Heat transfer engineering an international journal, tập 31, số 6, 2010

The optimization is car-ried out using an entropy generation minimization principle, and numerical results are presented on the effects of the heat transfer irreversibility in the hot- a

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903408268

e d i t o r i a l

Selected Papers From the 19th

National & 8th ISHMT-ASME Heat

and Mass Transfer Conference

SHRIPAD T REVANKAR1and SRINATH V EKKAD2

1School of Nuclear Engineering, Purdue University, West Lafayette, Indiana, USA

2Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia, USA

We are glad to present this special issue of Heat Transfer Engineering with a selection of papers presented at the 19th

National & 8th ISHMT-ASME Heat and Mass Transfer Conference, held January 3–5, 2008 The conference was jointly

sponsored by the Indian Society of Heat and Mass Transfer (ISHMT) and the American Society of Mechanical Engineers

(ASME) and was held at the Jawaharlal Nehru Technological University (JNTU), College of Engineering Kukatpally in

Hyderabad, India.

The National Heat and Mass Transfer Conferences (HMTC)

have been held biennially at various places in India since the

inception of ISHMT in 1971 The American Society of

Me-chanical Engineers (ASME) formally joined the ISHMT in

or-ganizing and sponsoring these conferences in 1994 This has

generated greater interaction between researchers from India

and other participating countries Many well-known experts

from abroad have participated, exchanged technical

informa-tion, and shared their expertise with Indian researchers through

these conferences and various follow-up workshops and short

courses on topics in heat and mass transfer At the 19th National

& 8th ISHMT-ASME Heat and Mass Transfer Conference, in

total 330 papers including 2 plenary and 14 keynote papers

were presented The conference was co-chaired by S

Srini-vasa Murthy of Indian Institute of Technology (IIT) Madras

and Srinath V Ekkad of Virginia Tech, with K V Sharma of

JNTU Hyderabad and T Sundararajan of IIT Madras as

con-ference secretaries About 500 participants including about 80

from 19 different countries participated in this heat transfer

conference

Address correspondence to Prof Shripad T Revankar, School of

Nu-clear Engineering, Purdue University, West Lafayette, IN 47907, USA E-mail:

shripad@ecn.purdue.edu

Here in this special issue eight selected papers covering heattransfer in turbines, electronic cooling, heat exchangers, refrig-eration systems, and materials and efficiencies in power plantsare included The first paper, “Methods for Conceptual Ther-mal Design,” presents three models and application methodsthat can be used to analyze temperature development in an elec-tronic product during conceptual design The first model applies

to electronic products used under normal conditions The secondmodel calculates hotspot temperature that can be used to eval-uate structural concepts during early design stages The thirdmodel can be used to estimate temperatures in steady-state situ-ations with known boundary conditions obtained from a thermalmock-up for a functional model These models are developed

in a resistor–capacitor (RC) network model and can be easilyused as tools for conceptual thermal design The second pa-per, “Correlation for Heat Transfer Under Nucleate Boiling onHorizontal Cylindrical Surface,” presents experimental data onnucleate boiling heat transfer on horizontal cylindrical heatingelements made out of copper in the medium of Forane aroundatmospheric conditions A heat of boiling/heat transfer correla-

tion is developed based on three nondimensional π groups The

πgroups incorporate the dynamics of bubble growth, dynamics

of flow of the surrounding fluid during the bubble dilatation,and the influence of the thermal aspects associated with liquid

431

432 S T REVANKAR AND S V EKKAD

vaporization responsible for the growth of the bubble The third

paper, “A Parametric Study of an Irreversible Closed Intercooled

Regenerative Brayton Cycle,” presents a thermodynamic

anal-ysis of an irreversible regenerated closed Brayton cycle with

variable-temperature heat reservoirs The optimization is

car-ried out using an entropy generation minimization principle,

and numerical results are presented on the effects of the heat

transfer irreversibility in the hot- and cold-side heat exchangers

and the regenerator, the irreversible compression and expansion

losses in the compressor and turbine, the pressure drop loss at

the heater, cooler, and regenerator as well as in the piping, and

the effect of the finite thermal capacity rate of the heat reservoirs

on the power and efficiency

The fourth paper, “Conjugate Heat Transfer Analysis in the

Trailing Region of a Gas Turbine Vane,” presents simulation

re-sults on the local values of pressure, wall, and fluid temperature,

and area-averaged values of friction factor and Nusselt number

between the smooth and pinned channels and cambered

con-verged channels with and without pin fins, simulating the trailing

region internal cooling passages of a gas turbine vane The

pa-per highlights interaction between the complex flow pattern and

conjugate heat transfer The fifth paper, “Experimental

Investi-gation of Cooling Performance of Metal-Based Microchannels,”

presents Al- and Cu-based high-aspect-ratio microchannel heat

exchanger fabrication, and demonstrates through experiment

that the metal-based micro heat exchangers provide

improve-ment in cooling efficiency for microelectronic systems Given

the energy needs of the world and given coal as the primary

fossil fuel of today, integvrated gasification combined cycle

(IGCC) technology has been identified as an efficient and

eco-nomic method for generating power from coal with substantially

reduced emissions The sixth paper, “Numerical Simulation of

Pressure Effects on the Gasification of Australian and Indian

Coals in a Tubular Gasifier,” shows that that the gasification

performance increases for both types of coal when the pressure

is increased

The seventh paper, “Shell-and-Tube Minichannel Condenser

for Low Refrigerant Charge,” presents a design of a

shell-and-tube heat pump condenser using 2-mm-ID minichannels with

the expected refrigerant charge less than half the quantity

re-quired by a brazed plate condenser giving the same capacity

Experimental data for heat transfer and pressure drop in this

novel condenser are reported The last paper, “Experimental

In-vestigation of the Effect of Tube-to-Tube Porous Medium

Inter-connectors on the Thermohydraulics of Confined Tube Banks,”

presents experiments on the effect of tube-to-tube copper porous

interconnectors on the thermohydraulic performance of an

in-line and staggered confined tube bank The data show that a

reduction in the pressure drop by 18% is observed in the inline

configuration, while the heat transfer is enhanced by 100% inthe staggered configuration, when compared to their respectiveconfigurations without the porous medium

We thank all the authors of these papers for their efforts inreporting their results, and all the reviewers who have helpedprovide timely and informative reviews We also thank Dr Af-

shin Ghajar, editor-in-chief of Heat Transfer Engineering, for

his interest in and support of this special issue

Shripad T Revankar is a professor of nuclear

engi-neering and director of the Multiphase and Fuel Cell Research Laboratory in the School of Nuclear Engi- neering at Purdue University He received his B.S., M.S., and Ph.D in physics from Karnatak University, India, M.Eng in Nuclear Engineering from McMas- ter University, Canada, and postdoctoral training at Lawrence Berkeley Laboratory and at the Nuclear Engineering Department of the University of Cali- fornia, Berkeley, from 1984 to 1987 His research interests are in the areas of nuclear reactor thermalhydraulics and safety, mul- tiphase heat transfer, multiphase flow in porous media, instrumentation and measurement, fuel cell design, simulation and power systems, and nuclear hy- drogen generation He has published more than 200 technical papers in archival journals and conference proceedings He is currently chair of the ASME K-13 Committee, executive member of the Transport and Energy Processes Division

of the American Institute of Chemical Engineers, and chair of the Nuclear and Radiological Division of the American Society for Engineering Education He has served as chair of the Thermal Hydraulics Division of the American Nu-

clear Society He is on the editorial board of the following four journals: Heat

Transfer Engineering, International Journal of Heat Exchangers, Journal of Thermodynamics, and ASME Journal of Fuel Cell Science and Technology He

is a fellow of the ASME.

Srinath V Ekkad received his B.Tech degree from

JNTU in Hyderabad, India, and then his M.S from Arizona State University and Ph.D from Texas A&M University, all in mechanical engineering He was a research associate at Texas A&M University and a senior project engineer at Rolls-Royce, Indianapolis, before he joined Louisiana State University as an as- sistant professor in 1998 He moved to Virginia Tech

as an associate professor of mechanical engineering

in Fall 2007 His research is primarily in the area of heat transfer and fluid mechanics with applications to heat exchangers, gas tur- bines, and electronic cooling He has written more than 100 articles in various journal and proceedings and one book on gas turbine cooling His research fo- cuses on enhanced heat transfer designs, with a variety of applications He has served as coordinator for the 8th ISHMT/ASME Joint Heat and Mass Transfer Conference held in Hyderabad, India, in January 2008 He was also the chief organizer for the heat transfer track at the 2004 ASME Turbo Expo He is also

an associate editor for Journal of Enhanced Heat Transfer and International

Journal of Thermal Sciences He was the inaugural recipient of the ASME

Bergles–Rohsenow Young Investigator in Heat Transfer Award in 2004 and the ASME Journal of Heat Transfer Outstanding Reviewer.

heat transfer engineering vol 31 no 6 2010

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903408318

Methods for Conceptual Thermal

Design

RUBEN STRIJK, HAN BREZET, and JORIS VERGEEST

Faculty of Industrial Design Engineering, Delft University of Technology, Delft, The Netherlands

This article describes three generic models and application methods that can be used to analyze temperature development

in an electronic product during conceptual design The models are based on generally known heat transfer and resistor–

capacitor network theory and are theoretically and numerically approximated The result is three easy-to-use tools for

conceptual thermal design Application of the models in design practice has been assessed using a usability experiment and

several in-depth interviews with industrial design engineers from the field.

INTRODUCTION

The latest changes in industry require companies to focus

on fast innovations The result is that time to market is

short-ened and development speed is increased [1] Therefore, we

have less time to develop products that are reliable and have

good quality In addition, the amount of electronics around us

is increasing, ubiquitous electronics [2], and the power density

is increasing by continuous miniaturization The result is that

reliability becomes an increasing important issue in

develop-ment of electronic products [3] and thermal design becomes a

bottleneck in the development process It is therefore necessary

to provide electronic and mechanical engineers with tools and

methods to take temperature into account in preliminary phases

in design

Some research has been done to improve thermal analysis in

the conceptual phases Ishizuka and Hayama [4], for instance,

describe models to simplify analysis of natural convective

cool-ing in preliminary analysis Yazawa and Bar-Cohen’s studies on

flow models [5] also contribute to this issue However, in our

best knowledge there are no generic models available that can

be used in conceptual design of electronic systems Our goal is

to extend the present knowledge on resistor–capacitor networks

(RC networks) and flow modeling to develop generic models

for application in conceptual thermal design

During our preliminary studies several designers from

prac-tice have been interviewed with the aim of verifying the

appli-cation of thermal management techniques in practice Different

Address correspondence to Professor Ruben Strijk, Faculty of Industrial

Design Engineering, Delft University of Technology, Landbergstraat 15, 2628

CE Delft, The Netherlands E-mail: r.strijk@tudelft.nl

views indicate how practicing designers work in the field ofthermal design Three key issues derived from interviews andliterature are:

1 Designers are unfamiliar with heat transfer and thermal sign theories Such designers lack the knowledge that wouldenable them to make basic design choices and evaluate howimportant temperature is to the design The choice betweenpassive and active cooling is currently based on experienceand trial and error

de-2 An evaluation of structural concepts on temperature opment is not supported by a standard approach

devel-3 Temperature measurements for mock-ups and functionalmodels are crucial in thermal design practice for findingreliable boundary conditions, but are time-consuming Theprocess of measuring could possibly be optimized by prop-erly integrating easy-to-use formulas that could be calibratedusing measurements determined from a thermal mock-up orfunctional model The effects of design changes could bepredicted by predefined rules of experience and estimations

Furthermore, as has been concluded from studying the erature and has been clearly expressed by participants duringinterviews, any tool used for conceptual design should be easy

lit-to use To resolve the three issues just listed, three models havebeen developed that contain the following three characteristics:Model 1 supports risk assessments put forth by the designer,even if he or she has no knowledge of heat transfer or thermaldesign [6–8] Model 2 supports finding and analyzing the mainheat path in structural concepts and is useful for estimatingrough temperatures in an electronic product [8–10] Model 3

433

434 R STRIJK ET AL.

supports the determination of the total transient behavior in a

device [8, 11] The contribution of this article is the proposal

and evaluation of these three models and application methods

APPROACH

This article is constructed of several sections to propose and

evaluate the three models In the approach for model 1, basic

heat transfer calculations are combined with measurements for

existing products Heat transfer calculations show maximum

boundary conditions of heat transfer for a surface area This

is done using several surface temperature differences within

the environment Measurements combined with these values

show a transition area that can be used as a guideline for a

particular design For model 2, an RC network is developed

and programmed into a small software program The industrial

designer can use this program to fill in variables and calculate

temperatures Finally, model 3 describes a mathematical model

for temperature prediction in an electronic product As a basis for

the model, an electronic product will be viewed as if it were one

single hotspot within an encasing In reality, the hotspot could be

a power-dissipating component, such as a coil, integrated circuit

(IC), or the average temperature of a printed circuit board The

model can be used to describe the effect of design changes on

hotspot temperature Several design variables will be taken into

account, including an open or closed encasing, passive cooling

or active cooling, and materials used for the encasing In this

article, four steps that define the models will be listed: model

description, results and discussion, practical application, and

conclusion

Step 1: Model description Describing the three proposed

mod-els based on general heat transfer theory and thermal

RC networks.

