Incorporation of Horizontal Fins into a PCM-Based Heat Sink to Enhance the Safe Operation Time

applied sciences Article

Incorporation of Horizontal Fins into a PCM-Based Heat Sink to Enhance the Safe Operation Time: Applicable in Electronic Device Cooling Amirhosein Mosavi 1,2 , Hossein Mehdizadeh 3 , Salman Abbasian-Naghneh 4 , Rasool Kalbasi 3 , Aliakbar Karimipour 5, * and Goshtasp Cheraghian 6 1 2 3 4 5 6

*

Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam; amirhosein.mosavi@tdtu.edu.vn Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran; hossein.mehdizade@gmail.com (H.M.); r.kalbasi@pmc.iaun.ac.ir (R.K.) Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran; s.abasian@pnu.iaun.ac.ir Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam Department of Civil Engineering, Technische Universität Braunschweig, 38106 Braunschweig, Germany; g.cheraghian@tu-braunschweig.de Correspondence: aliakbarkarimipour@duytan.edu.vn

Received: 10 July 2020; Accepted: 6 September 2020; Published: 10 September 2020

Abstract: In this study, the effect of the presence of horizontal fins on the safe operating time (SOT) of the PCM filled heat sink was examined. The effects of the number of horizontal fins, as well as fins length on SOT at different aspect ratios, was investigated. Horizontal fins, owing to their high thermal conductivity, cause uniformity in temperature distribution and improve the heat sink thermal conductivity (positive effect). Incorporating horizontal fins reduces the PCM volume fraction which consequently diminishes the ability of the heat sink to absorb the thermal energy (negative effect).

The competition between the former effect and the latter determines the efficacy of adding horizontal fins in the PCM filled heat sinks. As the number of horizontal fins increases up to five, the positive effect is superior to the negative one which in turn enlarges the safe operation time. By the further increase in the number of fins, the negative effect prevailed over the positive effect and therefore the safe operation time diminished. As the heat sink aspect ratio increased, convection heat transfer efficacy becomes more apparent. In this case, it is recommended to use horizontal fins with shorter lengths so that the PCM movement is not disturbed.

Keywords: PCM-based heat sink; safe operation time; horizontal fin; aspect ratio

1. Introduction Phase change materials (PCMs) have a high ability to store thermal energy [1,2]. Usually, they have high phase change enthalpy, hence during the phase change, absorb a great amount of energy at the low-temperature range (phase change temperature) [3]. Therefore, it seems that these materials can also be utilized to cool the electronic devices [4] due to their high energy storage capability [5]. Ren et al. [6] performed a numerical study on the potential of microencapsulated phase change material (MEPCM) on holding the temperature increase in electronic devices. They used expanded graphite (EG) nanoparticles with fin to enhance the thermal conductivity of MEPCM, but preliminary results showed that although fin improves the thermal conductivity of the heat sink, it also reduces the latent heat storage capability. They investigated two distinct heat sinks, the first heat sink used fin

