International Journal of Computer and Electrical Engineering, Vol. 5, No. 3, June 2013

291DOI: 10.7763/IJCEE.2013.V5.715

Abstract—A heat pipe optimization is known as a difficult

one because design variables have nonlinear interaction one

another and multiple constraints are involved. it is unsuitable to

Gradient-based methods. The object of present study is to

optimize the design variables of the heat pipe for a space

application using an evolutionary method.

In this study, Particle Swarm Optimization(PSO) method,

simple heuristic search method, is used to estimate variables

and improve search efficiency. The heat pipe configuration is

optimized regarding to seven parameters, such as diameter of

vapor core, thickness of wick, etc., and eighteen constraints

including operational, dimensional, and structural ones.

To verify the performance of the PSO method, a minimum

total mass estimation and searching efficiency are compared

with results obtained by generalized extremal

optimization(GEO). It is proven that PSO found optimized

solutions effectively than GEO for simultaneous estimation of

multi-parameters.

Index Terms—Optimization design, PSO (Particle Swarm

Optimization), heat pipe, mesh wick.

I. INTRODUCTION

Heat pipe, simple tube-shaped heat transfer device, is

using for cooling device of micro-semiconductor to huge oil

pipeline due to high heat transfer efficiency, light weight and

setup simplicity[1], Lately, it is important to decrease

manufacturing cost by design optimization for special

environment like satellite, space shuttle, and so on[2].

It is not suitable to optimize heat pipe configuration by

gradient-based method because nonlinear equation should be

solved for heat pipe design and several constraints should be

considered on heat pipe shape. Instead, stochastic algorithm

is effective for solving nonlinear problem like the heat pipe

design optimization[3]. Chengbin Zhang, et al. optimized

wick shape of heat pipe using NPGA(Niched Pareto Genetic

Algorithmes) which is modified GA(Genetic Algorithm)[4].

Fabiano L. S. et al. used GEO(Generalized Extremal

Optimization), one of stochastic algorithms, to estimate

minimum mass of mesh wick heat pipe[5].

In this study, for increasing searching efficiency,

PSO(Particle Swarm Optimization) method is applied to

obtain configuration variable for minimizing mass of heat

pipe. Optimization procedure is performed to investigate

multiple design factors, those determine shape of heat pipe

using methanol for working fluid with mesh type wick.

II. PARTICLE SWARM OPTIMIZATION

It is mimicked that bird flock find new area for nesting to

develop PSO(Particle Swarm Optimization) algorithm by

Kennedy and Eberhart[6]. PSO modifies its existing solution

referring personal best value and global best value, otherwise

Genetic Algorithm discards existing solution after creating

new value from existing value. This PSO algorithm is carried

out by below procedure.

1) Generating initial value of particles randomly in limit of

range of solution

2) Renewing velocity vector of each particle

1 1 1 2 2

i i i i g i

k k k k k kv wv c r p x c r p x (1)

3) Renewing value of each particle

1 1

i i i

k k kx x v (2)

x is position(value) of a particle. v is velocity vector of a

particle. Superscript is number of particle and subscript

means iteration step. p is best value up to now. Superscript g

represents the whole particles, swarm (global). Coefficient w,

c1 and c2 are inertia factor, self-confidence factor and swarm

confidence factor, respectively. Those determine how much

are each term considered. r1 and r2 is random value in 0 to 1

changing influence of personal best value and global best

value at each step. Therefore, vik+1, new velocity of i-th

particle, reflects existing velocity vik and distance (difference)

between xik, its existing position, and personal best value pi

k

and global best value pgk respectively. New position value of

particle is calculated by sum of existing position value xik and

new velocity vector vik+1. After renewing value of a particle,

personal best value pik and global best value pg

k are renewed

by comparing new and old value. Step 2) and 3) are repeated

while renewed pgk satisfy given condition of solution.

Genetic algorithm is relatively complex because it should

realize selection, crossing and mutation. As same reason, it

takes long time to find optimum solution. However, PSO is

composed by just two equations which are tracking a particle

that approach close to real solution, so it is simple and

effective to search the value [7].

III. HEAT PIPE

Heat pipe is confined pipe filled with working fluid. Wick

is installed in the pipe that liquid can flow in the wick.

Because heat is transferred by latent heat of working fluid,

heat pipe can transfer much more heat than normal metal pipe

or beam. Heat pipe has advantage to separate high

A Study on Heat Pipe Optimization Using PSO

Kwonho Kim, Kyun Ho Lee, and Seung Wook Baek

Manuscript received October 19, 2012; revised November 24, 2012

Kwonho Kim and Sung Wook Baek are with the Aerospace engineering,

KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea

(e-mail: bloodyred@kaist.ac.kr, swbaek@kaist.ac.kr).