Step 2: Results and discussion The application of the three

models will be described for example situations and

real products The heat transfer variables that are

needed in the equations are derived from standard

con-duction, convection, and radiation equations The

sec-tion follows with a descripsec-tion of the results of the

measurements The differences between the measured

and calculated values are discussed and directions for

improving the accuracy of the model are given

Step 3: Practical application The practical use of the models

in a design situation is described

Step 4: Conclusion Drawing conclusions from the research in

described in this article

MODEL DESCRIPTION

In this section a description of the proposed models is given

For model 1 the theoretical approximation of passive cooling

limits for an electronic product is explained The theoreticalcooling limit is derived by combining convective and radiativeheat transfer coefficients from an isothermal surface to an ambi-ent environment As a basis for model 2, an electronic product

is examined as one single hotspot within an encasing In reality,the hotspot can include a power dissipating component, such as

a coil, an integrated circuit (IC), or the components of a printedcircuit board (PCB) Model 3 is a framework for evaluating

various cooling concepts and is based on an RC network The

objective of the model is to give insight into transient behaviors

of the hotspot and encasing temperatures for different coolingconfigurations

Model 1

Passive cooling limits have been calculated for the ature differences between a hot surface with an ambient en-vironment By comparing these values with measurements forexisting products, boundary areas for the passive and activecooling of an electronic product and a maximum power-to-arearatio for electronic products can be defined These calculationsare for heat transfers between an isothermal surface tempera-

temper-ture T e and the ambient temperature T a = 296 K (= 23◦C) A

specific dimension for a vertical plate L cof 0.1m and thermal

conductivity of air k airis used to calculate the heat transfer

co-efficient for convection h cand the heat transfer coefficient for

radiation h r at temperature differences
T ( = T e − T a) of 5 K,

15 K and 25 K, shown in Table 1

The heat transfer coefficients h c and h r have been mated based on general heat transfer theory for a vertical platewith an isothermal temperature distribution across the surface

approxi-To determine h c, the Hilpert correlation, shown in Eq (1), hasbeen used to approximate the Nusselt number Nu [12]

h c= k airNuL

L [W/m2K]; Nusselt, NuL = 0.54Ra 0.25

The heat transfer coefficient of radiation h ris determined by

using the average temperature T av, and is shown in Eq (2) Here,

q r is the radiation heat transfer [W], ε is the emissivity of theradiating surface [1.0], σ is the Stefan–Boltzmann constant [5.67

The resulting total heat transfer coefficient h tot, given in

Eq (3), is then calculated by summing h c and h r The

tem-perature difference of 15 K is comparable with previous

stud-ies found in literature [5] The temperature differences of 5 K

and 25 K define a transition area between passive and active

cooling

h tot = h r + h c (3)Table 1 gives results for the three temperature differences

just described The results show that, for the given T a , h c is

significantly dependent on temperature differences between the

surface and the environment, while h r is not In addition, it can

be concluded that in passive cooling, radiation heat transfer can

play a significant role because it is in the same order of

mag-nitude as convection heat transfer However, this only accounts

for black- and gray-body radiation, where ε≈ 1.0

Model 2

As a basis for model 2 and model 3, this article examines an

electronic product as one single hotspot within an encasing In

reality, the hotspot can include a power dissipating component,

such as a coil, an integrated circuit (IC), or the components of a

printed circuit board (PCB) Based on this abstraction, various

models can be derived, ranging from a very simple RC network,

which is discussed in this section, to a complex RC network.

In this section, mathematical relations of the one-dimensional

heat transfer will be derived This is done by proposing a

one-dimensional RC network, given in Figure 1, that can be applied

to a variety of electronic products that are passively cooled and

have a closed encasing Based on insights gained through this

analysis, the mathematical model may be expanded into

some-thing more complex This will be explored in future research if

required

When designing electronic products, it can be important to

predict the behavior of a product within a certain period of time

For this particular model, it is necessary to take into account

transient temperature development By using transient

temper-ature prediction in the form of state space equations, the model

allows for the option of evaluating a usage scenario This

us-age scenario can then be evaluated and compared with defined

criteria Based on such results, the product can be properly

designed without overdimensioning, which would bring about

higher costs

Figure 1 Thermal RC network model 2.

The system consists of five types of variables: thermal

resis-tors R, temperature T , thermal capaciresis-tors C, heat flow q, and energy E Four thermal resistors include the following:

• The core of the hotspot to the surface of the hotspot, or R1.

• The hotspot surface to the interior surface of the encasing, or

The temperatures in the product result from the hotspot heat

flow q and the thermal resistors, q = R
T In this model, five

temperatures are defined:

• The temperature inside the hotspot, or T c

• The temperature of the hotspot surface, or T h

• The temperature of the interior surface of the encasing, or T i

• The temperature of the exterior surface of the encasing, or T e

• The ambient temperature, or T a

In order to calculate transient temperature development, mal capacity must be taken into account Generally, electronicproducts consist of an encasing on the outside and electronics

ther-on the inside Between the electrther-onics and the encasing, there isgenerally air Usually, this means that when a product is heated,there are three thermal capacitors (Figure 1) that cause temper-atures to rise at a steady rate:

• The thermal capacitance of the hotspot, or C1.

• The thermal capacitance of the inside air, or C2.

• The thermal capacitance of the encasing, or C3.

The main heat flow in the system q causes temperatures

to rise Three heat flow paths into thermal capacitances resultfrom this general heat flow The heat flow paths into these threethermal capacitances are defined as follows:

• Heat flow into C1, or q1

• Heat flow into C2, or q2

• Heat flow into C3, or q3.The heat flow in the model will result in four basic tempera-ture differences:

• From the core of the hotspot to the surface of the hotspot, or

T c − T h

• From hotspot surface to the interior of the encasing, or T h −T i

• From the interior of the encasing to the exterior of the

tempera-T h − T e , equals (T h − T i ) + (T i − T e) For practical reasons,heat transfer engineering vol 31 no 6 2010

436 R STRIJK ET AL.

only the temperatures T h , T e and T awill be measured and

com-pared, with resulting temperature differences of T h −T e , T e −T a,

and T h − T a

Finally, the total energy stored in the capacitances in the

system can be defined by the product of thermal capacitance

and temperature, or E = CT However, in the present case, of

greatest interest are temperature differences with regard to a

reference temperature T a Therefore, the energy stored in the

system is defined as reference energies E ref1= C1T a , E ref2=

C2T a and E ref3= C3T afor the following thermal capacitances:

• Energy stored in C1, or E1 = C1Tc − E ref1→ E1= C1(Tc−

State space equations allow for the possibility of dynamically

analyzing temperatures A designer may use the equations to

calculate temperature from any realistic starting condition For

instance, the model can be integrated and computed into a

soft-ware program in which the designer fulfills required parameters

and usage scenarios The program then calculates temperature

development in the device This section describes these state

space equations and their parameters State space equations

basically consist of two equations The first equation defines

air flow into thermal capacitances, ˙X (t) = AX(t) + BU(t).

The second equation is used to examine temperature

differ-ences Y (t) = CX(t) + DU(t) The matrices are defined as

follows [13]:

• X˙(t) are the heat flows into thermal capacitances.

• A is the system matrix and contains the values of thermal

resistances and capacitances

• X (t) is the vector describing the state of the system, which is

the energy stored in thermal capacitances with regards to the

reference temperature T a

• U (t) is the input vector and describes the quantity of heat that

flows from the hotspot into the system

• Bis the control matrix

• Y (t) is the output of the system.

• Cis the output matrix of the system

• Dis the feed-forward matrix

State space equations based on this system can be defined as

In this section, a framework for evaluating various cooling

concepts is described The framework is based on an RC

net-work, shown in Figure 2 The objective of the model is to giveinsight into transient behaviors of the hotspot and encasing tem-peratures

In the thermal RC network, there are several heat flows that

must be taken into account The source for the heat flow is

q As a result of q, the product begins to heat This property is represented by heat q1into thermal capacitance C As a result of the heat flow in C, the temperature of the product rises and heat

flows to an ambient environment The heat flow to the ambientenvironment can be divided in two flows First, a possible forced

or passively induced flow of air through the device via openings

in the encasing may exist This is represented by q2 Second,

a flow of heat in the form of natural convection and radiation

through the encasing q3may also be present

There are several thermal resistances that determine powerflows and temperature distribution within a system First, a ther-mal resistance models heat transfer through a flow of air through

the product R1 This can occur through either natural or forcedconvection For fully closed encasings, the value of this thermalresistance will be set to infinite∞ Second, the model contains

two thermal resistances that describe the heat flow q3throughthe encasing This includes heat flow from the hotspot to the

exterior of the encasing R2 and heat flow from the exterior of

Figure 2 Thermal RC-network model 3.

heat transfer engineering vol 31 no 6 2010

the encasing to an ambient environment R3 The result of these

described thermal resistances and heat flows of a product within

a specific ambient temperature T a is a hotspot temperature of T h

and an average encasing exterior temperature of T e Integration

of the previous equation results in the following equation:

T (t) = T m − e( RC −t ) (T m − T a) (5)From Eq (5) two equations can be derived given by Eq (6):

For a closed encasing, the value of R1 can be defined as

infinite, resulting in Eq (7):

RESULTS AND DISCUSSION

In this section the results and discussion of the three models

are presented and described A more extensive elaboration of

the results has been described in previous publications [7, 8, 10,

11]

Model 1

The surface area A and power dissipation q have been

mea-sured for a 66-product total Figure 3 shows both the calculated

heat transfer lines (Table 1) and the positioning of the

experi-mental results The values of A varied between 8.0× 10−3 m2

(portable radio) and 3.0 m2(washing machine), while q varied

between 2.0× 10−2W (portable radio) and 2.0× 103W (water

cooker) Figure 3 shows that most products that dissipate less

than 1 W of power are positioned below the 5 K temperature

line Product examples in this range include a Discman, radio,

MP3 player, and minidisk It is probable that thermal design

was not a major issue in the development of these products

Examples of products that are positioned around the 5 K line

up to the 15 K line include stereos, cathode ray tube TVs, LCD

(liquid crystal display) TVs, network switches, and routers It

would be likely that thermal design played a significant role in

the design process of these products For instance, an LCD TV

uses holes in the encasing, combined with a significant amount

of cooling fins on the inside of the product, to dissipate heat

from the printed circuit board to an ambient environment

Figure 3 Existing products and theoretical cooling limits, based on own surements.

mea-In the “actively cooled” range, between the 15 K and 25 Klines, products such as a laptop computer are positioned Thesetypes of products are generally regarded as in critical need ofproper thermal design In the area above 25 K, products such

as power tools, kitchen appliances, and slide projectors can befound Power tools that use an electromotor usually have a rel-atively short duty cycle and therefore generally do not reachtheir steady-state temperature Products that are convectivelycooled are cooled by airflow induced by a rotating component,sometimes a fan directly connected to the electromotor Otherproducts in this range, such as kitchen appliances and slideprojectors, generally give off a great deal of heat Thermal de-sign is very critical in these types of products Temperatures ofhotspots in these types of products are usually much higher than

in products within the range of 15 K to 25 K

Model 2

In order to investigate the accuracy of state space equationsand the assumptions made in the previous section, computationswill be based on the properties of an actual product, in this case,

a standard AC–DC adaptor shown in Figure 4 Comparisons ofthe measurements with the model will give conclusions aboutthe accuracy and applicability of the model for design engi-neering purposes The measurements have been executed usingthermocouples and an infrared sensor Data has been collected

by means of a data logger, which measures and stores the

tem-peratures of the hotspot T h , the encasing T e, and the ambient

temperature T a.For the purposes of this comparison, both measurements andcomputations have been subjected to two different degrees ofpower dissipation, including 1 W and 2 W The aim is to gaininsight into the extent to which the model can predict varia-tions in temperatures, depending on the different amounts ofheat transfer engineering vol 31 no 6 2010

438 R STRIJK ET AL.

Figure 4 Overview of an AC-DC adaptor.

dissipated power The heat transfer coefficients for convection

and radiation are influenced by factors such as temperature

dif-ferences and geometry In this model, a combined heat transfer

coefficient for convection and radiation is used Equation (1)

has been used to approximate the Nusselt number, Nu The

heat transfer coefficient of radiation is approximated by using

Eq (2) State space equations have been programmed using a

C++ script in order to determine their solutions The script is

an algorithm based on the explicit Euler method for

calculat-ing differential equations The script can be used to develop

a software program from which a practical application can be

tested

The results of the computed model and measured product

are shown in Figures 5 to 7 Two initial tests on the adaptor

have been carried out and include 1-W and 2-W heat

dissipa-tion Table 2 shows the results of the model and measurements

The first approximation results in steady-state temperatures that

significantly deviate from the measurements T h − T ehas been

computed using a factor of 2.46 (12.78/5.20), which is too high

T e − T ahas been computed using a factor of 0.48 (5.80/12.20),

which is too low

In addition, infrared measurements have been carried out on

the adaptor for steady-state temperatures shown in Figure 8

Figure 5 Measured and computed temperatures for 1W dissipation.

Figure 6 Measured and computed temperatures for 2W dissipation.

The approximate location of the hotspot is also shown in thisfigure The results illustrate that temperatures across the en-casing surface are not constant, but vary from 38.0◦C (= 311K) to 24.5◦C (= 297.5 K) The average of these two values is31.3◦C (= 304.3 K) From the figure, it can be determined thathigh temperature concentrations are found at the approximatelocation of the hotspot

From the data in Table 2, several conclusions can be drawn

We can see that t98%can be estimated within an accuracy of 17%

t98%, computed with the model, appears to be a relatively good

approximation with regard to the measured t98% In addition, themodel predicts the effects of temperature changes by observingchanges in the concept, in this case, a change in power dissi-pation The present results show that although measured andcomputed temperatures do not correspond, the temperatures ofthe computations do proportionally change with measured tem-peratures when dissipated power is changed from 1 W to 2 W.This is a positive effect, which shows that the model accurately

Figure 7 Measured and computed temperatures for improved model results for 1W dissipation.

heat transfer engineering vol 31 no 6 2010

Table 2 Measurement and computation results

However, the results also show that temperature differences

from a hotspot to the encasing and from the encasing to an

ambient environment are incorrectly computed (Figures 5 and

6) First, the measured T h − T e and T e − T avalues (in Figures 5,

6, and 7 these are squares and dots, respectively) deviate a

great deal from computed values However, the sum of the two

computed and measured values of T h − T e and T e − T a, namely,

T h −T a, does not deviate a great deal We can see that the model

predicts the hotspot temperature with an accuracy of 8% to

21%

The problem with the model is that the wrong

computa-tions for T i − T h and T e − T a are given The cause of this

miscalculation is an incorrect estimation of thermal resistances

R2 and R4 R2 has been computed too high, with a factor of

2.46 (12.78/5.20), resulting in a high estimation of T h − T e R4

has been computed too low, with a factor of 0.48 (5.80/12.20),

resulting in a low estimation of T e − T a (Table 2) The

re-mainder of this section discusses the probable causes of both

problems

Figure 8 Steady-state temperatures of the adaptor.

It is unlikely that the dissipated power q, the measured perature T h , or the surface area A h encompasses this problembecause these values were controlled during the test setup A

tem-different explanation is that the thermal resistance R2has beenincorrectly approximated Because the air layer between thehotspot and inside encasing is relatively thin, on average, mea-suring 2.5 mm, the conductive heat transfer through the insideair should be taken into account If done, the following improve-ment will result:

These calculations include the heat transfer coefficient of

conduction, h k , with the inside air results in
T of 7.98 K.