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and the second one utilized EG nanoparticles to improve MEPCM thermal conductivity. In the early stages, the performance of the former heat sink was much better than the latter one, but over time, the performance of the latter one became better. The authors also showed that if multiple PCM with different melting temperatures were used, thermal performance would be improved. The authors recommend that MEPCM with a higher melting temperature should be used near the heat source. By moving away from the heat source, the MEPCM melting temperature must also be reduced. Emam et al. [7] applied three PCMs of RT25, RT35, and RT44 for cooling of the electronic device under heat fluxes of 2000, 2950 and 3750 W m−2 . They observed that the base temperature of electronic devices which are equipped with PCMs, was lower by 69.8, 80.44, and 74.44 ◦ C than the simple device. The authors also investigated the effects of ambient temperature in the solidification duration and it was found that as the ambient temperature increased from 20 to 25 ◦ C, the solidification time of RT44HC raised by 94 min. This figure for the ambient temperature of 30 ◦ C was 178 min. Farzanehnia et al. [8] used paraffin PCM for the cooling of an electronic chipset. They also incorporated multi-walled carbon nanotubes (MWCNTs) nanoparticles to enhance the PCM thermal conductivity. Three heat sinks were prepared and examined to evaluate the effects of using PCM on the electronic device cooling. The first heat sink was simple, while the second and third ones were filled with PCM. In the third heat sink, in addition to PCM, nanoparticles of MWCNT were also added. It was found that adding MWCNTs into the PCM led to a cooling time reduction up to 6%. In the active mode, incorporation of PCM and NPCM reduced the rate of increases in temperature in the early stages of the heating process, while intensified the chipset temperature in the steady state conditions. Huang et al. [9] conducted many experimental tests to examine the thermal behavior of a novel PCM-based heat sink. They found that PCM layer thickness, PCM thermal conductivity, heat storage density and finally power load has an impact on the thermal behavior. At high input power, the PCM role in the thermal performance of the heat sink was more obvious than the conditions in which the input power is low. Heat thermal storage improvement led to more operation time of the device prior to reaching the critical temperature. The authors also observed that the PCM thermal conductivity increases the safe operation time slightly.

Also, they revealed that the PCM thickness efficacy on the safe operation time was more than the PCM thermal conductivity. Zhao et al. [10] compared the ability of a new low-melting-point alloy (LMPA) with paraffin of RT60 (both of them has approximately the same melting point). LMPA thermal conductivity was 50 times than the RT60 one. Also, LMPA volumetric latent heat storage was 2.1 times that of RT60. Results showed that using LMPA rather than the paraffin enlarged the safe operation time up to 50%. At the same time of operation, the maximum temperature in the heat sink equipped with LMPA was 15 ◦ C lower than the RT60 one. Hafiz and Arshad [11] evaluated a PCM-based heat sink equipped with pin fins (fin diameters ranged from 2 to 4 mm). A base heat sink (without fin) was also prepared for comparison. The volume fraction of fins was 9% but the PCM volume fraction was considered variable. In other words, the PCM height varied within the heat sink. According to the results, the 3 mm diameter pin fin have more ability to extend the safe operating time than the other cases. Also, they found that the heat sink should be filled with PCM as much as possible.

As mentioned, high-temperature gradients are caused owing to the PCM low conductivity, which eventually reduces the rate of phase change, and it is likely that large amounts of PCM will not melt.

Using high conductivity metal fins is and useful approaches to improve PCMs thermal conductivity (positive effect). But adding fins rises the system weight as well as the reduction in thermal energy storage potential (negative effect) due to the decrease in volume of materials with high phase change enthalpy (reduced PCM). Therefore, finding the optimal amount of fin is indispensable. The other negative effect of incorporation horizontal fins is the disruption to the convection heat transfer. In this study, the thermal behavior of a PCM-based heat sink in the presence of horizontal fins was numerically investigated. These types of heat sink can be effective in electronic cooling applications.

Independent variables included aspect ratio, number of horizontal fins and length ratio, while the objective function was defined to maximize the safe operation time (SOT). Finally, the competition between the positive and negative effects of adding fins will be discussed.

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2. Problem Description 2. Problem Description

As shown in Figure 1, PCM fills the gap between the horizontal fins. Paraffin wax (Table 1) is Asas shown Figure PCMenters fills the gap between the horizontal fins. to Paraffin wax (Tablethe 1) melted is considered PCM.inThe heat1, flux through the lower surface. Due the expanding considered as PCM. The heat flux enters through the lower surface. Due to the expanding the melted PCM, a space (air) above the heat sink is provided as shown in Figure 1.

PCM, a space (air) above the heat sink is provided as shown in Figure 1.

W

Hb

Air Lf Hb

Horizontal Fin

Phase Change Material

H

Y X

Heat Flux

Figure 1. PCM filledheat heatsink sink((đ?‘Š đ??ť) two horizontal fins fins (đ??ż Ă—Lđ??ťf Ă— ). Hb . ) equipped Figure 1. PCM filled W Ă—Ă—H equippedwith with two horizontal Table properties[12].

