 m × 0.2 m

As shown in Figure 2, a and b, by considering the total pressure

drop and rate of flow in this system the Reynolds number range,

which affects the regeneration of the boundary layer occurring

in the winglets surface, was chosen in a given range Similarly,

as shown in this figure, due to the flow requirement there are

secondary flows, too The chosen range of Reynolds number

requires overcoming the existing flow frictions that occur in the

main and secondary flow directions

The measured outlet temperature variations of the hot and

cold fluids with time are given graphically in Figure 5a for

both 4 and 8 kW heater powers for Re = 60,000 and ˙m =

0.225 kg/s Similarly, the measured outlet temperature variations

of the hot and cold fluids with time are given graphically in

Figure 5b for both 4 and 8 kW heater powers for Re= 42,000

and ˙m= 0.152 kg/s Considering both figures, for fluids, heater

powers, and the Reynolds numbers at the first 200-s time span,

the increase trend is rather sharp When considering the relation

of the Reynolds number with the fluid flow rate or the fluid mass

2030405060708090

2030405060708090

Figure 5 Variation of outlet flow temperatures with time for hot and cold fluids for (a) Re= 60,000 and ˙m = 0.225 kg/s and (b) Re = 42,000 and ˙m =

0.152 kg/s.

flow rate and the viscosity of the fluid (Eq (9)), the viscosity ofthe fluid increases as its temperature increases under the sameheater power effect Thus, as the Reynolds number increasesthe heater power effect on the cold fluid outlet temperature due

to temperature and viscosity effects is small, which was alsoobserved experimentally as shown in Figure 5

Comparing the two graphs given in Figure 5, a and b, dicates that the temperature value of hot or cold fluid reachessteady state earlier for 4 kW heater power Notice that while thevariation in the temperature for cold fluid is small, the variation

in-in the hot fluid is larger As also shown in-in Figure 5, a and b, thetime to reach steady state is reduced with increasing the massflow rate of the hot fluid, which indicates the enhancement inthe heat transfer in the apparatus As the Reynolds number in-creases, which corresponds to an increase in fluid bulk velocity,heat transfer also increases While the mean temperature of thehot fluid and the wall start to increase just after the step change,there is a temperature drop at the fin and cold fluid temperatureheat transfer engineering vol 32 no 1 2011

Figure 6 Variation of dissipation energy criterion with time for hot fluid.

due to the thermal resistances The outlet temperatures of the

hot and cold fluids begin to increase after the average flash time

of 8 s and reach nearly steady-state temperatures Especially

for the hot fluid, as the Reynolds number and the heater power

increase, the tendency to reach stationary state in between 10

and 1000 s becomes rapid

The dissipation energy criterion is a time-averaged quantity

and it is from the fluctuations related to the Reynolds number

For this reason, it is important to determine the relationship

between time-dependent dissipation energy criterion and time

in a turbulent flow plate-fin cross-flow heat exchanger from the

point of flow and heat transfer phenomenon

The time-dependent dissipation energy criterion (ie) as a

function of time for both hot and cold fluids at different Reynolds

numbers and heater powers is plotted in Figures 6 and 7,

re-spectively The trend of these graphs is nearly the same as

that of Nusselt number variations presented in Figures 3 and

4 for the hot and cold fluids The dissipation energy

crite-rion decreases continuously with time up to a certain limiting

value In addition, the dissipation energy criterion is higher

for the higher Reynolds number, indicating that the higher

time-dependent dissipation energy criterion values can be

ob-tained when the Reynolds number increases Similarly,

sepa-rating the plot into three regions, especially from the

begin-ning of the second region to the middle of the third region, the

time-dependent dissipation energy criterion decays sharply with

time

Taking a closer look at the data shown in Figure 6, for the

hot fluid at 4 and 8 kW heater powers and same Reynolds

num-bers, as the Reynolds number increases, the variation interval of

the time-dependent dissipation energy criterion also increases

This behavior at the different intervals of the previously given

Reynolds number is the same for the hot fluid Similarly, as

shown in Figure 7, for the cold fluid at 4 and 8 kW heater

pow-ers and the same Reynolds numbpow-ers, as the Reynolds number

increases the variation interval of the time-dependent

dissipa-tion energy criterion also increases Unlike the hot fluid, there is

11.21.41.61.822.22.42.6

Figure 7 Variation of dissipation energy criterion with time for cold fluid.

