research article analysis of effect of heat pipe...

Research ArticleAnalysis of Effect of Heat Pipe Parameters inMinimising the Entropy Generation Rate

Rakesh Hari and Chandrasekharan Muraleedharan

Department of Mechanical Engineering, National Institute of Technology Calicut, Kerala 673601, India

Correspondence should be addressed to Rakesh Hari; [email protected]

Received 26 September 2015; Revised 4 January 2016; Accepted 5 January 2016

Academic Editor: Pedro Jorge Martins Coelho

Copyright © 2016 R. Hari and C. Muraleedharan. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Heat transfer and fluid flow in the heat pipe system result in thermodynamic irreversibility generating entropy. The minimumentropy generation principle can be used for optimum design of flat heat pipe. The objective of the present work is to minimise thetotal entropy generation rate as the objective function with different parameters of the flat heat pipe subjected to some constraints.These constraints constitute the limitations on the heat transport capacity of the heat pipe. This physical nonlinear programmingproblemwith nonlinear constraints is solved using LINGO 15.0 software, which enables finding optimumvalues for the independentdesign variables for which entropy generation is minimum.The effect of heat load, length, and sink temperature on design variablesand corresponding entropy generation is studied. The second law analysis using minimum entropy generation principle is foundto be effective in designing performance enhanced heat pipe.

1. Introduction

Over the last few decades, entropy generation minimisa-tion principle [1] has been widely used, especially in ther-mal systems and engineering application devices since theconventional design methods do not assure the design tobe thermodynamically efficient. The extent up to which agiven system deviates from an ideal one can be establishedwith the help of entropy generation minimisation principleor thermodynamic optimisation. For thermal systems andtheir components to work at maximum efficiency condition,irreversibility which is a measure of entropy generation mustbe minimised. Second law analysis is an effective methodfor analyzing this generated entropy for the performanceimprovement of any thermal system. In the present work, aheat transfer device, namely, flat heat pipe, is analysed forwhich minimum entropy generation is calculated from theheat transfer and fluid flow irreversibility subjected to variousconstraints.

The heat pipe consists of a sealed container with a liningof porous wick structure adjacent to the wall containingliquid working fluid and a hollow space inside it havingvapour medium at the operating conditions [2, 3]. The

ability to transport large quantities of heat through a smallcross-sectional area over considerable distances with noadditional power input makes the heat pipe superior to otherconventional methods.

The heat pipe is axially divided into three parts, namely,the evaporator, the condenser, and a transport (adiabatic)section as shown in Figure 1. During the operation of heatpipe, heat applied on the pipe wall of the evaporator sectionis conducted through the container wall to the wick structurewhich vaporises the liquid inside the wick. The resultingvapour, due to the pressure difference, moves along thevapour core to the condenser section where it gets condensedreleasing the latent heat of vaporisation to the heat sink. Thecondensed liquid is forced back to the evaporator section dueto capillary action of the wick material. Thus heat pipe workscontinuously transporting latent heat from the evaporator tothe condenser as along as sufficient capillary pressure existsin the porous wick structure.

The investigations made in the area of heat pipe andentropy generation minimisation are presented in this sec-tion. A detailed overview regarding the heat pipe charac-teristics, its performance, and challenges has been reportedby Faghri [4] and also comments about the various physical

Hindawi Publishing CorporationJournal of ermodynamicsVolume 2016, Article ID 1562145, 8 pageshttp://dx.doi.org/10.1155/2016/1562145

2 Journal of Thermodynamics

WickContainer wall

Liquid returnthrough wick

Vapour core

Evaporator Adiabatic section CondenserLe La Lc

Figure 1: Schematic of flat heat pipe.

