A Study on Heat Pipe Optimization Using PSO - ijcee

Internati**on**al Journal of Computer and Electrical Engineering, Vol. 5, No. 3, June 2013

A **on** **Heat** **Pipe** Optimizati**on** **Using** **PSO**

Kw**on**ho Kim, Kyun Ho Lee, and Seung Wook Baek

Abstract—A heat pipe optimizati**on** is known as a difficult

**on**e because design variables have n**on**linear interacti**on** **on**e

another and multiple c**on**straints 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

applicati**on** using an evoluti**on**ary method.

In this study, Particle Swarm Optimizati**on**(**PSO**) method,

simple heuristic search method, is used to estimate variables

and improve search efficiency. The heat pipe c**on**figurati**on** is

optimized regarding to seven parameters, such as diameter of

vapor core, thickness of wick, etc., and eighteen c**on**straints

including operati**on**al, dimensi**on**al, and structural **on**es.

To verify the performance of the **PSO** method, a minimum

total mass estimati**on** and searching efficiency are compared

with results obtained by generalized extremal

optimizati**on**(GEO). It is proven that **PSO** found optimized

soluti**on**s effectively than GEO for simultaneous estimati**on** of

multi-parameters.

Index Terms—Optimizati**on** design, **PSO** (Particle Swarm

Optimizati**on**), heat pipe, mesh wick.

I. INTRODUCTION

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

using for cooling device of micro-semic**on**ductor 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 optimizati**on** for special

envir**on**ment like satellite, space shuttle, and so **on**[2].

It is not suitable to optimize heat pipe c**on**figurati**on** by

gradient-based method because n**on**linear equati**on** should be

solved for heat pipe design and several c**on**straints should be

c**on**sidered **on** heat pipe shape. Instead, stochastic algorithm

is effective for solving n**on**linear problem like the heat pipe

design optimizati**on**[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

Optimizati**on**), **on**e of stochastic algorithms, to estimate

minimum mass of mesh wick heat pipe[5].

In this study, for increasing searching efficiency,

**PSO**(Particle Swarm Optimizati**on**) method is applied to

obtain c**on**figurati**on** variable for minimizing mass of heat

pipe. Optimizati**on** procedure is performed to investigate

multiple design factors, those determine shape of heat pipe

using methanol for working fluid with mesh type wick.

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

Kw**on**ho Kim and Sung Wook Baek are with the Aerospace engineering,

KAIST, 291 Daehak-ro, Yuse**on**g-gu, Daeje**on** 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, Sej**on**g

University, 98 Gunja-d**on**g, Gwangjin-gu, Seoul 143-747, Republic of

Korea(e-mail: khlee0406@sej**on**g.ac.kr).

II. PARTICLE SWARM OPTIMIZATION

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

develop **PSO**(Particle Swarm Optimizati**on**) algorithm by

Kennedy and Eberhart[6]. **PSO** modifies its existing soluti**on**

referring pers**on**al best value and global best value, otherwise

Genetic Algorithm discards existing soluti**on** 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 soluti**on**

2) Renewing velocity vector of each particle

i i i i g i

v k 1

wv k

c1r 1

p k

x k

c2r2

p k

x (1)

k

3) Renewing value of each particle

x x v

(2)

i i i

k1 k k1

x is positi**on**(value) of a particle. v is velocity vector of a

particle. Superscript is number of particle and subscript

means iterati**on** step. p is best value up to now. Superscript g

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

c 1 and c 2 are inertia factor, self-c**on**fidence factor and swarm

c**on**fidence factor, respectively. Those determine how much

are each term c**on**sidered. r 1 and r 2 is random value in 0 to 1

changing influence of pers**on**al best value and global best

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

particle, reflects existing velocity v i k and distance (difference)

between x i k, its existing positi**on**, and pers**on**al best value p i k

and global best value p g k respectively. New positi**on** value of

particle is calculated by sum of existing positi**on** value x i k and

new velocity vector v i k+1. After renewing value of a particle,

pers**on**al best value p i k and global best value p g k are renewed

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

while renewed p g k satisfy given c**on**diti**on** of soluti**on**.

Genetic algorithm is relatively complex because it should

realize selecti**on**, crossing and mutati**on**. As same reas**on**, it

takes l**on**g time to find optimum soluti**on**. However, **PSO** is

composed by just two equati**on**s which are tracking a particle

that approach close to real soluti**on**, so it is simple and

effective to search the value [7].

III. HEAT PIPE

**Heat** pipe is c**on**fined 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

DOI: 10.7763/IJCEE.2013.V5.715

291

Internati**on**al Journal of Computer and Electrical Engineering, Vol. 5, No. 3, June 2013

temperature part and low temperature part due to its

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

limitati**on** of installing space.