no sharp decrease in the variation trend in the same interval ofthe Reynolds numbers There is a mild decrease starting fromthe second region and decreasing a little more in the third region.This behavior at the different intervals of the previously givenReynolds number is the same for the cold fluid When compar-ing hot and cold fluids in Figures 6 and 7, at the same heaterpowers and Reynolds numbers, for the hot fluid in the secondand third regions the decrease tendency with time is sharp Forthe hot fluid, the maximum variation is determined for the 8 kWheater power and Re= 60,000

Considering the time-dependent dissipation energy criterion

in the heat exchanger (Figures 6 and 7) for the same flow ditions, Reynolds number, and heater powers, the hot fluid hashigher value than that of the cold fluid The reason for this be-havior is the fact that the fluids having high temperatures havehigher heat transfer coefficients and lower friction factors Inother words, this difference between dissipation energy crite-rion values of hot and cold fluids is attributed to the differentturbulence levels in the heat exchanger where the dissipationenergy criterion being mainly due to the fluctuating velocitycomponents

con-The measured pressure drops (
P) for different average

ve-locities as a function of flow inlet velocity are plotted in Figure

8 for two different heater powers of 4 and 8 kW for both hotand cold fluids As can be seen from this figure, the increase inthe air velocity provides also an increase in the penalty of thepressure drop for the proposed vortex generator For example, at

u = 5.25 m/s, the
P of hot fluid at 4 kW heater power is 15%

larger than that of 8 kW heater power In addition, for the samevelocity, the measured pressure drop of cold fluid at 4 kW heaterpower is 25% larger than that for 8 kW heater power These val-

ues for the minimum velocity of u= 3.1 m/s for the hot and coldfluids are 28% and 25%, respectively As obtained from Eq (8),these numbers indicate that as the fluid velocity increases, thepressure drop difference for the same heater powers betweenhot and cold fluids also increases The fitted experimental datagiven in Figure 8 indicate that the pressure drop as a func-tion of velocity exhibits quadratic polynomial However, for theheat transfer engineering vol 32 no 1 2011

Figure 8 Variation of pressure drop with velocity for different heater powers.