phenomena and challenges in this area. A review on factorsthat contributes to the major transformation in variouscommercial applications showing great interest in heat pipesis carried out by Faghri [5]. A review of the evolutionof thermodynamics during the past few decades has beenillustrated by Bejan [6] to provide an insight for various engi-neered systems. A numerical approach for estimating entropygeneration is presented by Kumar andMuraleedharan [7] forthe flat heat pipe. Copper-water heat pipe was consideredand the model concluded that the entropy generation due tofluid flow is negligible compared to that due to heat transfer.Khalkhali et al. [8] introduced a thermodynamic model ofconventional cylindrical heat pipe and detailed parametricanalysis was presented in which the effects of various heatpipe parameters on entropy generation were examined. Thestudy showed that minimisation of entropy generation canbe accomplished by adjusting the heat pipe dimensionseffectively and also by controlling the external heating andcooling conditions. Maheshkumar and Muraleedharan [9]presented the second law analysis for flat heat pipe whichstrived tominimise the losses developed due to irreversibilityusing nonlinear programing software.Themodel was formu-lated with various heat transfer limits as constraints, whichshowed that adjustment in heat pipe dimensions will assistin reducing the entropy generation rate. The thermal perfor-mance of a miniature cylindrical heat pipe, based on secondlaw of thermodynamics, was carried out by Ghanbarpourand Khodabandeh [10] with water based Al

2O3and TiO

2

nanofluids at different concentrations as working substance.A reduction in entropy generation was observed for a goodrange of nanofluid concentrations. The recent works onentropy generation studies performed on porous media andviscous filled fluid in buoyancy induced flows in channelsand enclosures were summarised by Oztop and Al-Salem[11]. A simple procedure for minimising entropy generationin simultaneous heat and mass exchange devices has beenillustrated by Narayan et al. [12] using modified heat capacityratio. Second law analysis has been carried out analytically fora circular tube immersed in an isothermal fluid byAnand andNelanti [13]. Entropy generation and pumping power to heattransfer ratio of a laminar flow was established to determineappropriate thermal boundary conditions for each fluid withoptimum entropy generation. Various entropy generationminimisation models of heat transfer and fluid flow were

Roe Rce Rwe

Rwe

TH − TLRcon Rw

Roc Rcc

R�

Figure 2: Thermal circuit of flat heat pipe.

formulated [14, 15] and performance was compared withdifferent dimensionless parameters. Sahin [16] analyticallyinvestigated the entropy generation through a solid slab forboth steady and transient states, bringing out the effects ofthermal conductivity and internal heat generation on the totalrate of entropy generation. A multiparameter constrainedoptimisation procedure was proposed by Jian-hui et al. [17]to design a plate finned heat sink by minimising the rates ofentropy generation.

Although these published research papers over the pastfew decades show very encouraging results, efforts are notput in to draw a strong conclusion on entropy generationminimisation in heat pipe.

This paper proposes the scope of carrying out parametricinvestigations to evaluate the effect of various parametersof the heat pipe for optimising the entropy generation rate.This work is motivated by the fact that demand for highprecision heat pipes has been increasing rapidly as they aremore needed in cooling electronic equipment and spacecraftapplication. Thus the objective of the present study is todetermine the active sites which cause entropy generation inflat heat pipe, estimation of entropy, and its minimisation forenhancing the performance of the system.

2. Entropy Generation Principle

The major factor which results in generation of entropy ina flat heat pipe is heat transfer through a finite tempera-ture difference. The increase in temperature difference willincrease the irreversibility associatedwith the system, therebyincreasing the entropy generation rate.

The thermal resistance circuit of a flat heat pipe is shownin Figure 2. The thermal resistances along the vapour core,wick region, and container wall are in several orders ofmagnitude lower than other resistances due to the heat flowdirection from heat source to heat sink and hence can beignored, which is stated in assumptions. The rate of heattransfer in heat pipe with a nonzero temperature differenceis given by

𝑄 = (𝑇𝐻− 𝑇𝐿

𝑅eff) , (1)

where 𝑅eff is the effective thermal resistance which is given as𝑅eff = 𝑅oe+𝑅ce+𝑅we+𝑅wc+𝑅cc+𝑅oc.The individual thermalresistance for flat heat pipe is obtained from the geometry ofheat pipe and thermophysical properties:

Journal of Thermodynamics 3

𝑅oe, the convective resistance at the outer wall of theevaporator equals 1/ℎ

𝑒𝐴𝑒.