[12].

Table1.1. PCM PCM properties ◌ ◌ TTl/°C TT s/°C s/ C l/ C

RTRT-27 27

3030

2828

−1−1 k−1k−1 hfgh/kJ/kJ ccp/pkJ /kJkg kg fg −1 kgkg−1 Liquid Solid Liquid Solid

179 179

1800 1800

2400 2400

−3 −3 −1 K−1 K−1 Ď /kg mm k/Wk/W m−1 m Âľ/kg Ď /kg Âľ/kg −1 −1 β/Kβ/K −1 −1 −1 −1 m ms s Liquid Solid Liquid Solid Liquid Solid Liquid Solid

0.00342 0.00342 0.15 0.15 0.240.24 0.0005 0.0005

760 760

870 870

density PCMininthe the solid solid state constant while in theinliquid state, itstate, is changed by đ?œŒ = by The The density of of PCM stateis is constant while the liquid it is changed 760 760 . Note that Tl is the liquidus temperature (Table 1). Fins are made of aluminum alloy 6061 Ď = βđ?›˝(đ?‘‡ . Note that Tl is the liquidus temperature (Table 1). Fins are made of aluminum alloy (Tđ?‘™ −30)+1 −30)+1 l

−1 K−1 and properties of cp of = 875 J kg W km=−1 177 K−1. W m−1 K−1 .

6061 with withconstant constantthermophysical thermophysical properties cp = 875 J kg−1 kK=−1177 and (đ??´ The heat sink area = đ?‘Šđ??ť) is considered to be constant (problem constraint).

Input The heat sink area (A = WH ) is considered to be constant (problem constraint).

Input parameters

Lf parameters are defined as the aspect ratio (đ??´đ?‘… = ), length ratio đ??żđ?‘… = â „ and fins number (đ?‘›). are defined as the aspect ratio AR = W H , length ratio LR = W/2 and fins number (n). Note that the

Note that the fin thickness was considered to be constant (đ??ť = 0.25 mm). The objective function

fin thickness was considered to be constant (Hb = 0.25 mm). The objective function was defined to was defined to maximize safe operation time (SOT).

The applied heat flux changes so that the input maximize safe operation time (SOT). The applied heat flux changes so that the input energy per the energy per the total volume of heat sink remains constant. In other words, q00 W the value of

is

total volume of heat sink remains constant. In other words, the value of WH is constant for all PCM constant for all PCM filled heat sinks. The initial temperature is considered to be the same as the filledambient heat sinks.

The initial temperature is considered be is the as state. the ambient temperature (27 °C).

Following Table 1, at 27 °C,to PCM in same the solid All wallstemperature (except ◌ C, PCM is in the solid state. All walls (except the lower wall) are (27 ◌ C).

Following Table 1, at 27 the lower wall) are considered adiabatic. Under the worst conditions, all energy enter to the heat sink considered Under the worst conditions, all energy enter to the heat sink must be−đ?‘˜ absorbed must beadiabatic. absorbed by the PCM. Note that the boundary condition at the lower surface is đ?‘ž = . ∂T 00 by the PCM. Note that the boundary condition at the lower surface is q = −k .

In studies involving indicates what fraction of the In studies involving PCM, the volume fraction of PCM đ?œ‘ ∂y PCM,heatsink the volume fraction PCM (Ď•PCM ) indicates what fraction of the heatsink is occupied by PCM: is occupied by of PCM: Ď•PCM =

[HW − 2 Hb H − (W − 2Hb )Hb − 2nL f Hb PCM volume = PCM volume + Fin volume HW

(1)

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3. Mathematical Formulation In this study, two-phase heat transfer formulation is investigated [13–15]. There are two interfaces in this study [16]. The location of the interface between air and PCM (Figure 1) is tracked by using of the volume of fluid (VOF) technique. In the VOF technique, the momentum equations along the horizontal and vertical directions with modified properties are used [17]: ∂(Ď u) ∂t