This comes far closer to the measured temperature difference

of (5.20 K), compared to 12.78 K, derived from previous culations Therefore, for this product, air conduction inside theproduct plays a significant role in determining the tempera-ture difference between the encasing and the hotspot when airlayers are 2.5 mm Further exploration is advised and shouldtake into account more details of the hotspot and the encas-ing when calculating heat transfer coefficients and thermalresistance

cal-As can be seen in Figure 8, the temperature is not evenly tributed across the surface of the encasing A temperature differ-

dis-ence
T of 13.5 K between the lowest and highest temperatures

is measured If the
T between the maximum temperature and

the average temperature is calculated, the following results arereached: 38.0◦C – 31.25◦C = 6.75◦C = 6.75 K It is likelythat because only one thermocouple was used, a higher thanaverage temperature was measured on one hand, while the av-erage temperature was calculated on the other The differencesbetween measured and calculated temperatures are 12.20◦C –5.80◦C= 6.40◦C= 6.40 K, which comes close to
T between

the maximum and average temperatures In the previous section

it was concluded that R4 is computed with a too low factor of0.48 resulting in a low estimation of the temperature difference

T e − T a One option for correcting this factor includes ing the total heat transfer coefficient This, however, would be

increas-a very unreincreas-alistic increas-assumption It is unlikely thincreas-at the convection

and radiation heat transfer coefficients, h c in Eq (1) and h r in

Eq (2), have been estimated low The heat transfer coefficientfor convection has been estimated using a correlation for theNusselt number of a vertical plate [12] This correlation alreadyheat transfer engineering vol 31 no 6 2010

440 R STRIJK ET AL.

results in a relatively high convection coefficient In addition,

the radiation heat transfer coefficient also has been calculated

relatively high because a maximum emissivity ε= 1 and

maxi-mum view factor F 1,2= 1 have been used The previous section

discussed how conduction plays a significant role in calculating

R2because of a thin air layer between the hotspot surface and the

inside encasing surface It is unlikely that this has a significant

influence over the calculation of R4, since the air on the outside

of the product can move freely from the encasing surface to an

ambient environment A comprehensive elaboration is given in

Teerstra’s article on natural convection in electronic enclosures

[14]

Assuming that heat dissipation q and the area of heat transfer

A hhave been correctly controlled in measurement calculations,

the only option remaining is the deviation of temperatures on the

encasing surface with regard to the average temperature, which

is also calculated using the proposed model Infrared

measure-ments (Figure 8) indicate that temperatures of the encasing are

difficult to predict in detail The difference between

computa-tions and measurements, 12.2 K – 5.8 K= 6.4 K, is of the same

magnitude as differences measured, 6.75 K The model thus

pre-dicts the average temperature of the encasing, but cannot predict

local temperatures

The parameter t98%does not vary between various levels of

power dissipation in the model The temperature development

in the model is exactly the same for both rates of dissipation,

1 W and 2 W, namely 4500 s However, measurements

indi-cate that, in reality, there is a significant difference between the

measured value of t98% (1 W: 3840 s and 2 W: 5280 s) This

does not appear to be a result from a miscalculation of thermal

capacitances C1, C2, and C3because it is a straightforward

cal-culation Therefore, it can be concluded that the proposed model

does not take into account the effect of temperature on transient

temperature prediction This issue should be taken into account

when undergoing follow-up research

Model 3

In this section, the results of the thermocouple

measure-ments are presented There are several reasons for obtaining the

present measurements First, the measurements are needed to

obtain more insight into heat transfer and the distribution of

temperature within a mock-up Second, measurements give

in-sight into differences for possible cooling configurations Third,

the measurements will be used at the end of this chapter to

compare predictions with a calibrated model and evaluate the

predictability and accuracy of the model

Because the intention is to obtain insight into the effects of

design changes, these measurements will cover different

config-urations given in Figure 9 A mock-up is a device that contains

one hotspot, in this case, a piece of copper with a resistor inside

Many of these design options can be varied, as is shown in the

following:

Figure 9 Several mock-up configurations.

• The encasing material can be changed (polystyrene and minum)

alu-• The encasing can be either closed or open

• The airflow can be changed from natural convection to forcedconvection by integrating a small fan

• The surface area of the hotspot can be increased (cooling fins).The temperature of each setup has been measured by means

of a data logger All temperatures are logged once each minuteuntil a steady-state situation has been reached Temperaturemeasurements have been achieved within a laboratory environ-

ment, using an ambient temperature T a that varied by ±2 Karound an ambient temperature of approximately 296 K (=

23◦C) The fluctuations in ambient temperature fall within areasonable range To interpret the data, temperature differencesare used This is a convenient method for correcting fluctua-tions in ambient temperature T-type thermocouples have beenattached to the hotspot and the top, bottom, front, back, leftand right of the encasing The reference temperature has beenattached to the tripod that holds the mock-up Figure 10 gives anoverview of the measurement set-up and the components used

to build the different configurations

Each configuration has been tested for at least three differentranges of power dissipation The ranges were chosen in such away that the level of maximum power delivers a hotspot tem-perature between 333 K (= 60◦C) and 343 K (= 70◦C) This

temperature limit results from achieving the maximum allowedtemperature for the material used in the mock-up (polystyrene)

In total, 38 measurements have been executed The aim of thepresent study is to discuss the predictability of Eqs (5)–(7) Theaverage encasing temperature is derived from measurementstaken from the top, bottom, front, back, left, and right of theencasing

For configuration A, T his higher with aluminum than withpolystyrene For all other configurations, however, this is not thecase It could be suggested that in the case of configuration A,the emissivity of the encasing material plays a significant role.The emissivity of white plastic is between 0.84 and 0.95 [15] andheat transfer engineering vol 31 no 6 2010

Figure 10 Overview of the set-up for thermocouple mock-up measurement.

the emissivity of polished aluminum is between 0.04 and 0.06

[16], which should result in a large difference in heat transfer

coefficients between the two materials Radiation is a complex

phenomenon It would not be appropriate to conclude more

than the preceding suggestions based solely on thermocouple

measurements Figure 11 shows that for the thermal mock-up

presented here, the encasing material influences hotspot

tem-perature Implementing an encasing material with a high level

of conductivity (aluminum) will result in lower hotspot

tem-peratures, because heat can spread more easily throughout the

material This effect is highly noticed in the case of

configu-ration E, where the hotspot is attached to the encasing For a

power dissipation of 1.0 W, the
T of aluminum is 50% of the

Tof polystyrene

Comparing configuration C with configuration B in Figure 11

leads to the suggestion that, for open encasings, extending the

cooling surface by means of cooling fins results in a lower

hotspot temperature Figure 12 shows, however, that this is

not necessarily the case for an average encasing temperature

Figure 11 and Figure 12 suggest that a ventilated product, by

means of forced convection, significantly reduces both T hand

T e For configuration F, which is unvented but uses forced vection inside, an approximate 50% reduction in hotspot tem-perature, with regard to configuration A and B, is observed

con-In most cases, thermal resistance is higher at low power sipations This suggests that the effect is related to nonlinearbehavior of the heat transfer coefficient For configurations A,

dis-B, C, D, and F, the effects of changing encasing materials arerelatively small Configuration E (the hotspot is attached tothe encasing) indicates a significant difference between usingpolystyrene and aluminum as an encasing material For bothcases presented in configuration C, a clear reduction in hotspottemperature by enlarging the cooling surface (cooling fins) isrealized In general, the hotspot temperature is lower when analuminum encasing is used, and by adding a fan, the setup coulddissipate a significantly higher amount of power, resulting in

a factor of approximately seven times the power dissipation,compared to the average hotspot temperature With configura-tion E, the effects on hotspot temperature are very large in bothcases, with a 30% to 70% improvement Configuration F showsthat internal air circulation can reduce hotspot temperature byapproximately 50%, compared to configuration A

For configurations A and F, there is generally little ence between maximum encasing and average encasing tem-peratures Configurations C, D, and E show a large differencebetween maximum encasing temperature and average encas-ing temperature There is a noticeably large difference betweenaluminum and polystyrene Aluminum, with its higher thermalconductivity, better distributes heat and reduces differences be-tween average and maximum encasing temperatures By far,configuration E gives the highest rate between maximum andaverage encasing temperatures, which is likely due to the factthat the hotspot has been attached to the encasing

differ-Time constants derived using a function for unconstrainedminimization algorithm in Matlab are presented in Table 3 Timeconstants derived using data from temperature measurements forthe hotspot appear relatively consistent per configuration One

that significantly differs is Al E-0.25 This deviation is a result of

high fluctuations in temperature measurements during startup

Figure 11 Temperature differences from the hotspot to an ambient environment.

heat transfer engineering vol 31 no 6 2010

442 R STRIJK ET AL.

Figure 12 Temperature differences for the average encasing to an ambient environment.

The total thermal resistance and capacitance of Eq (5) can be

derived from measurements

The derived results of the thermal resistance and capacitance

for the 12 different configurations are displayed in Table 4 and

Table 5 Thermal resistance values and capacitance appear to

be relatively consistent per configuration Thermal resistance

significantly decreases in configuration D, where a fan was

used The large difference between thermal resistance values

for polystyrene configuration E and aluminum configuration E

explains the positive effect of heat spread by using a material

with high levels of thermal conductivity, compared to a material

with low levels of thermal conductivity Configurations A and

B have approximately the same thermal capacitance However,

the amount in configuration B is slightly less because some

material has been removed from the top and bottom of the

en-casing In configuration C, cooling fins have been added These

are made of aluminum and therefore result in a higher level of

thermal capacitance In configuration D, a small fan has been

added in addition to the cooling fins This, again, results in an

increase of thermal capacitance Configuration E has one value

for the aluminum encasing that is significantly different from

the other values This is most likely caused from derivations in

the measurements (see Figure 2) Configuration F shows a large

difference between derived thermal capacitances The cause for

this is presently unclear

Table 3 Time constants X = RC [s]

Figure 13 shows results for four experiments The iments encompass both configurations A and B (closed andopen encasings), using both polystyrene and aluminum encas-ing material The results show the influence encasing materialhas on temperature distribution along the encasing surface andthe reduction in hotspot temperature experienced by ventila-

exper-tion Ambient temperature T a and hotspot temperature T hhave

Table 4 Total thermal resistance R [K/W]

Note Polyst., polystyrene; alum., aluminum.

heat transfer engineering vol 31 no 6 2010

Table 5 Thermal capacitance C [J/K]

Note Polyst., polystyrene; alum., aluminum.

been obtained using measurements determined by means of

software, which is compatible with the infrared thermography

camera ThermaCAM Researcher [17] The results are given in

Table 6 An encasing with a higher level of thermal conductivity

shows a lower hotspot temperature, in this case, T h − T a = 12

K for aluminum versus T h − T a = 13 K for polystyrene with

configuration A and T h − T a = 12 K versus T h − T a= 9 K for

configuration B Ventilation holes appear to have an improved

effect on the hotspot temperature for this mock-up system

PRACTICAL APPLICATION

Model 1

Model 1, presented in Figure 14, gives guidelines that can

be used to evaluate whether passive cooling for a product is

Table 6 Infrared results Configuration T a[ ◦C] T h[◦C] T h − T a[K]

Note PS, polystyrene; Al, aluminum.

feasible These guidelines can be applied by estimating powerconsumption and the surface area of the minimum enclosingbox Depending on the type of product, the probability that acritical hotspot temperature will occur in the design may bepredicted

The application of this model is twofold First, the model is

to be used during the very early stages of design (conceptualphase) to gain insight into whether or not the use of active cool-

ing is necessary The designer begins by defining the ratio q/A.

Then, he or she continues with positioning the design in thegraph or comparing the results to the rule of thumb, describedearlier The analysis ends when a decision is made on whether ornot a fan will be used in the design (active cooling) and with anassessment of whether a detailed thermal analysis in subsequentdesign phases is needed Second, the rule of thumb can be used

as a means of communication between design and electronicsengineers The design team can use the graph to benchmark itsproducts, comparing them to those of competitors, and definetargets with regards to new or developed products For compa-rable studies, see Yazawa and Bar-Cohen [5]

In some cases, a graph can be difficult to read, especiallywhen products are on the boundary line between two areas

Therefore, a new measure is proposed that equals the ratio q/A.

If the ratio q/A changes when compared to previous designs

Figure 13 Results of the infrared (IR) experiment.

heat transfer engineering vol 31 no 6 2010

444 R STRIJK ET AL.

Figure 14 Model 1.

through either an increase in power consumption or a reduction

in product surface area, then the designer and electronic

engi-neer must again assess the product on the basis of the rule of

thumb and estimate whether or not a change in design or a more

extensive thermal analysis is required

By examining temperature lines, corresponding ratios of q/A

can be derived These include 5 K, with a ratio of q/A≈ 50,

15 K, with a ratio of q/A ≈ 150, and 25 K, with a ratio of

q/A≈ 300 The designer can obtain some insight on whether

a detailed analysis of temperatures within the product is

neces-sary, based on a simple rule of thumb However, the following

does not apply to the development of heating products (e.g.,

toaster, watercooker, etc.) A different approach other than that

presented here must be taken into account The model is applied

as follows for a given design:

1 Estimate q and A of your design.

2 Determine in which of the zones in Figure 14 your design is

positioned

a If q/A > 300, the design lies in zone 1 and active cooling,

with a detailed thermal analysis, is essential

b If 300 > q/A > 150, the design lies in zone 2 and active

cooling can be used with a low thermal risk

c If 150 > q/A > 50, the design lies in zone 3 and passive

cooling is an option, but a detailed thermal analysis is

essential

d If 50 > q/A, the design lies in zone 4 and the product

can be passively cooled

3 Make decisions, set criteria and reuse the model when

sig-nificant design changes in q or A occur.

Model 2

On the basis of Eq (4), a software program can easily be

de-veloped that computes required parameters The authors of this

study have developed such a software program, named

Ther-manizer, which numerically solves the system (Figure 15) The

model can now be easily applied to a given design by using the

following requirements:

Figure 15 Numerical solver Thermanizer.