𝑅ce, the conduction resistance across container wall atthe evaporator equals 𝑡

𝑒/𝐴𝑒𝑘𝑒.

𝑅we, the conduction resistance across the wick struc-ture at the evaporator equals 𝑡

𝑤/𝐴𝑒𝑘eff .

𝑅wc, the conduction resistance across the wick struc-ture at the condenser equals 𝑡

𝑤/𝐴𝑐𝑘eff .

𝑅cc, the conduction resistance across the containerwall at the condenser equals 𝑡

𝑐/𝐴𝑐𝑘𝑐.

𝑅oc, the convective resistance at the outer wall of thecondenser equals 1/ℎ

𝑐𝐴𝑐.

𝑘eff , the effective thermal conductivity of the wick is

𝑘eff =𝑘𝑙[(𝑘𝑙+ 𝑘𝑤) − (1 − 𝜀) (𝑘

𝑙− 𝑘𝑤)]

[(𝑘𝑙+ 𝑘𝑤) + (1 − 𝜀) (𝑘

𝑙− 𝑘𝑤)]

. (2)

From (1),

𝑇𝐻= 𝑇𝐿+ 𝑄𝑅eff , (3)

𝑆gen,Δ𝑇 =𝑄

𝑇𝐿

−𝑄

𝑇𝐻

. (4)

The rate of entropy generation due to heat transfer throughfinite temperature difference is given as

𝑆gen,Δ𝑇 = 𝑄(𝑇𝐻− 𝑇𝐿

𝑇𝐻𝑇𝐿

) =𝑄2𝑅eff

[𝑇𝐿(𝑇𝐿+ 𝑄𝑅eff )]

. (5)

As the working fluid flows through the different regions ofheat pipe, some energy is depleted in overcoming the frictionexerted by the wall and the wick structure on the fluid. Thisenergy lost cannot be recovered and hence it becomes asource of irreversibility, which in turn is proportional to theentropy generation rate. Applying first and second laws ofthermodynamics for a steady state flow of vapour through thevapour core, entropy generation due to vapour pressure dropis given by

𝑆gen,Δ𝑝V =(𝑚Δ𝑝V)

(𝜌V𝑇). (6)

The expression for vapour phase pressure drop is

Δ𝑝V = (12𝜇V𝑉𝑙eff

𝑡2V) . (7)

Taking 𝑄 = 𝑚ℎ𝑓𝑔, the entropy generation due to frictional

pressure drop of vapour along the vapour core is obtained as

𝑆gen,Δ𝑝V = (12𝜇V𝑉𝑙eff𝑄

𝑡2V𝜌V𝑇ℎ𝑓𝑔) . (8)

Liquid pressure drop in the wick through which liquid flowsis given by Darcy’s law:

Δ𝑝𝑙= (

8𝜇𝑙𝑚𝑙eff

𝜌𝑙𝜀𝑡𝑤𝑤𝑟2cap

) . (9)

Then the entropy generation due to liquid pressure drop inthe wick is

𝑆gen,Δ𝑝𝑙= (

8𝜇𝑙𝑄2𝑙eff

𝜌2𝑙𝜀𝑡𝑤𝑤𝑟2cap𝑇ℎ

2

𝑓𝑔

) . (10)

Thus the objective function is to minimise the total rate ofentropy generation which is expressed as

𝑆gen,Total = 𝑆gen,Δ𝑇 + 𝑆gen,Δ𝑝V+ 𝑆gen,Δ𝑝

𝑙. (11)

3. Constraints

The constraints constitute the limitations on the heat trans-port capability.

3.1. Heat Transfer Limits. The limits of heat transfer play asignificant role in the design of the heat pipe since the lowestlimit defines the maximum heat transport limitation at agiven temperature. The parameters limiting heat transportin the conventional heat pipe are capillary limit, sonic limit,viscous limit, entrainment limit, and boiling limit.