Usual heat pipe c**on**tacts 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 c**on**denser part. At c**on**denser part, working fluid

c**on**denses 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 c**on**figurati**on** variables are

optimized to minimize mass of heat pipe that can transfer

desired heat loads with given envir**on**ment temperature. The

seven c**on**figurati**on** variables are mesh number of wick (N),

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

of wick(t w ), length of evaporator secti**on**(L e ), length of

c**on**denser secti**on**(L c ) and thickness of pipe wall(t t ). Length

of adiabatic secti**on** is supposed 0.5m to compare with result

of previous research. In optimizati**on** procedure, total mass of

heat pipe is set for objective functi**on**. The total mass is sum

of mass of c**on**tainer(m c**on**t ), wick(m wd ), liquid in wick(m wl )

and vapor in vapor core(m vapor ).

mtotal mc**on**t mwd mwl mvapor

(3)

When desired heat load (Q) and temperature of c**on**denser

secti**on** are given, seven c**on**figurati**on** variables have

eighteen c**on**straints [8].

G1: Q Q , Q

c

c

P P

c

g

F F L

l v eff

(4)

G11:0.025 10 1.0 10

3 3

d (14)

G12:5.0 10 d v

80.0 10

3 3

(15)

G13:0.05 10 t w

10.0 10

3 3

(16)

G14:50.0 10 L e

400.0 10

3 3

(17)

G15:50.0 10 L c

400.0 10

3 3

(18)

G16:0.3 10 t t

3.0 10

3 3

(19)

P d d u

G17 :

d

2 2

o i ts

2 2

o

di

4

P d 2d u

G18:

2 d d 4

3 3

o i ts

3 3

o i

(20)

(21)

G1 to G7, c**on**straints caused by operati**on** characteristic of

heat pipe are called operati**on**al limit (8) . G8 to G16 are

dimensi**on**al limit which occur by limitati**on** of installing

space. Last two c**on**diti**on**s are structural limitati**on** to prevent

design that would lead to a burst of the tube

IV. RESULT

In this research, optimizati**on** is c**on**ducted 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 interpolati**on** 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.

G T T T

(5)

2:

so,min

so so,max

2

LekeT

v

2

G3: Q Qb , Qb Pc

v ln di dv rn

(6)

2

dv

v

G4 : Q Qe,

Qe

4

2r

rh ,

0.5

(7)

4

dv vPv

G5: Q Qv,

Q

v

(8)

256

L

v

eff

Fig. 1. Total mass of HP as a fucti**on** of Q to T si = -15.0℃, 0.0℃

8Q

G6 : M

v

0.2,

M

v

(9)

d

R T

3

v v v v

4Q

G7 : Re v

2300,Re v

d

(10)

G8:0.0001

0.9999 (11)

v

v

G9 : 2d t

(12)

w

G10:314 N

15000

(13)

Fig. 2. Total mass of HP as a fucti**on** of Q to T si = 15.0℃, 30.0℃

292

Internati**on**al Journal of Computer and Electrical Engineering, Vol. 5, No. 3, June 2013

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

Q=25.0W

m total N d 10 -3 d v 10 -3

**PSO**

0.032 314 0.025 6.1

GEO 0.035 315 0.025 6.4

t w 10 -3 L e 10 -3 L c 10 -3 t t 10 -3

**PSO** 0.19 57.1 50 0.3

GEO 0.21 71.9 50.3 0.3

Result of optimizati**on** by **PSO** is compared with result of

previous optimizati**on** research that is performed by GEO for

each c**on**diti**on**. 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

c**on**denser secti**on**. It is also come out that optimized mass by

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

T si =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 c**on**figurati**on** 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 variati**on** of total mass as a functi**on** of

Number of functi**on** evaluati**on** 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 optimizati**on** process. It means the **PSO** is more

efficient than the GEO **on** searching for the optimum design.

V. CONCLUSION

In this paper, by optimizati**on** 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

c**on**sidering multiple c**on**straints and n**on**linear equati**on**s

simultaneously. Total seven c**on**figurati**on** variable and

eighteen c**on**straints are c**on**sidered. it is drawn a below

c**on**clusi**on**s to compare result with previous research.

value at early stage of calculati**on**.

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

design value of heat pipe c**on**figurati**on** effectively by **PSO** in

place of GEO.

REFERENCES

[1] Y. S. Lee, “Design and Applicati**on** of the heat pipe”, Air-c**on**diti**on**ing

and refrigerati**on** 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

Optimizati**on** 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. Peters**on**, “Optimizati**on** 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 Optimizati**on**,” **Heat** Transfer

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

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

of the IEEE Int. C**on**f. Neural Networks, Perth, Australia, 1995, pp.

1952-1945

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

using repulsive particle swarm optimizati**on** algorithm,” Internati**on**al

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** **Pipe**s, New York: Pergam**on** Press, 1976,

pp. 272-277.

Kw**on**ho Kim received a B.S. in Aerospace Engineering

from the KAIST, Daeje**on**, 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 Y**on**sei University, Seoul, S. Korea, in

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

in Aerospace Engineering in KAIST, Daeje**on**, S. Korea,

in 2009. His research interests include space propulsi**on**,

combusti**on** and inverse analysis in heat transfer. He is

currently an assistant professor of Department of

Aerospace Engineering at Sej**on**g University.

Fig. 3. Minimum total HP mass as a fucti**on** of NFE at T si = 0.0℃, Q=25W

Seung Wook Baek received a B.S. in Mechanical

Engineering from Seoul Nati**on**al 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 combusti**on** and radiati**on**

phenomena.

He is a Professor in Aerospace Engineering in KAIST,

Daeje**on**, 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 Aer**on**autical and Space Science)

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

293