1 Gather the required design parameters

2 Start the software program and fill in required variables

3 Run the program

4 Use the results to make design decisions and evaluate designchanges

Figure 16 shows the results of Thermanizer The lute temperatures can be derived from these values by usingproper addition The temperature differences are described asfollows:

abso-• Core of the hotspot to hotspot encasing T c − T h

• Hotspot encasing to inside encasing T h − T i

• Inside encasing to outside encasing T i − T e

• Outside encasing to the ambient environment T e − T a.The present state of development for a software program iscurrently reliable enough for usability research, which is themain motivation for its development It is recommended, if theapplication is successful, to extend the program using additionalproduct configurations, including a valid area of application foreach addition Developing possibilities that would include usescenarios in order to improve transient analysis is also recom-mended

Model 3

In this section, a description is given of the practical use ofthe mathematical model, Eq (5), as a standard formula in thedesign of an electronic product The method is presented as astepwise plan that is easy to understand and should be applied

as follows:

1 Measure the hotspot temperature, average encasing ature, and the ambient temperature every minute until thetemperature has reached an approximate steady state Also,measure the amount of dissipated power coming from the de-vice It is advisable to choose dissipated power such that theheat transfer engineering vol 31 no 6 2010

temper-Figure 16 Graphs produced by Thermanizer.

temperature of the hotspot reaches its approximate maximum

allowable value

2 Derive the steady-state temperature and time constant X from

the measurements X = RC occurs at approximately the same

time as when the temperature of the hotspot reaches 63% of

its steady-state value

3 Derive the thermal resistance and thermal capacitance using

the following equations: R= T m −T a

q and C=X

R

4 Use the R and C values to calibrate the general equation

T (t) = T m − e( RC −t ) (T m − T a) Set up the matrix equations to

calculate hotspot and encasing temperatures

5 Use the equation to study design changes

Example

In this section, model 3 and its method for application are

applied to the variable mock-up system The model is first

cal-ibrated using results from the measurements shown in

configu-ration A, which was executed using polystyrene with a 0.5-W

power dissipation Then, the calibrated model is used to predict

the effects of design changes on configurations A, B, C, D, E,

and F, with 1 W power dissipation These results are compared

to the measurement data shown in Figure 17

Step 1 In a mock-up for a design, measure the hotspot,

av-erage encasing and ambient temperatures

Measure-ments are presented for T h , T e , and T a Configuration

Figure 17 Comparison of measurements and predictions for configuration A with a 0.5-W power dissipation.

heat transfer engineering vol 31 no 6 2010

446 R STRIJK ET AL.

Figure 18 Comparison of measurements and predictions for configuration A, B, C, D, E, and F.

A uses polystyrene material for the encasing and sets

the calibration at 0.5 W For power dissipation, see

Figure 17

Step 2 Derive the steady-state temperature and time constant

X from the measurements The time constant for this

configuration has been derived and is given in Table 3:

X= 746 s

Step 3 Derive the thermal resistance The following values

for R and C are given in Table 4 and Table 5: R =

38 K/W and C= 20 J/K The following measurement

for thermal resistance R3 is derived from the average

steady-state encasing temperature (Figure 12): R3 =

(T e − T a )/q= 10 K/W The following measurement for

thermal resistance inside the configuration R2 results

from differences between R and R3: R2 = R − R3 =

28 K/W Finally, the following thermal resistance R1

will be set to equal infinity, since the model is calibrated

for a fully closed encasing, R1= ∞ K/W

Step 4 Calibrate the general equation The results of the

cali-brated model are shown in Figure 17 Since the model

is calibrated for a fully closed encasing, the following

matrix equation is used:

Step 5 Based on the calibrated model, predictions are made forall configurations with a power dissipation of 1.0 W Resultsare compared to measurements for a polystyrene encasingand given in Figure 18 A summary of the variables and valuesused in the predictions is given in Table 7 The predictionshave been completed using the following assumptions:

PS A-1.0 Predicted by changing levels of power dissipation q to

1.0 W

PS B-1.0 In this prediction, R1thermal resistance is added cause the configuration is open and dissipation to the am-

be-bient environment must be taken into account R1 is

es-timated by taking into account the top area A = 2.4 ×

10−2× 3 × 10−2 = 7.2 × 10−4 m2 of the hotspot and the

heat transfer coeffcient h c = 10 W/m2K: R1 = 1/(h c A)=

139 K/W

heat transfer engineering vol 31 no 6 2010

Table 7 Variables and values used in predictions

Variable PSA0.5 PSA1.0 PSB1.0 PSC1.0 PSD1.0 PSE1.0 PSF1.0

PS C-1.0 For these predictions, R1thermal resistance is added

because the configuration is open and dissipation to the

am-bient environment must be taken into account In this

con-figuration, five cooling fins have been added R1is estimated

using the surface area of the cooling fins A= 2 × 5 × 1 ×

10−2× 3 × 10−2= 3 × 10−3m2and h c= 10 W/m2K This

results in a thermal resistance of R1= 1/(h c A)= 33 K/W

PS D-1.0 For the following predictions, R1 thermal resistance

is added because the configuration is open and dissipation to

the ambient environment must be taken into account

Cool-ing fins are attached to the hotspot R1is therefore estimated

as having an area of A= 2 × 5 × 1 × 10−2× 3 × 10−2 =

3× 10−3 m2 For forced convection, a heat transfer

coeffi-cient h c= 100 W/m2-K is proposed The results for thermal

resistance are R1= 1/(h c A)= 3 K/W

PS E-1.0 For predictions, the R2thermal resistance is changed

because the hotspot is attached to the encasing Between

the hotspot and encasing a thermal conductive foil has been

used with a thermal conductivity of k = 0.9 W/m-K and a

thickness of x= 0.2 × 10−3m The surface area is the same

as in configuration PS B, A= 2.4 × 10−2× 3 × 10−2= 7.2

× 10−4m2, which results in thermal resistance R2= x/(kA)

= 0.3 ≈ 0 K/W

PS F-1.0 These predictions incorporate changes in R2because

a fan is added inside the mock-up A forced convection heat

transfer coefficient of 100 W/m2-K is therefore proposed

This results in a thermal resistance of R2 = 2.8 ≈ 3 K/W,

which is 10 times smaller than those proposed in

configura-tion A

CONCLUSIONS

In this article, three models have been proposed to help solve

specific issues in the thermal design of electronic products

Model 1 is regarded as generally valid for electronic

ucts used under normal conditions Exceptions include

prod-ucts that must work in extreme ambient conditions, such as

those operating at high altitudes, outdoors, or with specific

er-gonomic requirements regarding encasing temperatures

Impor-tant guidelines for applying this model include the realization

that it does not prevent occurrences of or solutions for local

hotspots Model 2 can compute hotspot temperature with an

ac-curacy of 20%, which is accurate enough to evaluate structural

concepts during early design stages However, this model onlydiscusses the heat path for one single hotspot and, therefore,cannot be generally applied to all products The need for de-velopment and verification of similar models with the ability tolocate several hotspots has been advised by several participantsduring interviews and is suggested for consideration in futureresearch Model 3 is seen as a valid method for approximatingtemperatures in steady-state situations, once boundary condi-tions have been calibrated using measurements obtained from

a thermal mock-up for a functional model Global thermal pacitance can be derived from measurements using the transientbehavior of a specific heat path by means of the unconstrainedminimization method However, the model does not supporttransient behavior for devices in which there are significant dif-ferences in time constants Completing a curve-fitting analysis

ca-using detailed RC networks is suggested.

β temperature coefficient of volume expansion, 1/K

ε emissivity of radiating surface

448 R STRIJK ET AL.

REFERENCES

[1] Smith, P., and Reinertsen, D., Developing Products in Half the

Time; New Rules, New Tools, Van Nostrand Reinhold, New York,

1998

[2] Weiser, M., The Computer for the 21st Century, Scientific

Ameri-can, vol 265, no 3, pp 94–104, 1991.

[3] Joshi, Y., Azar, K., Blackburn, D., Lasance, C., Mahajan, R., and

Rantala, J., How Well Can We Assess Thermally Driven

Reliabil-ity Issues in Electronic Systems Today? Summary of Panel Held

at the Thermal Investigations of ICs and Systems (Therminic),

Microelectronics Journal, vol 34, no 12, pp 1195–1201, 2002.

[4] Ishizuka, M., Hayama, S., and Iwasaki, H., Application of a

Semi-Empirical Approach to the Thermal Design of Electronic

Equipment, 7th Intersociety Conference on Thermal and

Thermo-mechanical Phenomena in Electronic Systems (ITHERM), May

23–26, Las Vegas, NV, pp 99–106, 2000

[5] Yazawa, K., and Bar-Cohen, A., Energy Efficient Cooling of

Note-book Computers, 8th Intersociety Conference on Thermal and

Thermomechanical Phenomena in Electronic Systems (ITHERM),

May 30–June 1, San Diego, CA, pp 785–791, 2002

[6] Strijk, R., de Deugd, J A G., and Vergeest, J S M., Passive or

Ac-tive Cooling: A Model for Fast Thermal Exploration of Electronic

Product Concepts, Thermal Challenges in Next Generation

Elec-tronic Systems II (THERMES II), January 13–16, pp 415–422,

Santa Fe, NM, Rotterdam, Millpress, 2007

[7] Strijk, R., Raangs, A., de Deugd, J A G., and Vergeest, J S M.,

Fast Thermal Exploration in the Preliminar Design of Electronic

Products, 16th International Conference on Engineering Design

(ICED), August 28–31, pp 39–40, Paris, France, 2007.

[8] Strijk, R., Conceptual Thermal Design, Ph.D thesis, Delft

Uni-versity of Technology, Faculty of Industrial Design Engineering,

Delft, Netherlands, 2008

[9] Strijk, R., de Deugd, J A G., and Vergeest, J S M., Quick

estimation of hotspot temperature and encasing temperature of an

electronic product, 19th National & 8th ISHMT-ASME Heat and

Mass Transfer Conference, January 3–5, Hyderabad, India, 2008.

[10] Strijk, R., Deugd, J A G de., and Vergeest, J S M., Simple

Thermal Modeling of Hotspot and Encasing Temperature of

Elec-tronic Product Designs, 19th National & 8th ISHMT-ASME Heat

and Mass Transfer Conference, January 3–5, Hyderabad, India,

2008

[11] Strijk, R., Vergeest, J S M., and Brezet, J C., Quick Estimation

of Temperature in Electronic Products, Proceedings of the 7th

International Symposium on Tools and Methods of Competitive

Engineering (TMCE), April 21–25, eds I Horv´ath and Z Rus´ak,

pp 691–704, Izmir, Turkey, 2008

[12] Remsburg, R., Thermal Design of Electronic Equipment, CRC

Press, Boca Raton, FL, 2001

[13] Karnopp, D., Margolis, D L., and Rosenberg, R C., System namics: A Unified Approach, John Wiley & Sons, New York,

Dy-1990

[14] Teertstra, P., Yovanovich, M M., and Culham, J R., Modeling

of Natural Convection in Electronic Enclosures, 9th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITHERM), June 1–4, Las Vegas, NV, pp 140–

149, 2004

[15] Infrared Services, Inc., Emissivity Values for Common Materials,

http://www.infrared-thermography.com, date of access April 29,2008

[16] Holman, J P., Heat Transfer, McGraw-Hill, Boston, 2002 [17] FLIR Systems, Thermacam researcherTM, http://www.flirther-mography.com, date of access April 29, 2008

Ruben Strijk is an assistant professor in the Design

Engineering research group at the Delft University

of Technology, Delft, The Netherlands He received his Ph.D in Industrial Design Engineering from the Delft University of Technology in 2008 His research interests involve thermal design, energy efficiency, and renewable energy applied to the field of design engineering.

Han Brezet is a professor of the Design for

Sustain-ability Program at the Delft University of Technology, Delft, The Netherlands He received his Ph.D in en- vironmental sociology from the Rotterdam Erasmus University in 1993 His research interests involve the developments of theory and tools that help industry to develop sustainable products and so improving prod- uct development in an ecological, economical, and sociological sense.

Joris Vergeest is an associate professor in the

Com-puter Aided Design and Engineering research group

at the Delft University of Technology, Delft, The Netherlands He received his Ph.D in experimental physics from the Radboud University Nijmegen in

1979 His research interests involve design ing with a main focus on computer-aided design.

engineer-heat transfer engineering vol 31 no 6 2010

Copyright
Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903408334

Correlation for Heat Transfer in

Nucleate Boiling on Horizontal

Cylindrical Surface

P K SARMA,1V SRINIVAS,2K V SHARMA,3and V DHARMA RAO4

1International Academic Affairs, GITAM University, Rushikonda, Visakhapatnam, India

2Department of Mechanical Engineering, GITAM University, Visakhapatnam, India

3Faculty of Mechanical Engineering, Universiti Malaysia Pahang, Pahang, Malaysia

4Department of Chemical Engineering, A.U College of Engineering, Visakhapatnam, India

This experimental investigation deals with nucleate boiling studies on horizontal cylindrical heating elements made out of

copper in the medium of Forane around atmospheric conditions The data could be successfully correlated with the system of

criteria employed by the authors in their earlier study of nucleate boiling process on cylindrical heating elements Inclusion

of the data from the present experimental study on Forane and that of other investigators yielded a comprehensive correlation

with an average deviation of 20% and standard deviation of 25% over a wide range of system pressures.

INTRODUCTION

Studies on nucleate boiling are quite extensive in the heat

transfer literature [1–31] Rohsenow and his co-investigators [4,

16, 17] in their pioneering studies proposed the correlation

The constant C sf in the correlation is an important

characteriz-ing parameter that varies with surface–liquid combination The

values of variable constants C sf, s, and r can be obtained from

heat transfer handbooks

Pioro et al [29, 30] concluded that Eq (1) is the best among

the existing correlations However, the constant C sf is to be

amended depending on the roughness factor and the liquid–

surface combination A modification of Eq (1) is presented by

The first two authors acknowledge the support received from Dr M V V S.

Murthi, President of GITAM University The financial support for the

procure-ment of experiprocure-mental setup received from TEQIP, World Bank, by the Centre

for Energy Studies, JNTU College of Engineering, is acknowledged.