reduced parameters the best curve fit is obtained by power,

which is indicated in the figure

As shown in Figure 8, the penalty on pressure drops of

the proposed winglet-type CDLVGs geometry is relatively

insensitive to change of fluid velocity By examination of the

pressure drops of the winglet-type CDLVGs at the different

heater powers at the same fluid velocity, it is interesting to know

that the corresponding pressure drop of cold fluid at the same

heater powers is lower than that of the hot fluid This is

be-cause the density of the fluid increases with the pressure and

temperatures in the fluids where the air is used

The time-averaged Nusselt number variations with the

Reynolds number are plotted in Figure 9 for the hot and cold

fluid flows at two different heater powers It can be seen that the

Nusselt number increases logarithmically with increasing the

Reynolds number As expected from empirical relation given in

Eq (14), the Nusselt number increases for hot and cold fluid as

the heater power increases The discrepancy between the results

of hot and cold fluid is due to the difference between densities

of the fluids For instance, at Re= 60,000, the obtained Nusselt

number at 8 kW heater power for the hot air flow is 2% larger

than that obtained for 4 kW heater power and for 8 kW heater

power the Nusselt number is 3% larger than that of obtained for

4 kW cold air for the same Reynolds number These values for

the Reynolds number of 35,000 for the hot and cold fluids are

9.5% and 15%, respectively As obtained from Eq (14), these

numbers indicate that as the Reynolds number increases the

Nusselt number difference for the same heater powers between

hot and cold fluids decreases

The friction factor and mass flow velocity are the main two

potential reasons for the pressure drop Friction factor at the

cold fluid side gives higher pressure drop than hot air side

for the same heater power The variation of the friction

fac-tor with the Reynolds number for various heater powers in

the hot and cold fluid are plotted in Figure 10 It is observed

that friction factor decreases with the increase in the Reynolds

number

5060708090100110

Cold Air and 4 kWCold Air and 8 kWHot Air and 4 kWHot Air and 8 kW

Figure 9 Variation of time averaged Nusselt number with Reynolds number.

In order to obtain an idea of how accurate the measurementsare or how far the reported values are from the true values, theerror bars are indicated in Figure 10 The error bars indicate theamount of standard deviation of the uncertainty The uncertain-ties in the measured parameters are caused by the mass flowrate, fluid temperature, dimensions of the apparatus, manometercalibration coefficients, thermal fluid properties, and pressuredrop in the orifice plate The estimation is performed in terms

of standard deviation from the mean value The experimentalresults for friction factor for the Reynolds numbers up to 60,000are correlated and the highest uncertainties estimated for thecold air In this figure, because the variation of the data does notfit properly to any function, we included the error bars estimated

in terms of the data

According to the results obtained from the experiments, themost effective parameters are the Reynolds number and wingletinclination angle This is because with the winglet model andwinglet inclination angle designed for this study, creation ofthe vortex, boundary-layer formation, and heat transfer are im-portant as previously reported by Kotcioglu et al [17, 18] Asobtained from Eq (14), as the Reynolds number increases, the

0.020.0210.0220.0230.0240.025

Hot Air and 8 kWHot Air and 4 kWCold Air and 8 kWCold Air and 4 kW

30 I KOTCIOGLU ET AL.

Nusselt number difference for the same heater powers between

hot and cold fluids decreases The fitted experimental data given

in Figure 10 indicate that the pressure drop as a function of

ve-locity exhibits logarithmic behavior, which is an expected result

The thermal behavior of the heat exchanger was summarized by

Sohankar [13], and similar results for the V-shaped winglets

were also presented numerically in his study

The overall heat transfer coefficient for a heat exchanger

sys-tem is obtained by using the inclined winglet vortex generators

The heat transfer coefficient (h) decreases with decreasing

tem-perature of the hot fluid, and the Nusselt number also decreases

due to the fact that the Nusselt number is directly related to h

given in Eq (12) This situation shows similarity for both hot

and cold fluids at 4 and 8 kW heater powers This in turn

indi-cates how much the cross-flow heat exchanger with winglet-type

CDLVGs used in the experiments is effective in the heat transfer

In this system, the time to reach steady state is reduced with

increasing the mass flow rate of the hot fluid In order to obtain

an idea about how the geometry of the system affects the

re-sults, the geometric parameters such as channel width (L a ) and

height (bh) and the winglet inclination angle were considered in

the correlation models The reduced chi-square (χ2) and

root-mean-square error analysis (RMSE), obtained from Eqs (15)

and (16), depend on both experimental and predicted Y values.