+u

∂(Ď u) ∂x

+v

∂(Ď u) ∂y

+w

∂(Ď u) ∂z

+ Ď gx + = − ∂P ∂x ∂(Ď v) ∂t

+u

∂(Ď v) ∂x

+v

∂(Ď v) ∂y

+w

∂ ∂x

Âľ ∂u + ∂x

∂ ∂y

Âľ ∂v + ∂x

∂ ∂y

∂(Ď v) ∂z

= − ∂P + Ď g y + ∂y

∂ ∂x

Âľ ∂u + ∂y

∂v Âľ ∂y +

Âľ ∂u + ∂z

106 (1− )2 u 3 +0.001

(2)

Âľ ∂v + ∂z

106 (1− )2 v 3 +0.001

(3)

∂ ∂z

∂ ∂z

Due to the presence of two phases of PCM and air, modified thermophysical properties such as Ď , k and Âľ can be obtained by the following equations: Ď = βair Ď air + (1 − βair )Ď PCM

(4)

k = βair kair + (1 − βair )kPCM

(5)

Âľ = βair Âľair + (1 − βair )ÂľPCM

(6)

In the above equations, βair denote the air volume fraction and obtained by the following Equation: ∂ ∂ ∂ ∂ [Ď air βair ] + u [Ď air βair ] + v [Ď air βair ] + w [Ď air βair ] = 0 ∂t ∂x ∂y ∂z

(7)

Note that the PCM volume fraction is determined with βPCM = 1 − βair .

The well-known enthalpy-porosity technique is used for the PCM phase change process [18]. In this technique, the interface between solid and liquid is not explicitly tracked. In the enthalpy-porosity approximation, the cell domain is considered as a porous medium and the amount of porosity indicates the liquid fraction (Îľ). For Îľ = 1, the cell temperature is higher than the liquidus temperature (T ≼ Tl ), but the liquid fraction equal to zero indicates that the cell temperature is lower than the solidus temperature (T ≤ Ts ). For the cell temperature between Ts and Tl , the liquid fraction (Îľ) is between zero and one, and in this case, there is an interface between the liquid and solid phases [19]. The energy equation for problems involving phase change process is written as follow: ∂ ∂ (Ď h) + ∂x (Ď uh) ∂t

∂ ∂ (Ď vh) + ∂t (Ď âˆ†H ) + ∂y

∂ ∂ ∂T k − = ∂x k ∂T + ∂x ∂y ∂y

where h denote the sensible enthalpy (h = hre f +

RT

c Tre f p

∂ ∂ (Ď u∆H ) − ∂y (Ď v∆H ) ∂x

(8)

dT ) and ∆H is the latent enthalpy which

is related to the amount of liquid fraction (∆H = ÎľL). Note that L is the phase change enthalpy.

Second-order upwind and geo reconstruct discretization methods were applied on momentum/energy and liquid fraction equations, respectively. Considering the low velocity in the phase change process, the laminar flow is considered. The convergence criteria for energy, velocity and continuity equations was selected to be 10−9 , 10−4 and 10−4 , respectively.

4. Grid Study and Validation For computational grid independency, three computational grids with interval sizes of 0.2, 0.1 and 0.05 were selected. According to the results, as the interval size decreased from 0.1 to 0.05, the SOT did not change significantly. Therefore, a structured computational grid (interval size of 0.1 mm) was

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SOT did not change significantly. Therefore, a structured computational grid (interval size of 0.1 mm) chosen. Figure 2 shows the effect of time step size variation on the output response (SOT). As can be was chosen. Figure 2 shows the effect of time step size variation on the output response (SOT). As seen, reducing the time step up to 0.01 s, SOT decreases. Further reduction of the time step does not can be seen, reducing the time step up to 0.01 s, SOT decreases. Further reduction of the time step have a significant effect on SOT. does not have a significant effect on SOT.

