entropy minimization in plate-fin heat exchanger using cuckoo algorithm

Wyno Journal of Engineering & Technology Research

Vol. 1(2), PP. 21-29 April, 2013.

Available Online at http://www.wynoacademicjournals.org/egineering.html

ISSN 2315 - 9286 2013 Wynoacademic Journals.

Entropy minimization in Plate-fin heat exchanger using Cuckoo

Algorithm

Masoud Asadi

Department of Mechanical Engineering,

Azad Islamic University Science and Research branch,

Tehran, Iran,

Email: [email protected] ,

Tel:+98939-329-3465

Accepted Date: 15Th April ,2013

Abstract

One of the key stages in designing a heat exchanger is optimization process. The enhancement in thermal performance results

in a rise in pressure drop and total annual costs. So, finding optimal dimensions of heat exchanger is a key stage in designing

process. In this paper, optimization has been done based on entropy generation minimization, where Cuckoo Algorithm aided

to reach better results. Three types of heat exchangers are designed for heat recovery system from a microturbine 180 KW. The

optimization process showed a decrease in entropy generation number up to 23%. Although, after optimization process the

pressure drops decrease between 8% to 17 %, based on the type of fins, the total volume of the heat exchanger increased. The results show the possibility of saving energy up to 21% using this method.

Key words: Entropy Generation, Heat Recovery System, Optimization, Cuckoo Algorithm.

Introduction

A heat exchanger is a device to transfer thermal energy between two or more fluids, one comparatively hot and the other

comparatively cold. A special and important class of heat exchanger is used to achieve a very large heat transfer area per

volume. The compact heat exchangers, these devices have dense arrays of finned tubes or plates and are typically used when at

least one of the fluid is a gas , and is hence characterized by a small convection coefficient. Plate heat exchangers, finned tube

heat exchangers, and plate-fin heat exchangers are in the class of compact heat exchangers. The surface area density, , which

is defined as the ratio of the heat transfer area to the volume of the heat exchangers, is often used to describe the compactness

of heat exchangers. The compact heat exchangers have a surface area density greater than about 2 3600 /m m , or the hydraulic

diameter is smaller than about 6 mm operating in a gas stream.

To improve the heat transfer rate, the heat transfer area is increased by adding fins to heat exchanger. When a high

compactness is desirable, complex interrupted fin surfaces are preferred, such as offset strip fins, perforated fins, slit fins and

wavy fins. This type of fins prevents the formation of thick boundary layers and encourages flow destabilization. However, one

of the main drawbacks of the interrupted fin designs is pressure drop. In fact, the enhancement in thermal performance causes a

rise in pressure drop, which increases the load of pumping power. Consequently, the overall assessment of plat-fin heat

exchanger requires a trade-off between thermal performance and pressure drop. Entropy generation minimization (EGM)

method is based on this theory that a thermodynamically optimized system has the least irreversible or minimum entropy

generation in the system. This method was firstly introduced by Bejan et, al.(1982) as optimization tool in thermodynamic

systems for a broad range of engineering fields. The theory of EGM states that all real systems suffer their thermodynamic

imperfection due to heat transfer, fluid flow and mass transfer irreversibility. Therefore, the entropy generation can be used as a measure of systems departure from reversibility. Culham and Muzychka (2000) used the EGM tools to optimization of a plate fin heat sinks in electronics applications. Dealing with various geometric parameters, heat transfer rate and material

properties of heat sinks, the application of multi-parameter optimization is more productive than an analytical approach with

empirical equations and powerful numerical simulation which cannot simultaneously optimize more than two parameters.

Wen-Jei Yang et, al.(2002) studied the accuracy of this method and compared its results with numerical methods such as CFD

and reached this results that the EGM has acceptable performance. Although many researcher studied about this method and its

result, but there are scarce resources about the application of this method in mechanical design of a plate-fin heat exchanger. In

this study, it is designed a plate-fin heat exchanger for heat recovery in microturbine cycle. Mechanical design of heat

exchanger has been done based on sizing problem, and then its performance improved using the EGM method, which it is used

by new optimization algorthim, Cuckoo algorithm, to reach better performance. This algorithm was introduced in 2011 by

Ramin Rajabioun.

22. Engr. Tech. & Res.

Nomenclature

tA : heat transfer area P: pressure

PC : specific heat Re : Reynolds number

hD : hydraulic diameter

genS

:entropy generation

f: friction factor T : temperature of fluids

h: convective coefficient

Greek symbols

tH : tube height : fluid density

j: Colburn factor : dynamic viscosity

CK :Contraction coefficient Subscripts

eK : expansion coefficient h : hot stream

K :thermal conductivity c : cold stream

m : mass flow rate i : input

Ns :entropy generation number o : output

NTU :number of transfer unit

23. Asadi

Model Development for Thermodynamical

Optimization

Consider a point (x, y) in a fluid engaged in convective

heat transfer, where the fluid element dXdY surrounding

this point is part of a considerably more complex

convective heat transfer arrangement. It is regarded the

small element dXdY as an open thermodynamic system

subjected to mass fluxes, energy transfer, and entropy

transfer interactions that penetrate the fixed control surface

formed by dXdY rectangle of Fig.(1).