If the predicted value is perfectly close to the experimental value

χ2, the RMSE will be very small When R2is close to 1 andχ2,

and the RMSE is close to zero, it can be said that the correlations

derived for different variables are perfect As understood from

the results given in Figures 9 and 10, both Nusselt number and

friction factor correlations for the convergent–divergent

longi-tudinal vortex generators provide very high R2values and low

χ2and RMSE values In addition, the variation of the Nusselt

number with time is similar in both of the figures However,

for the same Reynolds numbers and heater powers, the Nusselt

number is rather low for the cold fluid This difference between

Nusselt number values of hot and cold fluids is basically due to

the differences in the temperatures of the fluids

CONCLUSIONS

In this study, the characteristics of unsteady turbulent fluid

flow and heat transfer in cross-flow heat exchangers with

winglets under various mass flow rates and heater powers

were experimentally investigated in detail In order to

evalu-ate the transient performance of the heat exchangers, the

time-dependent variations of the Nusselt number and dissipation

en-ergy criterion were presented The measured results showed

that the variations of the dissipation energy criterion increase

with the increase in the Reynolds number Within the tested

pa-rameters only, the best performance of this particular design of

the heat exchanger was found to be for the operating condition

of Re= 60,000 and 8 kW heater power

We found that the temperature fluctuations, turbulent kinetic

energy in the heat exchangers, and unsteadiness effects are

stronger in the region where the longitudinal vortices are more

active The time-dependent Nusselt number and time-dependentdissipation energy criterion decrease continuously with increas-ing time, but always less than the limiting value The time-dependent dissipation energy criterion decays with increasingReynolds number For the same Reynolds number, the dissipa-tion energy criterion number decreases with the heater power

A great improvement in the dissipation energy criterion isreached via obtaining the improvement in dissipation energycriterion in the heat exchanger For a cross-flow heat exchanger

of unmixed fluid, having different heater powers plays animportant role in the enhancement of the dissipation energycriterion The lower time-dependent dissipation energy criterion

in the designed heat exchanger indicates better heat transferenhancement

The results related with the friction factor variations plotted

as a function of the Reynolds number showed that the largestfriction factors were obtained for Re= 60,000 and 4 kW heaterpower The friction factor decreases with increasing Reynoldsnumber The friction factor at the cold air side gives higherpressure drop than that of hot air for the same heater power.The analysis presented in this study is important in manypractical transport processes, such as modern energy conversionand power utility systems, and the engineering and chemicalindustries It is expected that the thermal engineers may benefitfrom the results presented in this study, in the design of similarheat exchangers

NOMENCLATURE

A total heat transfer (fin) surface area

a, b, c, d, e and f correlation coefficients related to Nusselt

number

bh= bc fin height for hot fluid channel, height of

winglet and channel

C0 friction coefficient for square channel

g distance interval of winglets

h heat transfer coefficient

ie dissipation energy criterion

m correlation coefficient related to inclination

angleheat transfer engineering vol 32 no 1 2011

RMSE root-mean-square error

Tm average bulk temperature

tw plate and fin thickness

Tw surface temperature of the heat exchanger

core

V heat transfer volume between the plates

w width of winglet entrance for fluid

x location of the trailing edges of the winglets

Yexp, Ypre experimental and predicted values,

respec-tively

Greek Symbols

β inclination angle

βcomp compact rate

ε energy dissipation rate per unit mass

ηf fin efficiency

η Kolmogorov length scale

f ratio of friction factor

h ratio of heat transfer coefficient

µ dynamic viscosity of fluid

χ2 error (reduced chi-square)

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Mul-tifunctional Heat Exchangers by Artificially Generated

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An Experimental Investigation of Heat Transfer

Enhance-ment in a Rectangular Duct With Plate Fins, Heat Transfer

Research, vol 40, no 3, pp 263–280, 2009.

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of a Cross Flow Heat Exchanger With Wing-Type Vortex

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no 2, pp 113–127, 2008

[19] Wang, C C., Lo, J., Lin, Y T., and Wei, C S., Flow

Visu-alization of Annular and Delta Winglet Vortex Generators

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3803–3815, 2002

[20] Torii, K., Kwak, K M., and Kishino, K., Heat Transfer

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Isak Kotcioglu obtained his B.Sc in technical

ed-ucation from Gazi University, Turkey, in 1983 He became a research assistant in the Ataturk University

in 1983 He completed his M.Sc thesis in 1988 at the University of Gazi He obtained his Ph.D degree in