Address correspondence to Dr P K Sarma, International Academic

Af-fairs, GITAM University, Rushikonda, Visakhapatnam 530045, India E-mail:

18, 19] are also useful for the estimation of nucleate boiling heattransfer coefficients Of these, the equations of Labuntsov [18,19] and Kruzhilin [1, 2], given respectively as

450 P K SARMA ET AL.

PRESENT ANALYSIS

In a recent paper, Sarma et al [31], making use of the

dimen-sionless criteria, developed a correlation valid for a wide range

of system conditions using the data of Borishansky et al [6]

The choice of dimensionless criteria is based on the analyses of

previous investigators wherever applicable From Rohsenow’s

[4] turbulent convective analogy, the modified Reynolds

num-berµq l∗

l h f gis considered a significant π parameter where l∗is the

characteristic length The choice of l∗ may be the diameter of

the emerging bubble i.e C σ

(ρl−ρv)g where the value of C can

be included in the constant of multiplication to be finally arrived

at in the dimensionless correlation

Mostinski [9] and Borishansky [15] suggested that a better

correlation can be achieved by introducing P P

cr as an importantthermodynamic consideration Hence, significance is given to

this ratio in the analysis

Tien et al [8] considered the nucleate boiling heat transfer

as inverted stagnation flow normal toward the wall Hence,δt

D

is considered as another important π group where δt is the

thickness of thermal boundary layer, which can be of the order

1.65

(6)and valid for the following ranges of parameters:

Fluid: water:

1 bar < P < 200 bar [P cr = 221 bar]

4.9 mm < D < 6.94 mm

260 mm < L < 262 mm

Material: 18% Ni, 8% Cr steel

Fluid: ethyl alcohol:

1 bar < P < 60 bar [P cr = 64 bar]

4.9 mm < D < 6.94 mm

Table 1 Specifications of the experimental setup

Material of the test surface Copper

Diameter of the test section 12.7 mm

Maximum permissible temperature 220 ◦C

260 mm < L < 300 mm

Material: 18% Ni, 8% Cr steel

It is observed that nucleate boiling experimental data with theForane–copper combination are not available in the literature.The present study is organized to evaluate whether the corre-lations commonly cited in nucleate boiling literature can beemployed to estimate the heat transfer coefficients for copper–Forane [R-141b] surface–liquid combination and for a widerange of system parameters

DESCRIPTION OF EXPERIMENTAL SETUP

Experiments are conducted on a prefabricated nucleate ing heat transfer test rig manufactured by M/s P A Hilton,

boil-UK The salient specifications of the equipment are mentioned

in Table 1 The schematic diagram of the test rig shown asFigure 1 consists of a thick walled glass chamber of 80 mmbore and 300 mm long The chamber houses the heating ele-ment with a condenser coil placed above the free surface of theliquid bulk The heating element is a 600-W cartridge heater

Figure 1 Schematic of the nucleate boiling test rig.

heat transfer engineering vol 31 no 6 2010

Table 2 Summary of ranges of experimental results in the present

study

Heat transfer coefficient 3.2 to 15.8 kW/m 2 − ◦C

swaged into the copper test section to dissipate heat flux

uni-formly The test section is a copper tube of diameter 12.7 mm

and length 42 mm with an effective surface area of 0.018 m2

The orientation of test section is horizontal The test section

is submerged in a pool of Forane (R-141b) liquid Over the

test surface, six thermocouples are preened at regular

inter-vals and the average of these values can be read with the aid

of digital temperature indicator A phase angle controller to

give infinitely variable heat input to the test section

accom-plishes the heating The heat transfer rate can be read from a

digital wattmeter The heat flux is calculated using the

rela-tion q = Q

πDL where Q is the wattmeter reading and D the

outer diameter of the tube The condenser located in the free

vapor space is made of 9 coils of nickel coated copper tube

with a total surface area of 0.032 m2 The condenser coil

con-denses the vapor produced by the test surface and the

conden-sate returns to the bottom of the chamber by gravity The

pres-sure in the chamber is controlled by varying the cooling water

flow rate to the condenser A glass thermometer is mounted

in the bulk of the liquid to measure the liquid bulk or

satu-ration temperature TB corresponding to the system pressure

The heat transfer coefficient is calculated from the equation

h = q(T w − T b) The unit can also be interfaced to a

com-puter and parameters like heat flux q, temperature difference

T , wall temperature T W , gauge pressure P g, and heat transfer

coefficient h automatically registered for various heat inputs

All measuring instruments are of class I type and the error

will not be more than±3% The surface roughness of the test

section is not available Extensive experimentation had been

done on the test rig and the summary of the range of

appli-cability is given in Table 2 The results obtained from the test

setup for various system pressures are tabulated as entries in

Table 3

CORRELATION OF THE DATA

In an attempt to validate the criteria proposed by the

authors, the data of Borishansky et al [6] along with

the present experimental data are shown plotted in

Fig-ure 2 The entire set of data comprising 575 points could

be successfully correlated by the following equation with

a standard deviation of 25% and average deviation of

Figure 2 Comparison of the experimental data of Borishansky et al [6] and present data with correlation using Eq (7).

20%:

q

µl h f g

σ(ρl− ρv )g = 5.02 × 10−7

1.25(7)

In general, the correlations of various authors indicate thatthe heat transfer coefficient is independent of the diameter ofthe tube Hence to check the possibility of correlating the data

in terms of the characteristic diameter of the bubble l∗, theexperimental data is subjected to regression analysis for thefollowing system of criteria:

heat transfer engineering vol 31 no 6 2010

(Continued on next page)

heat transfer engineering vol 31 no 6 2010

Table 3 Experimental data (Continued)

Note P S, system pressure; TW , wall temperature; T= (TW– TB); qw, wall heat flux; Tb, bulk temperature; and h, heat transfer coefficient.

COMPARISON OF DATA WITH CORRELATIONS OF

OTHER INVESTIGATORS

The present data are shown plotted with the often-cited

cor-relations on nucleate boiling None of the corcor-relations could

satisfactorily agree with the present data taken with the Forane–

copper combination However Rohsenow’s Eq (1) is shown

plotted along with the present data Figure 4 For the choice of

C sf = 0.0026, r = 0.33, and s = 2, the data could be correlated

satisfactorily These constants are quite close to the prescribed

values for the R113–copper combination as originally suggested

by Rohsenow and co-investigators [4, 16, 17] Similarly, Eq

(3) developed by Labuntsov [18, 19] revealed substantial

dis-agreement with the present data as shown in Figure 5 The

constant 0.075 in the equation when replaced with 0.0215 hasyielded better agreement with the data as shown in Figure 6.Equation (4) of Kruzhilin [1, 2] as postulated by their originalanalysis has deviated considerably from the present data Re-placing the constant in Eq (4) with 1.64, better agreement can

be observed, as is evident from Figure 7

SIGNIFICANCE OF THE NEW DIMENSIONLESS TERM

The significance of the dimensionless term ( PD

µlh1/2fg ) is shown

in Figure 8 and can be well understood by expanding it as aheat transfer engineering vol 31 no 6 2010

454 P K SARMA ET AL.

Figure 3 Comparison of the experimental data of Borishansky et al [6] and

present data with correlation using Eq (9).

product of three dimensionless π groups



(12)

is the modified Reynolds number Further, π2 denotes the

dy-namics of flow of the surrounding fluid during the bubble

Energy associated with dilation of the bubble interface

Latent heat of vaporization

µlh1/2fg ) gives the combined influence of dynamics

of the bubble growth with the thermal effects in the thermal

Figure 5 Comparison of present experimental data with Eq (3) of Labuntsov [18, 19].

heat transfer engineering vol 31 no 6 2010

Figure 6 Comparison of present experimental data with Eq (3) of Labuntsov

[18, 19] replacing constant 0.075 with 0.0215.

boundary layer adjacent to the wall, named the Kakac

num-ber in honor of Prof Sadic Kakac on his 75th birthday for

his contributions to the understanding of two-phase flow heat

transfer

Figure 7 Comparison of present experimental data with Eq (4) of Kruzhilin

[1, 2] replacing constant 0.082 with 1.64.

Figure 8 Physical meaning of Kakac number.

CONCLUSIONS

1 The d imensionless criteria employed by Sarma et al [31]

as given in Eq (5) could comprehensively satisfy the datafor a wide range of parameters The heat transfer coefficientcan be predicted from Eq (7) or Eq (9) in the experimentalrange:

Diameter: 5–12.7 mm

Fluids: water, ethyl alcohol, and Forane

Surfaces: stainless steel and copper

Ranges of pressure: water [1 < P < 200 bar], ethyl alcohol [1 < P < 60 bar], and Forane [1 < P < 2.5

of the π parameter given by Eq (10) excludes the necessity

of considering the surface roughness factor as an essentialconsideration in the nucleate boiling studies

3 The present experimental data on nucleate boiling with thecopper–Forane combination could be successfully correlated

by Eq (1) of Rohsenow by employing the values of variable

constants C sf = 0.0026, r = 0.33, and s = 2

4 The correlations of Labuntsov [18, 19] and Kruzhilin [1,2] could also be successfully correlated by suggesting con-stants of multiplication as 0.0215 and 1.84 in the respectiveequations

NOMENCLATURE

A* constant in Borishansky equation

b constant in Labunstov equationheat transfer engineering vol 31 no 6 2010

456 P K SARMA ET AL.

C sf variable constant in Rohsenow equation

C∗

sf variable constant in Pioro equation

C p specific heat at constant Pressure, J/kg-K

D outer diameter, m

g acceleration due to gravity, m/s2

h heat transfer coefficient, W/m2-K

hf g latent heat of vaporization, J/kg

k thermal conductivity, W/m−K

l* characteristic length,

σ (ρl−ρv )g

L length of the tube, m

m variable constant in Pioro equation

r variable constant in Rohsenow’s equation

s variable constant in Rohsenow’s equation

T temperature,◦C

V velocity of growth of the bubble, m/s

Psat pressure difference corresponding to degree of

[1] Kruzhilin, G N., Free Convection Transfer of Heat From a

Hori-zontal Plate and Boiling Liquid, Doklady AN SSSR (Rep USSR

Academy of Science), vol 58, no 8, pp 1657–1660, 1947 (in

Russian)

[2] Kruzhilin, G N., Generalization of Experimental Data on Heat

Transfer During Boiling of Liquid With Natural Convection (in

Russian), Izvestya AN SSSR, OTN (News of Academy of Sciences

of the USSR, /Division of Technical Sciences), no 5, 1949

[3] Zmola, P., Investigation of the Mechanism of Boiling in Liquids,

Ph.D Thesis, Purdue University, West Lafayette, IN, 1950

[4] Rohsenow, W M., A Method of Correlating Heat Transfer Data

for Surface Boiling of Liquids, Trans ASME, vol 74, pp 969–

976, 1952

[5] Foster, H K., and Zuber, N., Dynamics of Vapor Bubbles and

Boiling Heat Transfer, AIChE Journal, vol 1, pp 531–539,

1955

[6] Borishansky, V M., Bodrovich, B I., and Minchenko, F P., HeatTransfer During Nucleate Boiling of Water and Ethyl Alcohol, in

Aspects of Heat Transfer and Hydraulics of Two-Phase Mixtures,

ed S S Kutateladze, Govt Energy Publishing House, Moscow,

pp 75–93, 1961

[7] Berenson, P J., Experiments on Pool Boiling Heat Transfer, national Journal of Heat and Mass Transfer, vol 5, pp 985–999,

Inter-1962

[8] Tien, C L., A Hydrodynamic Model for Nucleate Pool Boiling,

International Journal of Heat and Mass Transfer, vol 5, pp 533–

540, 1962

[9] Mostinski, I L., Teploenergetika, vol 4, p 63, 1963 (English abstract in Br Chem Eng., vol 8, pp 580–588, 1963).

[10] Zuber, N., Nucleate Boiling: The Region of Isolated Bubbles and

the Similarity With Natural Convection, International Journal of Heat and Mass Transfer, vol 6, pp 53–78, 1963.

[11] Labuntsov, D A., Approximate Theory of Heat Transfer at

Ad-vanced Nucleate Boiling, Izv AN SSSR, Energetika I Transport,

vol 1, pp 58–71, 1963

[12] Labuntsov, D A., Kolchugin, B A., and Golovin, V A.,

Investiga-tion of nucleate Water Boiling Mechanism With Camera, in Heat Transfer in Elements of Power Installations, Nauka Publishing

House, Moscow, pp 156–166, 1966 (in Russian)

[13] Labuntsov, D A., General Relationships for Heat Transfer During

Nucleate Boiling of Liquids, Teploenergetika, vol 7, pp 76–84,

Crit-dynamic Similarity, in Problems of Heat Transfer and Hydraulics

of Two-Phase Media, Pergamon Press, New York, pp 16–37,

[17] Mikic, B B., Rohsenow, W M., and Griffith, P., On Bubble

Growth Rates, International Journal of Heat and Mass fer, vol 13, pp 657–666, 1970.

Trans-[18] Labuntsov, D A., Heat Transfer Problems With Nucleate

Boil-ing of Liquids, Thermal EngineerBoil-ing, vol 19 no 9, pp 21–28,

1972

[19] Labuntsov, D A., Problems of Heat Transfer at Nucleate Boiling,

Teploenergetika, no 9, pp 14–19, 1972.

[20] Stephan, K., and Abdelsalam, M., Heat-Transfer Correlations for

Natural Convection Boiling International Journal of Heat and Mass Transfer, vol 23, pp 73–87, 1980.

[21] Bennet, D L., Davis, M W., and Hertzler B L., The Suppression

of Saturated Nucleate Boiling by Forced Convective Flow, AICHE Symp Ser., vol 76, no 199, pp 91–103, 1980.

[22] Roy Chowdhury, S K., and Winterton, R H S., Surface Effects

in Pool Boiling, International Journal of Heat and Mass Transfer,

vol 28, pp 1881–1889, 1985

heat transfer engineering vol 31 no 6 2010

[23] Katto, Y., and Yokoya, S., Principal Mechanism of Boiling Crisis

in Pool Boiling, International Journal of Heat and Mass Transfer,

vol 11, pp 993–1002, 1968

[24] Dhir, V K., Nucleate and Transition Boiling Heat Transfer Under

Pool and External Flow Conditions, Proc 9th International Heat

Transfer Conference, Jerusalem, pp 129–155, 1990.

[25] Benjamin, R J., and Balakrishnan, A R., Nucleate Pool Boiling

Heat Transfer of Pure Liquids at Low to Moderate Heat Fluxes,

International Journal of Heat and Mass Transfer, vol 39, no 12,

pp 2495–2504, 1996

[26] Tong, L S., and Tang, Y S., Boiling Heat Transfer and Two-Phase

Flow, 2nd ed., Taylor & Francis, New York, 1997.

[27] Rohsenow, W M., Hartnett, J P., and Cho, Y I., (Eds.),

Hand-book of Heat Transfer, 3rd ed., McGraw-Hill, New York, 1998.

[28] Pioro, I L., Experimental Evaluation of Constants for the

Rohsenow’s Pool Boiling Correlation, International Journal of

Heat and Mass Transfer, vol 42, pp 2003–2013, 1999.

[29] Pioro, I L., Rohsenow, W M., and Doerffer, S S., Nucleate

Pool-Boiling Heat Transfer I: Review of Parametric Effects of

Boiling Surface, International Journal of Heat and Mass Transfer,

vol 47, pp 5033–5044, 2004

[30] Pioro, I L., Rohsenow, W M., and Doerffer, S S., Nucleate

Pool-Boiling Heat Transfer II: Assessment of Prediction

Meth-ods, International Journal of Heat and Mass Transfer, vol 47,

pp 5045–5057, 2004

[31] Sarma, P K., Srinivas, V., Sharma, K V., Subrahmanyam, T., and

Kakac, S., A Correlation to Predict Heat Transfer Coefficient in

Nucleate Boiling on Cylindrical Heating Elements, International

Journal of Thermal Sciences, vol 47, pp 347–354, 2008.

P K Sarma did his graduation at Govt Engineering

College, Kakinada, in A.P India Subsequently he did his Ph.D at Moscow Power Institute, Moscow, Russia He has been responsible for starting post- graduate courses in thermal engineering at Andhra University, India He has published more than

100 technical articles in various journals He has guided sixteen scholars for Ph.D programs and initiated industrial research at Andhra University.