Figure 1: The local generation of entropy in a flow with convective heat transfer.

The element size is small enough so that the

thermodynamic state of the fluid inside the element may

be regarded as uniform ( Bejan et, al. 1996). However, the

thermodynamic state of the element may change with time.

Hence, based on this model , the entropy generation rate

per unit volume is:

yx

yxyx

gen

x

x

y

y

x y

qq q dyq dx qqyxS dxdy dy dx dy dxT T T T

T dx T dyx y

ss dx dx dx dy

x x x

ss dy dy dy dx

y y y

ss dy s dx dxdy

t

(1)

In this expression the first four terms account for the entropy transfer associated with heat transfer, the next four

terms represent the entropy converted into and out of the

system, and the last term represents the time rate of

entropy accumulation in the dXdY volume (Bejan et, al.

1996). Using some assumptions the irreversibility due to

heat transfer is:

, ,

, ,

h o c ogen P P

h i c ih c

T TS mC Ln mC Ln

T T

(2)

Where entropy changes associated with the frictional

pressure drops choutin

PP,

have not been included. For

Simplicity, consider a balanced counter flow arrangement

1C in which the stream to stream temperature difference and frictional pressure drops are not negligible.

So the entropy generation rate in this arrangement is:

, ,

, ,

, ,

, ,

h o c ogen P P

h i c ih c

h o c oh c

h i c i

T TS mC Ln mC Ln

T T

P Pm R Ln m R Ln

P P

(3)

Where the first two terms on the right represent the heat

transfer irreversibility and the last two terms account for

fluid friction. Thus, the entropy generation number

becomes.

2

, ,

, ,

1h i c i

Sh i c i P cc

P hh

T T R PN

T T C P

R P

C P

(4)

Where ,h iT and ,c iT are inlet temperatures. The heat

transfer irreversibility vanishes when the area is very large

NTU or when the counter flow is isothermal due to

end conditions . Also, the fluid friction irreversibility vanishes when the pressure drops on the two

sides of the surface are zero. Also, when both fluids are

unmixed the heat exchanger effectiveness is:

0.22 * 0.78*1

1 exp NTU exp C .NTU 1C

(5)

In the equation of (4), the pressure drop is defined as,

,2

,2

,1

, , ,2

,

, ,

1 1

1

2

2

i h

C h h

o h

h

i h i h i hh

h h e h

h m h o h

KG

Sf k

A

P

(6)

Where CK and eK are contraction and expansion

coefficients respectively. Here, S and A are total heat

transfer area and frontal area. ,f and G are also friction

factor, density and mass velocity respectively.

Cuckoo Algorithm

Figure of (2) demonstrates a flowchart of the proposed

algorithm. This algorithm, like any evolutionary algorithm,

starts with an initial population of cuckoos. These initial

cuckoos have some eggs in order to lay in some host birds nests. Some of these eggs which are more similar to the

host birds eggs have this opportunity to grow up and become a mature cuckoo. Host birds detect and kill the


remained eggs. Where more eggs survive, the more profit

is gained. So, the position in which more eggs survive will

be the term that COA is going to optimize.

To solve an optimization problem, it is necessary that the

values of problem variables be formed as an array (Ramin

Rajabioun et, al. 2011). In Genetic and Particle Swarm

algorithms (GA & PSO), this array has been called

chromosome and particle position, but , here, it is called

habitat. In a varN -dimensional optimization problem, a

habitat is an array of var1 N , representing current living

position of cuckoo(Ramin Rajabioun et, al. 2011). This

array is:

var1 2 N

habitat= x ,x ,...,x

(7)

The profit of a habitat is obtained by evaluation of profit

function, Pf .

var1 2 N

(habitat)= x ,x ,...,xP Pf f

(8)

To start the optimization algorithm, a candidate habitat

matrix of size varpopN N is generated. Another habitat

of real cuckoos is that they lay eggs within a maximum

distance from their habitats (Ramin Rajabioun et, al. 2011)

. This maximum range has been called Egg Laying Radius

(ELR). So, ELR is:

(9)

hi lowNumber of current cuckoo's eggs

ELR= var -varTotal number of eggs

(9)

Figure 2: Cuckoo Algorithm Flowchart

Here, is an integer, supposed to handle the maximum

value of ELR (Ramin Rajabioun et, al. 2011). Also hivar ,

and lowvar are the upper and the low limit of variables

respectively.