1993 from the same university He became an tant professor in 1994 in Atat¨urk University Some of his research interest areas are heat exchangers, elec- tronic cooling, mini and micro channels, and heat and mass transfer, as well as problems of fluid mechanics, heat pipes, and similar experimental research areas.

assis-Ahmet Cansiz is an associate professor in the

Electrical-Electronic Engineering Department of Atat¨urk University, Turkey He graduated from Istan- bul University in 1991 with a physics degree In 1993

he obtained a scholarship from the Turkish ment to continue his further studies in thermodynam- ics, resulting in a master’s degree and Ph.D from the Illinois Institute of Technology, USA, in 1999 While studying for his Ph.D he worked at Argonne National Laboratory and obtained wide experience in thermodynamics of the cryogenics systems regarding the superconductivity ap- plications He went on to join Cambridge University, Engineering Department,

govern-UK, with a postdoctoral position in 2000 He worked as a research associate on a project lasting approximately 2 years, which was related to the superconducting bearing system In 2001 he was appointed to his current position His research interest is in electromechanical systems and cryogenics.

Sinan Caliskan obtained his B.Sc in mechanical

en-gineering from Atat¨urk University, Turkey, in 2000.

He completed his M.Sc thesis in 2003 He became

a research assistant at Gazi University in 2005, and

he is working on his Ph.D degree at Gazi University Some of his areas of research interest are electronics cooling, heat exchangers, ventilation by convection, and fluid jets.

Senol Baskaya obtained his B.Sc in mechanical

en-gineering from Gazi University, Turkey, in 1988 He became a research assistant in the same department

in 1989 and completed his M.Sc thesis in 1991 He earned his PhD degree in 1996 from the University of Strathclyde, England He became an assistant profes- sor at Gazi University in 1997 and was appointed as

an associate professor in 1999 Finally he became a full professor in 2005 Some of his areas of research interest are electronics cooling, combustion technolo- gies and systems, ventilation by convection, fluid jets, application of numerical methods to energy systems, and heat and mass transfer, as well as problems of fluid mechanics, and similar numerical and experimental research areas.

heat transfer engineering vol 32 no 1 2011

Copyright
C Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457631003732854

Numerical Simulation of Forced

Convection Enhancement in a Pipe by Porous Inserts

MEHDI MAEREFAT, S YASSER MAHMOUDI, and KIUMARS MAZAHERI

Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

The effect of porous inserts on forced convection in a circular pipe is investigated numerically Two configurations are

considered: A porous material is inserted at the core of the pipe, and an annulus porous material is attached to the inner

wall The flow inside the porous material is modeled using the Darcy–Brinkman–Forchheimer model Effects of porous

thickness, Darcy number, and thermal conductivity on the Nusselt number are investigated In the first configuration,

increasing porous thickness increases Nusselt number, and the value of porous thickness that maximizes Nusselt number

varies from 0.8 to 0.95 as the value of Darcy number decreases from 10 −3 to 10 −6 In the second configuration, for low values

of thermal conductivity, increasing the porous thickness decreases Nusselt number, and the porous thickness that achieves the

lowest Nusselt number varies from 0.6 to 0.85 as the value of Darcy number decreases from 10 −3 to 10 −6 However, for high

values of thermal conductivity, increasing porous thickness increases Nusselt number At the expense of reasonable pressure

drop, optimum thickness of porous material is found to be 0.6, which maximizes Nusselt number in the first configuration

and minimizes it in the second configuration.