He organized the ISHMT conference and sequently international symposiums on two-phase flow and heat trans-

sub-fer while he was at Andhra University He is presently the International

Director of Academic Affairs of GITAM University, Visakhapatnam, dia, taking care of academic exchange programs at the international level.

In-V Srinivas is an associate professor in the

depart-ment of mechanical engineering at GITAM sity, Visakhapatnam, India He received his Ph.D.

Univer-in energy systems from JNT University, Hyderabad, India His area of research is two-phase flow heat transfer and nanofluid heat transfer He is presently working on a project to develop nano-powder dis- persed lubricants.

K V Sharma is a professor in the Centre for

Energy Studies at Jawaharlal Nehru Technological University, College of Engineering, Hyderabad, In- dia He received the B.Tech degree in mechani- cal engineering at J.N.T.U College of Engineer- ing, Anantapur, India, M.E degree in heat trans- fer at Andhra University, Visakhapatnam, India, and Ph.D degree in heat transfer at Jawaharlal Nehru Technological University, Hyderabad, India

in 1982, 1985, and 2000, respectively His rent research interests include boiling and two-phase heat transfer, heat transfer augmentation, renewable energy conversion, and nanofluid heat transfer He is presently on foreign assignment to University Malaysia Pahang.

cur-V Dharma Rao is a professor in the chemical

engi-neering department of Andhra University at patnam in India He has guided six candidates to the doctoral degree He has published 50 papers in in- ternational journals with various co-authors He has participated as a co-principal investigator in a coop- erative research project funded by National Science Foundation, USA, with the University of Miami, De- partment of Mechanical Engineering He is member

Visakha-of the academic senate Visakha-of Andhra University.

heat transfer engineering vol 31 no 6 2010

Copyright
C Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903408383

A Parametric Study of an

Irreversible Closed Intercooled

Regenerative Brayton Cycle

BRIAN WOLF and SHRIPAD T REVANKAR

School of Nuclear Engineering, Purdue University West Lafayette, Indiana, USA

Entropy generation minimization technique is used in the analysis of an irreversible closed intercooled regenerative Brayton

cycle coupled to variable-temperature heat reservoirs Mathematical models are developed for dimensionless power and

efficiency for a multi-stage Brayton cycle The dimensionless power and efficiency equations are used to analyze the effects

of total pressure ratio, intercooling pressure ratio, thermal capacity rates of the working fluid and heat reservoirs, and the

component (regenerator, intercooler, hot- and cold-side heat exchangers) effectiveness Using detailed numerical examples,

the optimal power and efficiency corresponding to variable component effectiveness, compressor and turbine efficiencies,

intercooling pressure ratio, total pressure ratio, pressure recovery coefficients, heat reservoir inlet temperature ratio, and

the cooling fluid in the intercooler and the cold-side heat reservoir inlet temperature ratio are analyzed.

INTRODUCTION

Because of its high efficiency and more simple design the

high-temperature gas reactors (HTGR) technology currently

fa-vors a gas turbine or Brayton cycle generator The HTGR and

the gas turbine generator can be practically coupled in various

configurations In a typical Brayton cycle high-temperature and

high-pressure helium from the reactor core flows into the

tur-bine directly to rotate the turtur-bine by gas expansion, which in turn

drives the generator and compressors simultaneously to supply

electric power to the grid and to force the helium circulation in

the primary system As the temperature of the turbine exhaust

gas is still high, the recuperator is equipped to recover the

ex-haust energy, in which the cold helium from the high-pressure

compressor is preheated by the turbine exhaust gas The

tur-bine exhaust gas becomes low-pressure and low-temperature

helium after flowing through the recuperator and precooler The

obtained high-pressure and low-temperature helium enters the

other side of the recuperator to be preheated Finally the helium

flows into the reactor core again to be heated for repeating the

thermodynamic cycle

The ever-increasing demand for power generation and recent

concerns about greenhouse gas emissions have pushed

utili-Address correspondence to Professor Shripad T Revankar, School of

Nu-clear Engineering, Purdue University, West Lafayette, IN 47907, USA E-mail:

shripad@ecn.purdue.edu

ties to increase power output while also increasing efficiency.The Brayton cycle is one of the most important gas cycles forpower generation, as it has potential for high thermal efficiency.Many large stationary power plants make use of either single-

or multi-stage Brayton cycles Therefore, optimization of suchcycles is an important topic today The performance character-istic of a Brayton cycle in terms of thermal efficiency needs to

be optimized for particular design of the Brayton cycle sincethe thermal efficiency has a major impact on the operating cost.Several studies have been conducted to improve the thermalefficiency of a real Brayton cycle using some modified design[1–4] and intercooling [5, 6]

Power optimization studies of heat engines using finite timethermodynamics analysis were first introduced by Chambadal[7] and Novikov [8] in 1957 and 1958 Curzon and Ahlborn[9] extended the reversible Carnot cycle analysis to the endore-versible cycle by taking the irreversibility of finite-time heattransfer into account Since early 1980, research work on iden-tifying the performance bounds of thermal systems and opti-mizing thermodynamic processes and cycles has achieved largeprogress in both physics and engineering This optimization in-cludes finite-time, finite-rate, and finite-size constraints, nowknown as finite-time thermodynamics (FTT), endoreversiblethermodynamics, entropy generation minimization (EGM), orthermodynamic modeling and optimization The key idea here

is to bridge the gap between thermodynamics, heat transfer,and fluid mechanics and to thermodynamically optimize the

458

performance of real finite-time and/or finite-size

thermody-namic systems with the irreversibility of heat transfer, fluid flow,

and mass transfer toward decreasing the irreversibility of the

to-tal system [10–16] This theory of thermodynamic optimization

has been applied to performance analysis and optimization for

open and closed, simple and regenerated, constant- and

variable-temperature heat reservoirs and endoreversible and irreversible

Brayton (gas turbine) cycles [15, 17–19] The power, power

den-sity (ratio of power output to maximum specific volume in the

cycle), and efficiency were taken as the optimization objectives

The maximum power density (MPD) analysis as an

opti-mization criterion was introduced by Sahin et al [20] Using

the maximum power density criterion, they investigated

opti-mal performance conditions for reversible [20] and irreversible

[21] non-regenerative Joule–Brayton heat engines By

maxi-mizing the power density (the ratio of power to the maximum

specific volume in the cycle) the design parameters at

maxi-mum power density conditions were determined, which led to

smaller and more efficient Joule–Brayton engines than those

engines working at maximum power conditions Several other

investigators—Erbay et al [22], Erbay and Yavuz [23], Chen

et al [24], and Medina et al [25]—applied the maximum power

density criterion to the Ericsson, Stirling, Atkinson, and

regener-ative Joule–Brayton engines [22–25] In the analyses the

advan-tages of the MPD performance conditions in comparison to the

maximum power conditions in terms of thermal efficiency and

engine sizes were discussed Sahin et al [26] applied the

maxi-mum power density technique to the endoreversible Carnot heat

engine, which can be considered as a theoretical comparison

standard for all real heat engines in finite-time thermodynamics

and thus generalized the endoreversible MPD analyses results

Sahin et al [27] studied an internal irreversible

regenera-tive reheating Brayton cycle free of heat transfer irreversibility

using the maximum power density method Chen et al [28]

applied maximum power density of an endoreversible simple

Brayton cycle coupled to constant-temperature heat reservoirs

with only external heat transfer irreversibility and optimized

the distribution of the heat exchanger inventory Chen et al

[29] studied maximum power density performance of a closed

variable-temperature heat reservoirs endoreversible Brayton

cy-cle coupled with only external heat transfer irreversibility

In this paper, analysis of an irreversible regenerated closed

Brayton cycle with variable-temperature heat reservoirs is

con-sidered The optimization of this cycle is carried out using the

principles of EGM [11–15], where power is chosen as an

ob-jective function to obtain cycle parameters at which power and

the thermal efficiency are maximum The Brayton cycle

consid-ered has the heat transfer irreversibility in the hot- and cold-side

heat exchangers and the regenerator, the irreversible

compres-sion and expancompres-sion losses in the compressor and turbine, the

pressure drop loss at the heater, cooler, and regenerator as well

as in the piping, and the effect of the finite thermal capacity rate

of the heat reservoirs The significance of the variable reservoir

temperature is to assess the impact of the environmental

temper-ature on the cycle performance Analytical expressions on the

dimensionless power and efficiency are derived through modynamics analysis The effects of component (regenerator,intercooler, and hot- and cold-side heat exchangers) effective-nesses, compressor and turbine efficiencies, pressure recoverycoefficients, heat reservoir inlet temperature ratio, and coolingfluid in the intercooler and cold-side heat reservoir inlet temper-ature ratio on optimal power and its corresponding intercoolingpressure ratio, as well as optimal efficiency and its correspond-ing intercooling pressure ratio, are analyzed Especially, theintercooling pressure ratio is optimized for optimal power andoptimal efficiency, respectively

ther-THERMODYNAMIC ANALYSIS

The Brayton cycle is shown in Figure 1 The base case design

is an indirect single-shaft single turbine with two compressors,

an intercooler, a recuperator, a precooler, and a generator Theprimary and secondary loops are coupled through an interme-diate heat exchanger (IHX) Figure 2 shows the temperature–entropy (T-S) representation of the base case Brayton cycleprocess path 1–2–3–4–5–6–7–8–1 Processes 1–2 and 3–4 arenon-isentropic adiabatic compression processes in the low-and high-pressure compressors, while process 6–7 is the non-isentropic expansion process in the turbine Process 2–3 is anisobaric intercooling process in the intercooler with transfer of

Q I heat Process 4–5 is an isobaric absorbed heat (Q R)

pro-cess, and process 7–8 is an isobar evolved heat (Q R) process

in the recuperator Process 5–6 is an isobaric absorbed heat

(Q H) process in the IHX from primary coolant, and process

8–1 is an isobar evolved heat (Q L) process in the cold-side heatexchanger Processes 1–2s, 3–4s, and 6–7s are isentropic adia-batic processes representing the processes in the ideal low- andhigh-pressure compressors and ideal turbine, respectively.Assuming that the working fluid used in the cycle is an idealgas, and all heat exchangers are counterflow heat exchangers,

Figure 1 Base case closed intercooled, single shaft with recuperator and precooler indirect Brayton cycle coupled to high-temperature gas cooled reactor.

heat transfer engineering vol 31 no 6 2010

460 B WOLF AND S T REVANKAR

Figure 2 Temperature–entropy (T-S) diagram for base case Brayton cycle.

then the expressions for the transferred heat Q are given as:

Here C y (y = H, I, L, R) are the thermal capacity rates of

IHX (H), precooler (L), intercooler (I), and recuperator (R),

re-spectively C wf is the thermal capacity rate of the working fluid

U y is the heat exchanger thermal conductance (heat transfer

coefficient times the surface area) Figures 1 and 2 show

tem-perature locations The heat exchanger effectiveness terms E y

(6)

where C Xmin and C Xmax are the smaller and larger of the two

capacitance rates, C X and C wf and

N H1 = U H /C Hmin, N L1 = U L /C Lmin,

N R = U R /C wf , N I1 = U I /C Imin

C Xmin = min{C X , C wf }, C Xmax= max{C X , C wf },

x = H, I, L (7)The high-pressure compressor, low-pressure compressor, andturbine efficiencies are respectively given as

ηcL = (T 2s − T1) / (T2− T1) , η cH = (T 4s − T3) / (T4− T3) ,

ηt = (T6− T7) / (T6− T 7s) (8)The piping losses are taken account by defining the pressurerecovery coefficients as

D1 = P6/P4, D2= P1/P7 (9)

From thermodynamics the ratio of temperatures (x, y) and

pressures (π1, π) are defined as:

P = Q H − Q L − Q I

= C wf (T1− T2+ T3+ T6− T5− T8) (12)

η= P /Q H = 1 − (T8− T1+ T2+ T3)/(T6− T5) (13)Substituting Eqs (1)–(11) in Eqs (12) and (13), one canobtain power and efficiency as function of temperature ratios

(x, y) and pressure ratios (π1, π), pressure recovery coefficients

(D1, D2,), turbine and compressor efficiencies (ηt, ηcH, ηcL),

heat exchanger effectiveness (E y), heat exchanger thermal

con-ductance (U y), thermal capacity rate of fluid and heat exchangers(Cy), and working fluid thermal and transport properties (θ)

P = P (x, y, π1, π, D1, D2, η t , η cH , η cL , E y , U y , C y , θ)

(14)

η= η(x, y, π1, π, D1, D2, η t , η cH , η cL , E y , U y , C y , θ)

(15)heat transfer engineering vol 31 no 6 2010

By expressing the power as dimensionless power P =

P /C L T Lin and using Eqs (1)–(11), (12), and (14) the

dimen-sionless power is written as [30]:

ciency expression is given as [30]:

T H in /T Lin, and τ2= T I in /T Lin

RESULTS AND DISCUSSION

Here the results of the parametric study are first presented.The dependence of the dimensionless power and the efficiency

on the effectiveness of the regenerator, intercooler, and hot- andcold-side heat exchangers, the efficiencies of the compressor andturbine, the pressure recovery coefficients, the heat reservoir in-let temperature ratio, and the cooling fluid in the intercoolerand the cold-side heat reservoir inlet temperature ratio are pre-sented The intercooling pressure ratios corresponding to theoptimal power or efficiency are also presented

The characteristics of the dimensionless power (P ) and the

efficiency (η) versus total pressure ratio (π) and intercoolingpressure ratio (π1) were obtained for heat exchanger effective-

ness E H1 = E L1 = E I1 = 0.9, turbine and compressor ciencies ηt = ηc = 0.82, C wf = 1.0 kW/K ,D1 = D2 = 0.96,

effi-τ1 = 4.5, and τ2 = 1.0, and these are shown in Figures 3 and

4 When the total pressure ratio is fixed, there exists an optimal

intercooling pressure ratio that makes dimensionless power (P ) reach the optimal (P opt) Similarly, for fixed total pressure ratiothere exists an optimal intercooling pressure ratio that makes ηreach the optimal value ηopt If the total pressure ratio is notfixed and is variable, there exist an optimal total pressure ra-tio πP opt and an optimal intercooling pressure ratio π1P opt that

make (P ) reach the maximum (Pmax) Similarly with variabletotal pressure ratio, there exist an optimal total pressure ratioand an optimal intercooling pressure ratio that make η reach themaximum (ηmax)

Fixed Total Pressure Ratio

For fixed total pressure ratio, π= 9, and k = 1.4, C wf = 1.0kW/K, τ1= 4.33, and τ2= 1.00, the effects of heat exchanger