Kyun Ho Lee is with the Department of Aerospace Engineering, Sejong

University, 98 Gunja-dong, Gwangjin-gu, Seoul 143-747, Republic of

Korea(e-mail: khlee0406@sejong.ac.kr).

temperature part and low temperature part due to its

tube-shape. Also, it is simple to install heat pipe despite

limitation of installing space.

Usual heat pipe contacts its each end with high

temperature part and low temperature part. When heat pipe is

heated up at high temperature part, in other words, evaporator

part, working fluid in wick evaporates and pressurizes heat

pipe end of high temperature part. As the result, vaporized

working fluid moves on to low temperature part that is also

called condenser part. At condenser part, working fluid

condenses with putting the heat out. Liquefied working fluid

returns to evaporator part by capillary effect. The heat is

transferred from high temperature part to low temperature

part in this recurrent process.

In this research, seven configuration variables are

optimized to minimize mass of heat pipe that can transfer

desired heat loads with given environment temperature. The

seven configuration variables are mesh number of wick (N),

diameter of wick wire(d), vapor core diameter(dv), thickness

of wick(tw), length of evaporator section(Le), length of

condenser section(Lc) and thickness of pipe wall(tt). Length

of adiabatic section is supposed 0.5m to compare with result

of previous research. In optimization procedure, total mass of

heat pipe is set for objective function. The total mass is sum

of mass of container(mcont), wick(mwd), liquid in wick(mwl)

and vapor in vapor core(mvapor).

total cont wd wl vaporm m m m m (3)

When desired heat load (Q) and temperature of condenser

section are given, seven configuration variables have

eighteen constraints [8].

1: ,c g

c c

l v eff

P PG Q Q Q

F F L

(4)

,min ,max2: so so soG T T T (5)

2 23: ,

ln

e e vb b c

v i v n

L k TG Q Q Q P

d d r

(6)

0.52

,

4 : ,4 2

v ve e

r h

dG Q Q Q

r

(7)

4

5 : ,256

v v vv v

v eff

d PG Q Q Q

L

(8)

3

86 : 0.2,v v

v v v v

QG M M

d R T (9)

47 : Re 2300,Rev v

v v

QG

d (10)

8:0.0001 0.9999G (11)

9 : 2 wG d t (12)

10:314 15000G N (13)

3 311:0.025 10 1.0 10G d (14)

3 312:5.0 10 80.0 10vG d (15)

3 313:0.05 10 10.0 10wG t (16)

3 314:50.0 10 400.0 10eG L (17)

3 315:50.0 10 400.0 10cG L (18)

3 316:0.3 10 3.0 10tG t (19)

2 2

2 217 :

4

o i ts

o i

P d d uG

d d

(20)

3 3

3 3

218 :

42

o i ts

o i

P d d uG

d d

(21)

G1 to G7, constraints caused by operation characteristic of

heat pipe are called operational limit (8). G8 to G16 are

dimensional limit which occur by limitation of installing

space. Last two conditions are structural limitation to prevent

design that would lead to a burst of the tube

IV. RESULT

In this research, optimization is conducted for stainless

steel (SS304) heat pipe using methanol working fluid.

Methanol properties are assumed to dependent on the

operating temperature of the heat pipe, and data from Dunn

and Reay were used to obtain interpolation curves [9]. The

temperature of low temperature part goes from -15℃ to 30

℃ with step 15℃. Desired heat load is set from 25W to

100W with steps of 25W.

Fig. 1. Total mass of HP as a fuction of Q to Tsi = -15.0℃, 0.0℃

Fig. 2. Total mass of HP as a fuction of Q to Tsi = 15.0℃, 30.0℃

International Journal of Computer and Electrical Engineering, Vol. 5, No. 3, June 2013

292

International Journal of Computer and Electrical Engineering, Vol. 5, No. 3, June 2013

293

TABLE I: VALUE FOR DESIGN VARIABLE FOR THE CONDITION: TSI = 0.0℃,

Q=25.0W

mtotal N d 10-3 dv 10-3

PSO 0.032 314 0.025 6.1

GEO 0.035 315 0.025 6.4

tw 10-3 Le 10-3 Lc 10-3 tt 10-3

PSO 0.19 57.1 50 0.3 GEO 0.21 71.9 50.3 0.3

Result of optimization by PSO is compared with result of

previous optimization research that is performed by GEO for

each condition. Those are noted on Fig. 3 and 4. From those

figures, it can be seen that total mass of heat pipe increase

with desired heat load increasing for same temperature of

condenser section. It is also come out that optimized mass by

PSO is lighter than design mass from GEO. For the case of

Tsi=15℃, Q

=25W, the mass from PSO is as 16% as lighter then mass get

by GEO. On average, PSO method estimates 10% lighter

heat pipe then GEO method. Seven configuration values are

calculated by PSO and GEO is addressed at table 1. It is

easily shown that two results has difference in dv, tw and Le.