INTRODUCTION

Forced convection in a composite region, part of which is

occupied by a clear fluid and the other part by a fluid-saturated

porous medium, has recently attracted considerable attention

and has become the subject of numerous investigations This

in-terest is due to many important thermal engineering applications

relevant to this problem, such as solid matrix heat exchangers,

food drying, and insulation [1] High thermal conductivity

porous substrate is also used to enhance forced convection

heat transfer in many engineering applications, such as nuclear

cooling, heat exchangers, and solar collectors [2, 3] Different

methods of heat transfer enhancement in heat exchangers have

been extensively studied by Webb [4] Using porous medium to

enhance the rate of heat transfer in heat exchangers has many

advantages; the value of Nusselt number would be higher than

the values predicted in pipes without porous medium Pavel

[5] investigated the effect of a metallic porous matrix, inserted

in a pipe, on the rate of heat transfer under constant wall heat

Address correspondence to Dr M Maerefat, Department of Mechanical

Engineering, Tarbiat Modares University, Tehran, P.O Box 14115-143, Iran.

E-mail: maerefat@modares.ac.ir

flux boundary conditions, for both laminar and turbulent flows.Pavel reported that higher heat transfer rates are achieved whenusing porous inserts at the expense of a reasonable pressuredrop, which depends on the permeability of the porous matrix.Kaviany [6] considered laminar developing flow through aporous layer sandwiched between isothermal parallel plates.Rizk and Kleinstreuer [7] have investigated steady laminarforced-convection cooling of discrete heated blocks in open andporous matrix channels They reported that the low-porosityporous material-filled channel configuration yields the bestresults in terms of net heat removal However, the pressure dropfor porous material-filled channel flow is measurably higherthan that for open-channel flow As a compromise, using a high-porosity porous matrix, the efficiency of the new configuration

is 50% higher when compared with the channel without porousmaterial Forced convection in a channel whose walls arelayered by a porous medium was considered by Poulikakos andKazmierczak [8] for constant heat flux and constant wall tem-perature conditions, both analytically and numerically Al-Nimrand Alkam [9] numerically investigated thermal performance of

a concentric tube heat exchanger, by inserting porous substrates

at the inner wall of both tubes Results show that inserting theporous substrate may enhance the heat exchanger effectiveness

A numerical study was presented by Jang and Chen [10] for a

45

46 M MAEREFAT ET AL

forced flow in a parallel channel partially filled with a porous

medium by adopting the Darcy–Brinkman–Forchheimer model

with a thermal dispersion term Chikh et al [11, 12] presented

an analytical solution for the fully developed flow in annulus

configuration partially filled with a porous medium Mohamad

[13] and Mohamad and Pavel [14] numerically investigated the

heat transfer enhancement in the channel or pipe partially filled

with a porous medium They reported that the value of porous

thickness (R r) that maximizes the Nusselt number doesn’t

change with Darcy number and is equal to 0.8

This work deals with the problem of forced convection flow

in a pipe partly or fully filled with a porous medium under

constant wall temperature or constant wall heat flux boundary

condition The effects of different parameters, such as different

Darcy number, porous thickness, inertia coefficient, and

ther-mal conductivity, are investigated Porous substrate has been

inserted both at the core of the pipe, the first configuration,

and attached to the inner wall, the second configuration The

previous investigations neglected to study the effects of Darcy

number and thermal conductivity of the porous medium on the

maximum Nusselt number in the pipe Regarding this issue, in

the first configuration, emphasis is placed on dependence of the

value of porous thickness that yields the highest Nusselt number

and on the value of Darcy number in the most critical range of

porous thickness, which is from 0.8 to 1 In addition, the effect

of thermal conductivity of the porous medium on the rate of

heat transfer is studied for both configurations

GOVERNING EQUATIONS

The physical domain and coordinate system are shown in

Figure 1 A two-dimensional, laminar, incompressible, steady

flow of a Newtonian fluid with constant properties takes place

in both the fluid and porous region The pipe is subjected to

a constant wall temperature or constant wall heat flux

bound-ary condition A porous material of prescribed thickness is

de-posited at the core of the pipe or at the inner wall of the pipe

At the entrance of the pipe, the fluid velocity and temperature

are uniform and constant It is assumed that porous medium is

homogeneous, isotropic, consolidated, saturated with fluid The

flow is modeled by the Darcy–Brinkman–Forchheimer equation

in the porous matrix and by the Navier–Stokes equation in the

fluid domain Due to the symmetry consideration, one half of

the domain is considered

The conservation equations for mass, momentum, and energy

are written as follows [15, 16]:

−δρFε√

k |u| v − µf v

εr2 (3)Where µe is the effective viscosity, Al-Azmi [17] showedthat changingµefromµf to 7.5µf has a minor effect on thevelocity profile Also he reported that the effect of changingeffective viscosity has a minor effect on the temperature andNusselt number distributions Therefore, in this studyµeis setequal to µf In fact,µe = µfis a good approximation in therange of 0.7< ε <1 and it is widely adopted in the literature

[6]

Energy

In modeling of energy transport, it is assumed that the localthermal equilibrium (LTE) exists between solid and fluid phases

In fact, LTE is justified when the volumetric heat transfer

co-efficient h vis very high A thermal equilibrium condition wasadopted by Kaviany [6] The local thermal equilibrium condi-tion is investigated by the authors (not reported) in a channel

or pipe partially filled with a porous medium Results showedheat transfer engineering vol 32 no 1 2011

M MAEREFAT ET AL 47that the difference between the solid and fluid phases is not

significant Also, Mohammad and Karim [18] revealed that the

thermal equilibrium assumption is valid as far as there is no

heat released in the fluid phase (combustion, for instance) or in

the solid phase (catalytic effect, for instance) Mohammad [13]

and Pavel and Mohammad [14] considered the LTE condition

in their study to investigate the effect of porous material on the

rate of heat transfer Alkam et al [19] investigated the transient

forced convection in a channel partially filled with a porous

medium and used the assumption of LTE in their study

By assuming local thermal equilibrium between fluid and

solid phases, and neglecting viscous dissipation, the energy

transport equation can be written as follows:

where k e , c e,andρeare effective thermal conductivity,

effec-tive specific heat, and effeceffec-tive density, respeceffec-tively

The set of equations (1) to (4) is used for both the fluid and

the porous regions by using the following binary flag:

δ =



1 for porous region 0< ε < 1

0 for clear regionε = 1 (5)There are two approaches to solving the governing equations

of partially filled porous material: (1) Consider the two regions

and solve the governing equations separately in each region;

then couple them by using the appropriate interfacial thermal

and hydrodynamics boundary conditions, such that the

appropri-ate boundary conditions at the interface can be summarized as:

for inner loop iteration, in order to ensure interfacial boundary

conditions

Both approaches are implemented to solve the governing

equations, and there is no difference between the results of these

two approaches so the results are exactly the same Furthermore,

applying the unified approach to solve the governing equations

leads to a computational time that is two to three times lower than

the computational time needed for applying the first approach

So the governing equations are solved by using the unified domain approach, which automatically ensures the momentumand energy continuity at the interface between the clear fluid andthe fluid saturated porous medium, so there is no need for innerloop iteration, in order to ensure interfacial boundary conditions[20, 21]

one-The conditions at the pipe inlet, z= 0 are uniform velocity

and temperature profiles At the exit, z = L the pipe length,

L, is long enough to ensure that the velocity and temperature

profiles are fully developed At the impermeable wall r = r0ano-slip boundary condition and constant temperature or constantflux boundary conditions are applied Axisymmetric boundary

conditions are applied at r= 0 The relevant boundary conditionsare [16, 22, 23]:

The outflow boundary condition (z = L) for constant wall

temperature can be expressed as:

Equations (1) to (4) are transformed into dimensionless forms

by using the inlet velocity (uin), constant wall heat flux or wall

constant temperature (q w or T w ), and the pipe radius as erences to scale velocity components, temperature, and length,respectively

ref-The dimensionless set of equations is as follows:

heat transfer engineering vol 32 no 1 2011