Figure 3 Dimensionless Brayton cycle power versus total pressure ratio and

intercooling pressure ratio with k = 1.4, ηt = ηc = 0.82,C wf = 1.0 kW/K,

τ 1 = 4.5, τ 2= 1,E H1= E L1= E I = 0.9.

heat transfer engineering vol 31 no 6 2010

462 B WOLF AND S T REVANKAR

Figure 4 Dimensionless Brayton cycle efficiency versus total pressure ratio

and intercooling pressure ratio with k= 1.4, ηt= ηc = 0.82,C wf= 1.0 kW/K,

τ 1= 4.5, τ = 1, E H1= E L1= E I = 0.9.

effectiveness E R and E I1 ,compressor and turbine efficiencies

ηc ,and ηt , and pressure recovery coefficients D1and D2on the

dimensional power and efficiency were studied The results of

these parametric studies are shown in Figures 5–8 These figures

show that the dimensionless power reaches the optimal values

rapidly, and then decreases steadily as π1increases from 1 to

π= 9.The dimensionless power and the efficiency increase with

increases in ER , E I1 ,η, ηc , D1, and D2

In Figure 5 the effect of E R on the dimensionless power

and efficiency is shown as function of intercooling pressure

ratio (π1) with E H1 = E L1 = E I1 = 0.9, ηt = ηc= 0.82, and

D1= D2= 0.96 The optimal dimensionless power is observed

for π1ranging from 2 to 3 for E R = 0 to 1.0 whereas the optimal

efficiency is observed for π1ranging from 1 to 3 for E R = 0 to

1.0 In Figure 6 the effect of E I1on dimensionless power and

efficiency is shown as function of intercooling pressure ratio

(π1) with E H1 = E L1 = E R1 = 0.9, ηt = ηc = 0.82, and

Figure 5 Dimensionless power (solid line) and efficiency (dashed line) as

function of intercooling pressure ratio and effectiveness of the recuperator for

for E I1= 0.7 to 1.0 The maximum optimal dimensional power

is 56% and optimal cycle efficiency is 38% at E I1= 1.0

In Figure 7 the effect of turbine and compressor efficiency onthe dimensionless power and efficiency is shown as function ofintercooling pressure ratio (π1) with E H1= E L1 = E R1 = E I1=

0.9 and D1= D2= 0.96 In this case the optimal dimensionalpower and optimal efficiency are observed for π1ranging from

1 to 3 for turbine and compressor efficiencies ranging from 0.85

to 1 The maximum optimal dimensional power is 98% andoptimal cycle efficiency is 57% if both turbine and compressorefficiencies are 100%

Figure 7 Dimensionless power (solid line) and efficiency (dashed line) as

function of turbine and compressor efficiencies for k = 1.4, π = 9, C wf = 1.0 kW/K, τ 1 = 4.5, τ 2 = 1, EH1 = EL1 = EI = ER = 0.9, and D1= D2 = 0.96.

heat transfer engineering vol 31 no 6 2010

Figure 8 Dimensionless power (solid line) and efficiency (dashed line) as

function of pressure recovery coefficients for k = 1.4, π= 9, C wf = 1.0 kW/K,

τ 1 = 4.5, τ 2 = 1, ηt= ηc = 0.82, and E H1= E L1= E I = E R= 0.9.

In Figure 8 the effect of pressure recovery coefficients D1

and D2on the dimensionless power and efficiency is shown as

function of intercooling pressure ratio (π1) with E H1 = E L1 =

E R1 = E I1 = 0.9, and ηt = ηc= 0.82 The optimal dimensional

power and optimal efficiency are observed for π1ranging from

2 to 3 for pressure recovery coefficients D1and D2ranging from

0.96 to 1.0 The maximum optimal dimensional power is 73%

and optimal cycle efficiency is 45% for D1 = D2= 1.0

Variable Total Pressure Ratio

From the parametric analysis the optimal values of

dimen-sionless power and optimal values of the efficiency were

ob-tained for given total pressure ratio (π) and unique value of

in-tercooling pressure ratio (π1) The optimal dimensional power

and optimal efficiency were then studied as a function of variable

total pressure

In Figure 9 the effect of E R on the optimal dimensionless

power and optimal efficiency as a function of total pressure

ra-tio π is shown for k = 1.4, C wf = 1.0 kW/K, τ1 = 4.5, τ2 =

1, η t = ηc = 0.82, and E H1 = E L1 = E I1 = 0.9 The figure

shows that there is a critical value of the total pressure ratio

π= 9 at which the optimal dimensional power is maximum

When the total pressure ratio is less than the critical value,

opti-mal dimensional power increases with increasing E R However,

when the total pressure ratio is greater than the critical value,

the optimal dimensionless power decreases with increasing E R

The optimal efficiency behaves in a similar fashion The large

total pressure ratio gives lower optimal dimensionless power

and optimal efficiency because when the total pressure ratio

is large the outlet temperature at the high-pressure ratio

com-pressor is higher than the outlet temperature at the turbines;

this leads to the lower heat transfer to the working fluid in the

(E I1) from 0.7 to 1.0 The maximum optimal dimensional power

is 59% and optimal cycle efficiency is 43% for E I1= 1.0.Figure 11 shows the effect of heat exchanger effectiveness

(E H I and E L1) on the optimal dimensionless power and optimal

efficiency as a function of total pressure ratio π for k = 1.4,

Figure 10 Optimal dimensionless power (solid line) and optimal efficiency (dashed line) as function of intercooling pressure ratio and effectiveness of the

intercooler for k= 1.4, ηt = ηc = 0.82, C wf = 1.0 kW/K, τ 1 = 4.5, τ 2 = 1,

E H1= E L1= E R = 0.9, and D1= D2 = 0.96.

heat transfer engineering vol 31 no 6 2010

464 B WOLF AND S T REVANKAR

Figure 11 Optimal dimensionless power (solid line) and optimal efficiency

(dashed line) as function of heat exchanger effectiveness E H1and E L1, for k=

1.4, ηt = ηc = 0.82, C wf = 1.0 kW/K, τ 1 = 4.5, τ 2 = 1, EI = ER= 0.9,

and D1= D2 = 0.96.

D1 = D2 = 0.96, C wf = 1.0 kW/K, τ1 = 4.5, τ2 = 1, ηt =

ηc = 0.82, and E I1 = E R = 0.9 In this case the optimal

dimensional power is observed for π ranging from 7 to 14 and

the optimal efficiency is observed for π ranging from 3 to 4 for

a range of effectiveness of the intercooler (E I1) from 0.8 to 1.0

The maximum optimal dimensional power is 66% and optimal

cycle efficiency is 46% for E H1 = E L1= 1.0

Figure 12 shows the effect of turbine and compressor

effi-ciencies (ηt and ηc) on the optimal dimensionless power and

optimal efficiency as a function of total pressure ratio π for k=

1.4, D1= D2= 0.96, C wf = 1.0 kW/K, τ1= 4.5, τ2= 1, and

Figure 12 Optimal dimensionless power (solid line) and optimal efficiency

(dashed line) as function of turbine and compressor efficiencies for k= 1.4,

C wf = 1.0 kW/K, τ 1 = 4.5, τ 2 = 1, E H1 = E L1 = E I = E R = 0.9, and

D1= D2 = 0.96.

Figure 13 Optimal dimensionless power (solid line) and optimal efficiency

(dashed line) as function of pressure recovery coefficients for k = 1.4, C wf = 1.0 kW/K, τ 1 = 4.5, τ 2 = 1, ηt= ηc = 0.82, and E H1= E L1= E I = E R= 0.9.

E H1 = E L1 = E I1 = E R = 0.9 The increases in turbine andcompressor efficiencies linearly increase the optimal power andoptimal efficiency The optimal dimensional power is observedfor π ranging from 8 to 15 and the optimal efficiency is observedfor π ranging from 3 to 4 for a range of turbine and compressorefficiencies from 0.85 to 1.0 The maximum optimal dimen-sional power is 95% and it occurs at the total pressure ratio of

15 and ηt = ηc= 1.0 The optimal cycle efficiency is 58% and

it occurs at the total pressure ratio of 4 and ηt = ηc = 1.0 It

should be noted that these maximum values of P optand ηoptaredue to assumed 100% turbine efficiency

Figure 13 shows the effects of pressure recovery

coeffi-cients D1 and D2 on the optimal dimensionless power andoptimal efficiency as a function of total pressure ratio π for

k = 1.4, C wf = 1.0 kW/K, τ1 = 4.5, τ2 = 1, ηt = ηc =

0.82, and E H1 = E L1 = E I1 = E R = 0.9 In this case theoptimal dimensional power is observed for π ranging from

7 to 9 and the optimal efficiency is observed for π ranging

from 3 to 4 for a range of pressure recovery coefficients D1

and D2 from 0.96 to 1.0 The maximum optimal dimensionalpower is 57% and maximum optimal cycle efficiency is 44% for

D1= D2= 1.0

Figure 14 shows the effect of cycle hot- and cold heat voir inlet temperature ratio τ1 on the optimal dimensionlesspower and optimal efficiency as a function of total pressure ra-

reser-tio π for k = 1.4,D1 = D2 = 0.96, C wf = 1.0 kW/K, τ2 = 1,

ηt = ηc = 0.82, and E H1 = E L1 = E I1 = E R = 0.9 For thiscase the optimal dimensional power is observed for π rangingfrom 7 to 13 and the optimal efficiency is observed for π rang-ing from 4 to 5 for range of τ1from 4.5 to 5.5 The maximumoptimal dimensional power is 85% and maximum optimal cycleefficiency is 49% for τ1= 5.5

heat transfer engineering vol 31 no 6 2010

Figure 14 Optimal dimensionless power (solid line) and optimal efficiency

(dashed line) as function of cycle heat reservoir inlet temperature ratio τ 1 , for

k = 1.4, D1 = D2 = 0.96, C wf = 1.0 kW/K, τ 2 = 1, ηt = ηc= 0.82, and

E H1= E L1= E I = E R= 0.9.

Figure 15 shows the effect of cooling fluid in the

inter-cooler and cold-side heat reservoir inlet temperature ratio τ2

on the optimal dimensionless power and optimal efficiency as a

function of total pressure ratio π for k = 1.4, D1 = D2 =

0.96, C wf = 1.0 kW/K, τ1 = 4.5, ηt = ηc = 0.82, and

E H1 = E L1 = E I1 = E R = 0.9 The optimal power and

optimal efficiency decrease with increase in the value of τ2.

The optimal dimensional power is observed for π ranging from

6 to 8 and the optimal efficiency is observed for π ranging from

3 to 4 for range of τ2from 1 to 1.6 The maximum optimal

di-Figure 15 Optimal dimensionless power (solid line) and optimal efficiency

(dashed line) as function of cooling fluid in the intercooler and cold-side heat

reservoir inlet temperature ratio τ 2, for k = 1.4, D1= D2= 0.96, C wf = 1.0

kW/K, τ 1 = 4.5, ηt= ηc = 0.82, and E H1= E L1= E I = E R= 0.9.

mensional power is 85% and maximum optimal cycle efficiency

is 49% for τ1= 5.5

Figures 9–15 show that the optimal dimensionless power

as a function of total pressure ratio π increases rapidly with

π with a maximum value of optimal dimensionless power

at an optimal total pressure ratio These figures also cate that the optimal dimensionless power increases with the

indi-E H1 , E L1 , E I1, E R , D1, D2, τ1, η t, and ηcand it decreases with

τ2.The optimal efficiency shows characteristics similar to those

of optimal dimensionless power as a function of π, E H1 , E L1 ,

E I1, E R , D1, D2, τ1, τ2, η t, and ηc

CONCLUSIONS

Power and thermal efficiency optimization of an irreversibleclosed Brayton cycle coupled to variable temperature heat reser-voirs was carried out using EGM For optimization, cycle powerwas used as an objective function to obtain cycle parameters Ananalytical expression for the dimensionless power and efficiency

of the cycle were derived The intercooling pressure ratio wasoptimized for the optimal dimensionless power and the optimalefficiency, respectively The parameters studied were the effec-tiveness of regenerator, intercooler, and hot- and cold-side heatexchangers, the compressor and turbine efficiencies, the pres-sure recovery coefficients, the heat reservoir inlet temperatureratio, the cooling fluid in the intercooler and the cold-side heatreservoir inlet temperature ratio, and the intercooling pressureratio

The numerical results showed that for fixed total pressureratio there exists an optimal dimensionless power for a uniquevalue of intercooling pressure ratio For variable total pressureratio, there exist an optimal total pressure ratio and an optimalintercooling pressure ratio that make dimensionless power reachthe maximum The optimal dimensional power density and op-timal cycle efficiency increase with increase in the effectiveness

of the heat exchangers (regenerator, intercooler, and hot andcold side), turbine efficiencies, intercooling pressure ratios, andthe heat reservoir inlet temperature ratio But the optimal dimen-sional power and optimal efficiency decrease with increase inthe cooling fluid in the intercooler and the cold-side heat reser-voir inlet temperature ratio The highest values of optimal powerdensity and efficiency can be obtained for cycle heat reservoirinlet temperature ratio greater than 5.5

NOMENCLATURE

C H , C L thermal capacity rates of high- and

low-temperature heat reservoirs

C I thermal capacity rate of cooling fluid in

inter-cooler

C wf thermal capacity rate of working fluid (mass

flow rate and specific heat product)heat transfer engineering vol 31 no 6 2010

466 B WOLF AND S T REVANKAR

D1, D2, pressure recovery coefficients

E H1 , E L1 effectiveness values of hot- and cold-side heat

exchangers

E R effectiveness of regenerator

E I1 effectiveness of intercooler

HPC high-pressure compressor

IHX intermediate heat exchanger

k ratio of specific heats

LPC low-pressure compressor

MPD maximum power density

N H1, N L1 number of heat transfer units of hot- and

cold-side heat exchangers

N I1 number of heat transfer units of intercooler

N R number of heat transfer units of regenerator

p1, , p6 pressures at working states 1, 2, 3, 4, 5, 6

P power

P dimensionless power

P opt optimal dimensionless power

Q H rate at which heat is transferred from heat source

to working fluid

Q L rate at which heat is transferred from working

fluid to heat sink

Q R rate of heat regenerated in the regenerator

Q I rate of heat rejected from working fluid to

cool-ing fluid in intercooler

T1, , T8 temperature at states of 1, 2, 2s, 3, 4, 4s, 5, 6,

6s, 7, 8

T H in , T H out inlet and outlet temperatures of heating fluid

T Lin , T Lout inlet and outlet temperatures of cooling fluid

T I in , T I out inlet and outlet temperatures of cooling fluid in

intercooler

U H , U L conductances of hot- and cold-side heat

ex-changers (heat transfer surface area and heat

transfer coefficient product)

U R conductance of regenerator

U I conductance of intercooler

x working fluid isentropic temperature ratio for

low-pressure compressor

y working fluid isentropic temperature ratio for

whole-cycle pressure ratio

1, , 8 working states

Greek Symbols

ηc , η t compressor and turbine efficiencies

η efficiency

ηopt optimal efficiency

π total pressure ratio

π1 intercooling pressure ratio

τ1 cycle hot and cold heat reservoir inlet

tempera-ture ratio

τ2 cooling fluid in the intercooler and cold-side

heat reservoir inlet temperature ratio

REFERENCES

[1] Erbay, L B., Go `Ektun, S., and Yavuz, H., Optimal Design of theRegenerative Gas Turbine Engine With Isothermal Heat Addition,

Applied Energy, vol 68, pp 249–269, 2001.