3.1.1. Capillary Limit. The ability of the capillary wick struc-ture to provide continuous circulation of working fluid islimited with a constraint or limit called capillary limit orhydrodynamic limitation.When the heat transfer is increasedabove this limit, pumping rate of the working fluid will not besufficient to provide enough liquid to the evaporator section.This occurs due to the fact that maximum capillary pressurethat the wick can sustain is lower than the sum of liquid andvapour pressure drops in the heat pipe.The expression for thecapillary limitation is given as

𝑄cap =ℎ𝑓𝑔[(2𝜎𝑙/𝑟cap) cos 𝜃 + 𝜌𝑙𝑔𝑙 sin𝛼]

(2𝜇V/𝑡3

V𝜌V + 𝜇𝑙/2𝐾𝑡𝑤𝜌𝑙). (12)

The constraint for the limit is expressed as 𝑄 − 𝑄cap ≤ 0.

3.1.2. Sonic Limit. At higher temperatures, when the vapourflow velocity becomes equal to or higher than the sonicvelocity, it results in a choked flow condition. This limit iscalled sonic limit. There is a maximum axial heat transferrate at this limit and subsequently it does not increase bydecreasing the condenser temperature under choked flowcondition. The expression for the limit can be written as

𝑄𝑠= 0.5ℎ

𝑓𝑔𝑡V𝑤 (𝑝V𝜌V)

0.5

, (13)

where 𝑄 − 𝑄𝑠≤ 0.

3.1.3. Entrainment Limit. There exists shear forces at theliquid-vapour interface, since both the vapour and the liquidinside the heat pipemove in the opposite direction.When thecorresponding velocities of vapour and liquid are relativelyhigh, a limit is reached where liquid will be torn off fromthe wick surface and entrained to the vapour region flowingtowards the condenser section.When the entrainment begins


and becomes predominant, it results in dry out of the wick atthe evaporator section.The entrainment heat load for flat heatpipe is obtained as

𝑄ent = 𝑤𝑡Vℎ𝑓𝑔 (2𝜋𝜎𝜌V

𝑟hs)

0.5

. (14)

The limit of entrainment can be represented as 𝑄 − 𝑄ent ≤ 0.

3.1.4. Viscous Limit. At low operating temperature the vapourpressure difference between the evaporator and condenserend will be small. Viscous forces may be dominant andlimit the operation of the heat pipe. This flow conditionwhere total vapour pressure in the vapour region becomesinsufficient to sustain an increased flow is called viscous limit.The expression for viscous limit is obtained as

𝑄vis = (𝑡3

V𝑤ℎ𝑓𝑔𝑝V𝜌V

24𝜇V𝑙eff) , (15)

where the limit is written as 𝑄 − 𝑄vis ≤ 0.

3.1.5. Boiling Limit. Heat transfer across the liquid saturatedwick is accompanied by a transverse temperature gradient inthe liquid. When this heat flux in the evaporator becomeshigh, thewall temperature becomes excessively high resultingin boiling of liquid in the evaporator.The vapour bubbles thatform in the wick structure cause hot spots and obstruct thecirculation of fluid which leads to dry out of the wick in theevaporator. This limitation of heat transfer due to transverseheat flux density is termed as boiling limitation. Unlike theother heat pipe limits discussed above which are due to axialheat flux limitation, the boiling limitation is a transverse heatflux limit. The expression for the boiling heat transfer limit isobtained as

𝑄𝑏=2𝑤𝐿𝑒𝑘eff𝑇 [(2𝜎/𝑟𝑛) − 𝑃𝑐]

(ℎ𝑓𝑔𝜌V𝑡𝑤)

. (16)

The constraint of 𝑄 − 𝑄𝑏≤ 0 should be satisfied.

Thus the present optimization problem can be formulatedto find 𝑋 which minimizes the objective function 𝐹(𝑋)

subjected to constraints: 𝑔𝑖(𝑋) ≤ 0, 𝑖 = 1, 2, 3, . . . , 𝑚 where

𝑋 = 𝑁, 𝑡𝑤, 𝑇𝐿, 𝐿𝑎.

𝐹(𝑋) is the entropy generation in a heat pipe system.𝑔𝑖(𝑋) is the functional constraints.

𝑚 is the number of constraints.