From that result, it is verified that PSO produces more

optimized mass then GEO by estimating optimum value of

design variables.

Lastly, In Fig. 5, the variation of total mass as a function of

Number of function evaluation is shown for the PSO and

GEO. It can be seen that value of PSO comes close to

optimum value more quickly than GEO, especially, at the

early stage of optimization process. It means the PSO is more

efficient than the GEO on searching for the optimum design.

V. CONCLUSION

In this paper, by optimization technique, value of design

variables of heat pipe are estimated to minimize total mass of

heat pipe with maintaining proper heat transfer performance

of it. PSO is applied to search optimum value efficiently

considering multiple constraints and nonlinear equations

simultaneously. Total seven configuration variable and

eighteen constraints are considered. it is drawn a below

conclusions to compare result with previous research.

Fig. 3. Minimum total HP mass as a fuction of NFE at Tsi = 0.0℃, Q=25W

1) As a result of applying PSO method, it is obtained

design value of the heat pipe that is as 10~15% as light

then GEO.

2) PSO has better performance to estimate optimum value

then GEO. Especially, PSO quickly comes close to optimum

value at early stage of calculation.

It is made a judgment that it is useful to estimate optimum

design value of heat pipe configuration effectively by PSO in

place of GEO.

REFERENCES

[1] Y. S. Lee, “Design and Application of the heat pipe”, Air-conditioning

and refrigeration engineering, vol ,26, no.1, pp34-45, 1997

[2] J.H. Boo, “열수송용 히트파이프,” Journal of the KARSE, vol. 16, no.

11, pp. 48-66, 1999.

[3] M. J. Colaco, M. R. B. Orlande, and G. S. Dulikravich, “Inverse and

Optimization Problems in Heat Transfer,” J. of the Braz. Soc. Of Mech.

Sci. & Eng., vol. 28, no. 1, pp. 1-24, 2006.

[4] C. Zhang, Y. Chen, M. Shi, G. P. Peterson, “Optimization of heat pipe

with axial “Ω”-Shaped Micro Grooves Based on a Niched Pareto

Genetic Algorithm(NPGA),” Applied Thermal Engineering, vol. 29,

no. 16, pp. 3340-3345, 2009.

[5] F. L. D. Sousa, F. M. Ramos, and V. V. Vlassov, “Heat Pipe Design

Through Generalized Extremal Optimization,” Heat Transfer

Engineering, vol. 25, no. 7, pp. 34-45, 2004.

[6] J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” in Proc.

of the IEEE Int. Conf. Neural Networks, Perth, Australia, 1995, pp.

1952-1945

[7] K. H. Lee, S. W. Baek, and K. W. Kim, “Inverse radiation analysis

using repulsive particle swarm optimization algorithm,” International

Journal of Heat and Mass Transfer, vol. 51, pp. 2772-2783, 2008.

[8] S. W. Chi, Heat Pipe Theory and Practice, A Sourcebook, New York :

McGraw-Hill Book Company, 1976, pp 33-95

[9] P. Dunn and D. A. Reay, Heat Pipes, New York: Pergamon Press, 1976,

pp. 272-277.

Kwonho Kim received a B.S. in Aerospace Engineering

from the KAIST, Daejeon, S. Korea, in 2011. His

research interests include optimized design by inverse

analysis and hybrid rocket.

He currently takes a course for master degree in aerospace

engineering from the KAIST.

Kyun Ho Lee received a B.S. in Mechanical

Engineering from Yonsei University, Seoul, S. Korea, in

1998, M.Sc. in same major and university, in 2000, Ph.D.

in Aerospace Engineering in KAIST, Daejeon, S. Korea,

in 2009. His research interests include space propulsion,

combustion and inverse analysis in heat transfer. He is

currently an assistant professor of Department of

Aerospace Engineering at Sejong University.

Seung Wook Baek received a B.S. in Mechanical

Engineering from Seoul National University, Seoul, S.

Korea, in 1978, a M.Sc. in same major from same

university, in 1981 and a Ph. D. in Aerospace Engineering,

from University of Michigan, Michigan, in 1985. His

Research interests include with combustion and radiation

phenomena.

He is a Professor in Aerospace Engineering in KAIST,

Daejeon, S. Korea, from 1989 to now on. He also work in Guest researcher in

NIST and NRL.

Prof. Baek is in AIAA senior membership. He also participate in

KSME(Korean Sociey of Mechanical Engineers) and KSAS(Korean Society

for Aeronautical and Space Science)