[2] Go `Ektun, S., and Yavuz, H., Thermal Efficiency of a Regenerative

Brayton Cycle With Isothermal Heat Addition, Energy sion and Management, vol 40, pp 1259–1266, 1999.

Conver-[3] Kaushik, S C., Tyagi, S K., and Singhal, M K., ParametricStudy of an Irreversible Regenerative Brayton Heat Engine With

Isothermal Heat Addition, Energy Conversion And Management,

vol 43, pp 2013–2025, 2003

[4] Vecchiarelli, J., Kawall, J G., and Wallace, J S., Analysis of

a Concept for Increasing the Efficiency of a Brayton Cycle via

Isothermal Heat Addition, International Journal of Energy search, vol 21, pp 113–127, 1997.

Re-[5] Cheng, C Y., and Chen, C K., Maximum Power of an

Endore-versible Intercooled Brayton Cycle, International Journal of ergy Research, vol 24, pp 485-494, 2000.

En-[6] Wang, W., Chen, L., Sun, F., and Wu, C., Performance sis of an Irreversible Variable Temperature Heat Reservoir Closed

Analy-Intercooled Regenerated Brayton Cycle, Energy Conversion agement, vol 44, pp 2713–2732, 2003.

Man-[7] Chambadal, P., Les Centrales Nucl´eaires, Armand Colin, Paris,

pp 41–58, 1957

[8] Novikov, I I., The Efficiency of Atomic Power Stations (A

Re-view), Journal of Nuclear Energy, pp 125–132, 1958.

[9] Curzon, F L., and Ahlborn, B., Efficiency of a Carnot Engine at

Maximum Power Output, American Journal of Physics, vol 43,

pp 22–26, 1975

[10] Bejan, A., Tsatsaronis, G., and Moran, M J., Thermal Design and Optimization, Wiley, New York, 1996.

[11] Andresen, B., Finite-Time Thermodynamics, Physics Laboratory

II, University of Copenhagen, Copenhagen, Denmark, 1983

[12] Sieniutycz, S., and Salamon, P., Eds., Advances in ics: Finite-Time Thermodynamics and Thermoeconomics, vol 4,

Thermodynam-Taylor & Francis, New York, 1990

[13] Bejan, A., Entropy Generation Minimization, CRC Press, Boca

[16] Berry, R S., Kazakov, V., Sieniutycz, S., Szwast, Z., and Tsirlin,

A M., Thermodynamic Optimization of Finite-Time Processes,

Wiley, New York, 2000

[17] Cheng, C Y., and Chen, C K., Efficiency Optimizations of an

Irreversible Brayton Heat Engine, Trans ASME Journal of Energy Research Technology, vol 120, pp 143–148, 1998.

[18] Radcenco, V., Vergas, J V C., and Bejan, A., ThermodynamicOptimization of a Gas Turbine Power Plant With Pressure Drop

Irreversibilities, Trans ASME Journal of Energy Research nology, vol 120, pp 233–240, 1998.

Tech-[19] Chen, L., Zheng, J., Sun, F., and Wu, C., Power Density Analysisand Optimization of a Regenerated Closed Variable Temperature

Heat Reservoir Brayton Cycle, Journal of Physics D: Applied Physics, vol 34, pp 1727–1739, 2001.

heat transfer engineering vol 31 no 6 2010

[20] Sahin, B., Kodal, A., and Yavuz, H., Efficiency of a Joule–Brayton

Engine at Maximum Power Density, Journal of Physics D:

Ap-plied Physics, vol 28, pp 1309–1313, 1995.

[21] Sahin, B., Kodal, A., Yilmaz, T., and Yavuz, H., Maximum Power

Density Analysis of an Irreversible Joule–Brayton Engine,

Jour-nal of Physics D: Applied Physics, vol 29, pp 1162–1167, 1996.

[22] Erbay, L B., Sisman, A., and Yavuz, H., Analysis of Ericsson

Cycle at Maximum Power Density Conditions, ECOS’96,

(Stock-holm 25–27 June 1996), pp 175–178, 1996

[23] Erbay, L B., and Yavuz, H., Analysis of the Stirling Heat Engine

at Maximum Power Conditions, Energy, vol 22, pp 645–650,

1997

[24] Chen, L., Zheng, J., Sun, F., and Wu C., Efficiency of an

Atkin-son Engine at Maximum Power Density, Energy Conversion and

Management, vol 39, pp 337–341, 1998.

[25] Medina, A., Roco, J M M., and Hernandez, C., Regenerative

Gas Turbines at Maximum Power Density Conditions, Journal of

Physics D: Applied Physics, vol 29, pp 2802–2805, 1996.

[26] Sahin, B., Kodal, A., and Yavuz, H., Maximum Power Density

Analysis of an Endoreversible Carnot Engine, Exergy, The

Inter-national Journal of, vol 21, pp 1219–1225, 1996.

[27] Sahin, B., Kodal, A., and Kaya, S S., A Comparative

Perfor-mance Analysis of Irreversible Regenerative Reheating Joule–

Brayton Engines Under Maximum Power Density and Maximum

Power Conditions, Journal of Physics D: Applied Physics, vol 31,

pp 2125–2131, 1998

[28] Chen, L., Zheng, J., Sun, F., and Wu, C., Optimal Distribution

of Heat Exchanger Inventory for Power Density Optimization of

An Endoreversible Closed Brayton Cycle, Journal of Physics D:

Applied Physics, vol 34, pp 422–427, 2001.

[29] Chen, L., Zheng, J., Sun, F., and Wu, C., Performance Comparison

of an Endoreversible Closed Variable-Temperature Heat Reservoir

Brayton Cycle Under Maximum Power Density and Maximum

Power Conditions, Energy Conversion and Management, vol 43,

pp 33-43, 2002

[30] Revankar, S T., and Wolf, B., Thermodynamic Analysis of a rect Closed Loop Brayton Cycle Coupled to a High-TemperatureGas Cooled Reactor, Purdue University Report, PU-NE/6-04,2006

Di-Brian Wolf is a graduate student pursuing a Ph.D in

nuclear engineering at Purdue University He received his B.S and M.S in nuclear engineering from the School of Nuclear Engineering, Purdue University,

in 2005 and 2007, respectively For his M.S thesis

he carried out analysis of a molten carbonate fuel cell coupled to a gas turbine His current interests are

in the Brayton cycle, multi-phase heat transfer, and steam generator tube integrity assessment.

Shripad T Revankar is a professor of nuclear

engi-neering and director of the Multiphase and Fuel Cell Research Laboratory in the School of Nuclear Engi- neering at Purdue University He received his B.S., M.S., and Ph.D in physics from Karnatak University, India, M.Eng in nuclear engineering from McMas- ter University, Canada, and postdoctoral training at Lawrence Berkeley National Laboratory and at the Nuclear Engineering Department of the University

of California, Berkeley, from 1984 to 1987 His search interests are in the areas of nuclear reactor thermal hydraulics and safety, multiphase heat transfer, multiphase flow in porous media, instrumentation and measurement, fuel cell design, simulation and power systems, and nuclear hy- drogen generation He has published more than 200 technical papers in archival journals and conference proceedings He is currently chair of the ASME K-13 Committee, executive member of the Transport and Energy Processes Division

re-of American Institute re-of Chemical Engineers, and chair re-of the Nuclear and diological Division of the American Society for Engineering Education He has served as chair of the Thermal Hydraulics Division of the American Nuclear

Ra-Society He is on the editorial board of the following journals: Heat Transfer

Engineering, International Journal of Heat Exchangers, Journal of namics, and ASME Journal of Fuel Cell Science and Technology He is a fellow

Thermody-of the ASME.

heat transfer engineering vol 31 no 6 2010

Copyright
C Taylor and Francis Group, LLC

ISSN: 0145-7632 print / 1521-0537 online

DOI: 10.1080/01457630903409605

Conjugate Heat Transfer Analysis

in the Trailing Region of a Gas

Turbine Vane

N KULASEKHARAN and B V S S S PRASAD

Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India

Conjugate heat transfer calculations are performed on cambered converged channels with and without pin fins, simulating

the trailing region internal cooling passages of a gas turbine vane Simulations are carried out for an engine representative

Reynolds number of 20,000, based on the hydraulic diameter at the entry of coolant channel The effect of conjugation is

brought out by varying the solid to fluid thermal conductivity ratio from 7 to 16,016 The interaction between the complex flow

pattern and conjugate heat transfer is highlighted The local values of pressure, wall and fluid temperature, area-averaged

values of friction factor, and Nusselt number of the smooth and pinned channels are compared.

INTRODUCTION

The continuing thrust toward higher thermal efficiencies of

gas turbines has resulted in a continuous increase of the turbine

inlet temperature (TIT) As a result of this trend, even industrial

gas turbines with TIT of 1500◦C, such as those used in combined

cycle power plants, are being manufactured; more recently, a

TIT of 1700◦C is contemplated Prediction of life of the blades

needs a better understanding of the heat loads at various parts

of the blade, which in turn requires reliable tools to predict

the temperature distribution within the precision limits In this

context, the prediction of internal and external heat transfer

coefficients and metal temperature distribution for the chosen

cooling scheme of a gas turbine nozzle guide vane assumes

significance

Although the gas-side convection depends upon the complex

external flow and boundary layer development, the internal

con-vection heat transfer coefficient widely varies with the scheme

of cooling employed The major concern of this paper is to

esti-mate the flow and heat transfer characteristics for the internally

cooled curved channel in the trailing edge region of the gas

tur-bine vane Cooling by short pin-fin arrays is commonly adopted

in the trailing edge region Increasing the internal surface area

and increasing the consequent flow disturbances generated due

Address correspondence to Prof B V S S S Prasad, Thermal

Turboma-chines Laboratory, Department of Mechanical Engineering, Indian Institute of

Technology Madras, Chennai–600036, India E-mail: prasad@iitm.ac.in

to cross flow past the pin-fin array are the predominating anisms for the increased heat transfer in this region

mech-In order to assess the heat transfer from the pin-fin bly to the coolant fluid, a realistic temperature distribution ofthe pins is essential The quantity of heat transferred from thepins to the internal cooling fluid may be conventionally com-puted by assuming a heat transfer coefficient from the textbookcorrelations with prescribed constant temperature or heat flux

assem-as boundary conditions at the pin surfaces and pin bassem-ase Thisapproach has two major disadvantages First, the actual compu-tation of heat transfer from the pin depends on the knowledge ofthe pin-base temperature/heat flux, which is not available Sec-ond, the temperature of the pin surface depends on the details ofthe flow and thermal characteristics of the coolant past the pins.These, in turn, partly depend on the juncture flow at the pin andpressure side (PS)/suction side (SS) intersections Heat trans-fer correlations in such complex flow situations are not readilyavailable Therefore, the assessment of heat transfer rate and pinsurface temperature is essentially a conjugate thermal problem.Recent studies of Kusterer et al [1] and Mazure et al [2]emphasized the need for conjugate heat transfer analysis for ac-curate predictions of metal temperatures in cooled gas turbinevanes Basic conjugate heat transfer studies on flat plates werereported by several investigators [3–5] The important param-eters identified to influence the heat transfer coefficient under

the condition of conjugation are the conductivity ratio k s /k f,Prandtl number, and plate axial distance to thickness ratio.The convection flow on the surfaces experiencing the pressure

468

gradient (e.g., circular cylinder) and the conjugate heat transfer

from such surfaces are a strong function of the pressure

vari-ation [6, 7] The conjugate heat transfer in the trailing edge

region involves coupling of conduction in the blade wall and the

cylindrical pin faces with convection around them The

convec-tion in the trailing region pin-fin channels is in itself a complex

problem due to the cambered and converged channel shape and

turned flow through the pin-fin array

In the present work, importance is given to estimating

the pressure and heat transfer variations in such cambered–

converged channels and to studying the effect of conjugation

PHYSICAL MODEL

Figure 1a shows the schematic diagram of a cooled gas

tur-bine vane The coolant channels were formed by dividing the

internal cavity of the vane by thin radial walls The leading

channels (LC1and LC2) normally have rib turbulated and/or

im-pingement cooling Although the trailing region channels (TC)

may also have rib turbulators along with pin-fin arrays, they

Figure 1 Schematic of cooled gas turbine vane.

Figure 2 Trailing region coolant channel formation.

are not considered in the present work for the sake of ity Coolant enters the cooling channel as shown in Figure 1bthrough the inlet at the top to the unobstructed portion of thechannel (portion A), takes a 90-degree turn toward the pin-finchannel (portion B), and ejects out finally through the trailingedge slot The pin-fin array is described by the pin diameter,height, and the spanwise and streamwise spacing Because ofthe narrow trailing region for the most of the turbine blades, theheight-to-diameter ratio of the pins is typically of the order ofunity, causing strong flow interactions between the pin fin andblade walls, at the pin endwall junctions

simplic-For the purpose of present analysis, a cambered and verged channel is constructed by choosing the symmetricalNACA0012 as the base profile (Figure 2a), between the 30% to90% axial chord locations (Figure 2b) A constant-radius cam-ber curve with a radius of unity, similar to that of a practicalturbine vane, is chosen (Figure 2c) The thickness distribution

con-of the NACA0012 prcon-ofile, between the chosen axial chord, ismapped onto this camber curve to have the trailing region cool-ing channel profile (Figure 2d)

This profile is then scaled up and extruded in the third mension to form the smooth fluid channel domain The channel

di-camber length to channel height ratio (l c / h d) is 1.2 and the

channel leading edge width to the camber length ratio (w le / l c)

is 0.2 The solid thickness t is then added to the coolant channel thus formed with a thickness to pin diameter ratio of (t/d) of

0.22, to conduct the conjugate heat transfer analysis of smoothchannels The staggered uniform array of cylindrical pins ismodeled and incorporated in the smooth channel, between theconvex and concave walls, to create the pin-finned channel Theheat transfer engineering vol 31 no 6 2010