4. Methodology

In the present work a flat heat pipe is analysed with followingassumptions.

(1) The operation of the heat pipe is carried out at steadystate.

(2) The fluid is laminar and incompressible.

Table 1: Thermophysical properties taken as input parameters fordesign.

Thermophysical properties Design valueDensity of water 985 kg/m3

Density of water vapour 0.13 kg/m3

Viscosity of water 0.000797N⋅s/m2

Viscosity of water vapour 0.0000134N⋅s/m2

Surface tension of water 0.070N/mLatent heat of vapourisation 2300000 J/kgThermal conductivity of water 0.608W/mK

(3) The heat transfer through the liquid wick is modelledas pure conduction with an effective thermal conduc-tivity.

(4) The temperature difference which exists within theliquid-vapour interface between the vapour core andwick structure is small and neglected.

(5) The axial heat conduction through the container walland wick is neglected.

Analysis has been carried out for a heat pipe with horizontalorientation.The heat input and sink temperature are taken asinput parameters while surface temperature of the evaporatoris switched as a function of heat input, sink temperature,and thermal resistance in the heat pipe. The selection ofworking fluid is important since it depends on the operatingtemperature of the heat pipe and the compatibility withthe material of the container wall and the wick. Copper isused as the material for the container wall and wrappedwire wick (mesh number = 4000). Thermal conductivity ofcopper is taken as 385W/mK.Theworking fluid used is water.The thermophysical properties of water at correspondingoperating temperature and pressure taken for the analysisare summarised in Table 1. Heat transfer coefficient is takenas 600W/m2K, assuming evaporator and condenser sectionbeing maintained at desired temperature by circulating waterin a constant temperature bath.

A flat heat pipe of one-meter length (combining length ofevaporator, adiabatic section, and condenser) is consideredfor the analysis.The length of adiabatic section is varied from0 to 0.5m to study the effect of variation in entropy generationrate. The wick thickness is taken as a design variable and itsvalue is assumed to be varying from 0.0005 to 0.0015m. Thelower and upper limit values are specified in the program asan additional constraint.Meanwhile, the length of evaporatorand condenser is influenced by the length of adiabatic section,since the latter is a design variable. The linear dimensionin the transverse direction (i.e., perpendicular to the flowdirection) cannot be defined since it is determined by thesum of the container wall, wick, and vapour core thicknesses,which varies according to design requirement in each case.However upper bound limit to the transverse length of theheat pipe is fixed to 0.05m as a design constraint.

The present problem is a nonlinear programming prob-lem with nonlinear inequality constraint. The optimisationor rather minimisation is to obtain a set of design variables


0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Entro

py g

ener

atio

n ra

te (W

/m3K)

150 200 250 300 350 400 450 500 550 600100Heat load (W)

La = 0.0mLa = 0.1mLa = 0.2m

La = 0.3mLa = 0.4mLa = 0.5m

Figure 3: Variation in entropy generation rate against heat load fordifferent lengths of adiabatic section.

which gives minimum entropy generation. The problem ismodelled using optimisation modelling software “LINGO15.0.” It provides completely integrated built-in solver forsolving the nonlinear optimisation model to get globaloptimum solution. The entropy generation rate is calculatedwith respect to different heat pipe parameters.

5. Results and Discussion

The variation of entropy generation rate is studied for differ-ent heat pipe parameters such as heat load, sink temperature,and various lengths of adiabatic section using the software.From the present analysis, it is inferred that entropy generatedin a heat pipe is mainly due to heat transfer, and the entropygenerated due to fluid friction of the vapour and liquid flowis negligibly small. Hence the dimensionless parameter calledBejan number (ratio of entropy generated due to heat transferto total entropy generated or sum of entropy generated byheat transfer and fluid friction) tends to 1 in this prob-lem, which clearly indicates that heat transfer irreversibilitycontributes almost 100% to the total entropy generation.Figure 3 shows the variation of entropy generation againstheat load for different lengths of adiabatic section with aconstant sink temperature of 303K. Entropy generation rateis found to increase with heat load, and the rate of increaseis more when heat load increases. This is due to the factthat, with the increase in heat load, temperature differencebetween the walls of evaporator and condenser increases andmoreover increase in pressure drop also results in entropygeneration rate. For the same operating conditions, entropygeneration rate is found to increasewith increase in the lengthof adiabatic section. As the length of the transport sectionincreases, effective length of the heat pipe increases; this inturn increases pressure drop in the liquid wick and vapourcore along the heat pipe which results in increase of entropy