Figure (2) denotes that each cuckoos starts laying eggs

randomly in the host birds nests. After egg laying process, P% of all eggs (usually 10%), with less profit values, will

be detected and killed.

Figure 3: Random egg laying in ELR, central red star is

the initial habitat of the cuckoo with 5 eggs; pink stars are

the eggs new nest. The host birds feed the rest of the eggs. Interestingly, only

one egg has the chance to grow in each nest, because of

her three times bigger body. She pushes other chicks and

eat more. As after couple of days the host birds own chicks die due to hunger. When cuckoos become mature,

they live in their own society. In the time of the egg laying, the young cuckoos immigrate to new environment,

where there are more similarity of eggs to host birds. After

the cuckoo groups are formed in different areas, the

society with best profit value is selected as the goal point

for other cuckoos to immigrate (Ramin Rajabioun et, al.

2011). When moving toward goal point, the cuckoos do

not fly all the way to the destination habitat. They only fly

a part of the way and also have a deviation. Here,

parameters of and help the cuckoos to search much

more positions in all environments.

0,1: U

(10)

,: U

(11)

Where is a parameter which constraints the deviation

from goal habitat.

Figure 4: Immigration of a sample cuckoo toward goal

habitat.

Figure 5: Plate-Fin Heat Exchanger

25. Asadi

The next question is what to use for an iteration variable.

A very convenient variable is the mass velocity G for each

side of the heat exchanger, since it is easy to make a

reasonable initial estimate of both Gs. When hG and cG

are specified, the frontal areas HW and HD are fixed. The

complete dimensions of the heat exchanger are then

established when the volume V is determined. The important note is that NTU is determined for the desired

heat exchanger effectiveness, based on the min max/C C

and the heat exchanger efficiency. Here, a plate-fin heat

exchanger is designed for heat recovery. The operating

conditions are according to Table. (2)

Results and Discussion

Designing information before optimization process is

according to Table of (3). As it is evident, the fin type of

11.44-3/8 W has better performance compared with the other types of fins, because for cold stream its pressure

drop is about 186% and 84% less than 11.5-3/8 W and

17.8-3/8 W fins. However, for hot stream, it is 54% and 50

% more respectively. In the optimization process the variables are width, depth and height of the heat

exchanger. To limit search area it is better introducing the

variables in a restricted area. Figure of (6), (7) and (8)

show the optimization results for 11.44-3/8 W, 11.5-3/8 W

and 17.8-3/8 W.

Table 1 .Fin Geometric Properties

Plate

Spacing(mm)

Hydraulic

Diameter(mm)

Fin

Thickness(mm)

Wavelength(mm) Double Wave

Amplitude(mm)

Heat Transfer

Area/ Volume

Between

Plates

Fin

Area/Total

Area

11.44-3/8 W 10.49 3.23 0.152 9.53 1.97 1152 0.847

11.5-3/8 W 9.53 3.02 0.254 9.53 1.98 1138 0.822

17.8-3/8 W 10.49 2.12 0.152 9.53 1.97 1686 0.892

Table 2: Operating Conditions

Data Variables

6 Allowable pressure drop for hot side(%) 3 Allowable pressure drop for hot side(%)

321 Outlet gas temperature(K) 950 Inlet gas temperature(K) 875 Outlet air temperature(K)

175 Inlet air temperature(kK) 304 Inlet pressure for Air side(Kpa)

160.8 Inlet pressure for Gas side(Kpa)

0.685 Gas mass flow rate (kg/s) 0.662 Air mass flow rate(kg/s)


Table 3: Designing Information Before Optimization Process

11.44-3/8 W 11.5-3/8 W 17.8-3/8 W

Air Gas Air Gas Air Gas

Re 22.4 40.1 18.5 40.2 16.1 31.5

j 0.019 0.018 0.02 0.02 0.016 0.016

f 0.13 0.12 0.13 0.12 0.09 0.09

2h / .w m k 7.03 16.5 6.8 17.8 6.3 15.6

f 0.81 0.73 0.82 0.70 0.82 0.75

o 0.83 0.77 0.85 0.75 0.83 0.77

2U w/m .k 3.98 3.98 4.03 4.03 3.64 3.64

NTU 17.24 17.24 17.24 17.24 17.24 17.24

2S m 474.59 474.59 413.82 413.82 575.3 575.3 567.7 567.7 525.16 525.16 882.36 882.36

3V m 0.836 0.836 0.788 0.788 0.652 0.652 0.457 0.457 0.396 0.396 0.468 0.468

Width mm 750 750 630 630 580 580

Depth mm 800 800 900 900 726 726

Heith mm 1360 1360 1380 1380 1540 1540

P Kpa 6.179 2.604 17.693 1.182 11.415 1.323

sN 2.54 2.54 2.12 2.12 1.91 1.91

Figure 6: Optimization results for fin of 11.44-3/8 W.