0

0.005

0.01

0.015

0.02

0.025

0.03

Entro

py g

ener

atio

n ra

te (W

/m3K)

298 303 308 313 318 323293Sink temperature (K)

Q = 100WQ = 200WQ = 300W

Q = 400WQ = 500W

Figure 4: Variation in entropy generation rate against sink temper-ature for different heat loads.

generation rate. The rate of increase is found to be more athigher heat flux values. Entropy generation rate is found toincrease from 1.09 ∗ 10

−3 to 3.88 ∗ 10−2W/m3K for the heatinput range of 100 to 600W without the transport section.The entropy rate is found to be almost doubled when thelength of adiabatic section is varied from 0 to 0.5m, for thecorresponding heat flux value.

The decrease in entropy generation rate with the increasein condenser temperature without the transport region isdepicted in Figure 4.The increase in sink temperature resultsin drop of temperature difference between the heat sourceand sink which decreases the irreversibility associated withit, thereby decreasing the entropy generation rate. For lowvalues of heat load, there is notmuch difference in the entropygeneration rate for different sink temperatures. The variationis found to be 2.07 ∗ 10

−4W/m3K for a heat load of 100Wover the entire sink temperature range. But at higher heatload, the variation is found to be comparable. At heat loadof 500W the variation is found to be 5.1 ∗ 10

−3W/m3Kfor the entire sink temperature range. Entropy generationrate is found to increase by 25 times when the heat loadis increased from 100 to 500W. The graph shows similarvariation pattern for the entire range of sink temperature.For a constant heat load the variation in entropy generationrate against the length of adiabatic section for different sinktemperatures is depicted in Figure 5. The increase in entropygeneration rate is due to the increase in effective length of heatpipe. Similarly the decrease in entropy generation rate withincrease in sink temperature for different lengths of adiabaticsection is observed with a constant heat load. The decrease isdue to the fall in finite temperature difference when the sinktemperature is increased.The variation of entropy generationfor the entire sink temperature values with a constant heatload of 200W is found to be almost uniform.

Figure 6 shows the entropy generation rate for differentvalues of mesh number. The decrease in entropy generation


×10−3

3

4

5

6

7

8

9

10

Entro

py g

ener

atio

n ra

te (W

/m3K)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50Length of adiabatic section (m)

Tsi = 293KTsi = 303K

Tsi = 313KTsi = 323K

Figure 5: Variation in entropy generation rate against length ofadiabatic section for different sink temperatures.

Q = 100WQ = 300WQ = 500W

2500 3000 3500 4000 4500 5000 5500 6000 6500 70002000Mesh number (1/m)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Entro

py g

ener

atio

n ra

te (W

/m3K)

Figure 6: Variation in entropy generation rate againstmesh numberfor different heat loads.

rate with the increase in mesh number is due to the effectof equivalent thermal conductivity, which in turn dependson effective resistance. With the increase in heat load, thepressure drop will be high which leads to increase in entropygeneration rate. But with the increase in mesh number, thecapillary pressure will be increased which in turn providesbetter circulation of working fluid; in that case, the entropygeneration rate will be decreased. Permeability and corre-sponding values of mesh number are shown in Figure 7.Permeability is found to increase with the decrease in meshnumber. The mesh number is inversely proportional to thesurface pore size. The increase in pore size makes the liquidflow from the condenser to the evaporator more easily due

×10−10

Q = 100WQ = 300WQ = 500W

2500 3000 3500 4000 4500 5000 5500 6000 6500 70002000Mesh number (1/m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Perm

eabi

lity

(m2)

Figure 7: Variation in permeability against mesh number fordifferent heat loads.

tw = 0.0005mtw = 0.001mtw = 0.0015m

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Entro

py g

ener

atio

n ra

te (W

/m3K)

150 200 250 300 350 400 450 500100Heat load (W)

Figure 8: Variation in entropy generation rate against heat load fordifferent wick thicknesses.

to the increase in the flow area inside the wick therebyincreasing the permeability.