27. Asadi



The cost function, here, is entropy generation number. This algorithm has an excellent performance compared with GA and

PSO algorithm, because after 40 habitats, maximum, has reached to the optimal value. Table.(4) gives the width , depth and

height of the heat exchanger for three types of fins ( After optimization process).


Table: (4) Optimal Values of the Variables

11.44-3/8 W 11.5-3/8 W 17.8-3/8 W

Height(mm) 2112 2228 2560 Width(mm) 736 647 821

Depth(mm) 1524 1879 2113

Total volume( 3m ) 2.37 2.58 4.33

Table: (5) Designing Information after Optimization Process

11.44-3/8 W 11.5-3/8 W 17.8-3/8 W

Air Gas Air Gas Air Gas

Re 897 1000.8 1363.1 682 847 418

j 0.017 0.015 0.014 0.018 0.013 0.018

f 0.09 0.08 0.1 0.07 0.063 0.09

2h / .w m k 265.8 343.7 355.1 300.9 292.3 262.5

f 0.28 0.25 0.25 0.26 0.26 0.28

o 0.37 0.37 0.39 0.39 0.33 0.33

2U w/m .k 55.31 55.31 63.41 63.41 45.63 45.63

NTU 17.24 17.24 17.24 17.24 17.24 17.24

2S m 474.71 474.71 414.07 414.07 575.68 575.68 567.7 567.7 525.16 525.16 882.36 882.36

3V m 0.836 0.836 0.788 0.788 0.652 0.652 0.457 0.457 0.396 0.396 0.468 0.468

Width mm 750 750 630 630 580 580

Depth mm 800 800 900 900 726 726

Heith mm 1360 1360 1380 1380 1540 1540

P Kpa -35.3610 -38.8610 -33.4210 -312.910 -32.2610 -310.510

sN 1.67 1.67 1.18 1.18 1.13 1.13

Table of (4) and (5) denote information after optimization process. According to the equation of (4) entropy generation number

is only a function of pressure drop, because our problem is a sizing problem and inlet and outlets temperature are determined. The results show that the cuckoo algorithm has decreased pressure dramatically in order to reach the optimal value of entropy

generation number. The important note is that, here, the cuckoo algorithm has not any effects on entropy generation arising

heat transfer, because inlet and outlet temperature are constant. So, there are some limitations for optimal value of the entropy

generation number. The other interesting note is that the optimal value of the Depth is much more than the Width value, since

the algorithm has increased the flow length in the hot side in order to set the pressure drops in the same range. The fan power

can be calculated by,

fanf

mPower = .P

. (12)

Where, f is fan efficiency, and is assumed to be 0.8 for both streams. The results shows that saving energy about 98% in

operating costs is possible with this new method , Of course if there is not any limitations for total volume or on surface area.

However, if total volume and surface area be limited, we can use this this method to save energy between 20% to 80% based on the dimensions of the heat exchangers.

References Bejan, A. (1996) , Entropy Generation Minimization, CRC Press, New York. Bejan, A. (1982), Entropy Generation Through Heat and Fluid Flow, John Wiley and Sons Ltd., New York.

Bejan, A. (1980) and Pfister P. A., Evaluation of Heat Transfer Augmentation Techniques, Letters in Heat and Mass Transfer, Vol. 7, pp. 97-106.

29. Asadi

Culham, J. R. and Muzychka, Y. S. (2000),Optimization of Plate Fin Heat Sinks Using Entropy Generation Minimization, Inter Society Conference on Thermal Phenomena,, pp. 8-15.

Wen-Jei Yang,(2002),Reliability of Heat Sink Optimization Using Entropy Generation Minimization, Thermophysics and

Heat Transfer Conference, Louis, Missouri, USA.

Ramin Rajabioun,(2011), Cuckoo Optimization Algorithm, Applied Soft Computing 11 (2011) 55085518. Masoud Asadi and Dr R.H.Khoshkhoo, Investigation into radiation of a plate-fin heat exchanger with strip fins , Journal of

Mechanical Engineering Research, April 2013.

Masoud Asadi and Dr R.H.Khoshkhoo,Entropy Generation in a Plate-Fin Compact Heat Exchanger with Louvered Fins ,

International Journal Energy Engineering, , March2013.

Masoud Asadi and Nasrin Dindar Mehrabani, Minimization entropy generation into compact heat exchanger with Louvered

fins , Journal of Petroleum and Gas Engineering ,2013.

Masoud Asadi and Dr R.H.Khoshkhoo, Effects of mass flow rate in terms of pressure drop and heat transfer characteristics , Merit Research Journal of Environmental Science and Toxicology Vol. 1(1), February, 2013.

entropy minimization in plate-fin heat exchanger using cuckoo algorithm

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