The variation of entropy generation rate with respect todifferent heat loads for various wick thickness is shown inFigure 8. While reducing the wick thickness, the thermalresistance decreases and hence the entropy generation ratedue to heat transfer also decreases. So decreasing the wickthickness is one of the methods for decreasing the entropygeneration rate. For a heat load of 100W the difference inentropy generation rate over 0.001m thickness is found tobe 3.6 ∗ 10

−4W/m3K. But the difference increases to 8.8 ∗

10−3W/m3K for the heat load of 500W. The comparison of


tw = 0.0005mtw = 0.001mtw = 0.0015m

×10−3

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Entro

py g

ener

atio

n ra

te (W

/m3K)

298 303 308 313 318 323293Sink temperature (K)

Figure 9: Variation in entropy generation rate against sink temper-ature for different wick thicknesses.

entropy generation rate at different wick thicknesses showsthat the variation is more prominent for higher values of heatload.

Figure 9 depicts the variation of entropy generation rateagainst sink temperature for different wick thicknesses. Asthe sink temperature increases, there will be a correspondingdecrease in the temperature difference between the heatsource and the sink which results in decrease of entropygeneration rate. The reduction in entropy generation ratewith decrease in wick thickness is due to the same reason asmentioned in the above case.

6. Conclusions

Entropy generation rate associated with the flat heat pipe hasbeen estimated and minimised for reducing the irreversibil-ity.Themodel has been formulated and solved as a nonlinearprogramming problemwith nonlinear functional constraintsusing commercial software (LINGO 15.0).The analysis showsthat fluid friction and heat transfer contribute to entropygeneration and has to be considered for the improvement inthe performance of the device. Entropy generation is foundto increase with heat load and length of the adiabatic section,while a decrease in the former is observed with increasein sink temperature. The following design modification canbe recommended to improve the system performance byreducing entropy generation rate:

(i) Reducing the length of the adiabatic section as far aspossible.

(ii) Increasing the condenser temperature.(iii) Decreasing the wick thickness.(iv) Increasing the mesh number.

The parametric study carried out employing the second lawanalysis facilitated a way in arriving at the optimal design ofhigh capacity heat pipe.

Nomenclature

𝐴: Area (m2)ℎ: Heat transfer coefficient (W/m2K)ℎ𝑓𝑔: Latent heat of vaporisation (J/kg)

𝑘: Thermal conductivity (W/mK)𝐾: Permeability (m2)𝑙: Length (m)𝑚: Mass flow rate (kg/s)𝑁: Mesh number (1/m)𝑝: Pressure (Pa)𝑃𝐶: Capillary pressure (Pa)

𝑄: Heat transfer rate (W)𝑟: Radius (m)𝑅: Resistance (K/W)𝑆: Entropy (J/kgK)𝑡: Thickness (m)𝑇: Temperature (K)𝑉: Velocity (m/s)𝑤: Width (m).

Greek Symbols

𝜇: Viscosity (Ns/m2)𝜌: Density (kg/m3)𝜎: Surface tension (N/m)𝜀: Porosity𝜃: Contact angle (degree)𝛼: Inclination angle (degree).

Subscripts

𝑎: Adiabatic section𝑐: Condenser section𝑒: Evaporator sectioneff: Effectivegen: Generatedhs: Hydraulic radius𝐻: Source𝑙: Liquid𝐿: Sink𝑛: Nucleation𝑜: OutsideV: Vapour𝑤: Wick𝑏: Boilingcap: Capillarycon: Containerent: Entrainment𝑠: Sonicvis: Viscous.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.


References

[1] A. Bejan, Entropy Generation throughHeat and Fluid Flow, JohnWiley & Sons, New York, NY, USA, 1982.

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