SOT/s

559

558

Δt = 0.01/s

557

10-1

10-2

10-3

10-4

10-5

Time step/s (∆t).

Figure2.2.Independency Independencyof ofthe thetime timestep stepsize size (∆đ?‘Ą).

Figure

The numerical numerical method method used used in in this this study study was was validated validated by by experiments experiments carried carried out out by by The authors studied a PCM-based heatequipped sink equipped with vertical Hosseinizadehetetal.al.[20].

[20].

Hosseinizadeh TheThe authors studied a PCM-based heat sink with vertical fins to fins to enhance the heat sink thermal conductivity.

The electrical power applied to the enhance the heat sink thermal conductivity. The electrical power applied to the bottom bottom wall waswall 45 â—Ś C, hence the was 45 W, while the other walls were well insulated.

The ambient temperature was 27 W, while the other walls were well insulated. The ambient temperature was 27 °C, hence the heat ◌ C. Applying heat flux on the bottom wall, its temperature begins heat initial sink initial temperature was°C. 27Applying sink temperature was 27 heat flux on the bottom wall, its temperature begins to to rise. temperature variations bottom wall areshown shownininFigure Figure3.3.As Ascan canbe beseen, seen,the the base base rise.

TheThe temperature variations of of thethe bottom wall are temperature variations variations can can be be divided divided into into three three zones. zones. In Inthe thefirst firstand and third third zones, zones, the the rate rate of of the the temperature variations (slope) is greater than in the middle zone.

In the middle zone, the PCM undergoes phase variations (slope) is greater than in the middle zone. In the middle zone, the PCM undergoes phase change. The Thethermal thermalenergy energyin inthis thiszone zoneisisstored storedas as the the latent latent heat, heat, but but in in the the other other two two zones, zones, the the change. heat stored stored is is sensible. sensible. The Thesame sametrend trend can can be beseen seenfor forthe thesimulated simulated results. results. As Asshown, shown,the thenumerical numerical heat method can well predict the temperature variations of the PCM-based heat sink at three zones. method can well predict the temperature variations of the PCM-based heat sink at three zones.

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200 Current study

Temperature/oC

165

130

95

Experimental Data

60

25

0

5

10

15

20

25

30

Time/min Figure3.3.Comparison Comparisonbetween betweenthe thecurrent currentstudy studyand andthe theexperimental experimentaldata data[20].

[20].

Figure

5. Results 5. Results In general, by loading fins to the PCM, heat transfer within the PCM can be enhanced to maximize In general, by loading fins to the PCM, heat transfer within the PCM can be enhanced to the objective function. The objective function is different for various applications. In electronic cooling maximize the objective function. The objective function is different for various applications. In applications, the objective function is defined as enlarging SOT. For this purpose, given the problem electronic cooling applications, the objective function is defined as enlarging SOT. For this purpose, constraints (constant volume of the heat sink), the optimal number of horizontal fins within PCM will given the problem constraints (constant volume of the heat sink), the optimal number of horizontal be examined. The presence of horizontal fins is expected to improve heat distribution within the PCM. fins within PCM will be examined. The presence of horizontal fins is expected to improve heat For this purpose, the variations of SOT in the PCM filled heat sink equipped with horizontal fins was distribution within the PCM. For this purpose, the variations of SOT in the PCM filled heat sink compared with the corresponding value in the PCM filled heat sink (without horizontal fins). The equipped with horizontal fins was compared with the corresponding value in the PCM filled heat variations of SOT are shown in Figure 4. sink (without horizontal fins). The variations of SOT are shown in Figure 4.

As can be seen in Figure 4, by adding horizontal fins, the contact surface between PCM and fins As can be seen in Figure 4, by adding horizontal fins, the contact surface between PCM and fins intensified which consequently increased the objective function (SOT) in each aspect ratio AR = W . intensified which consequently increased the objective function (SOT) in each aspect ratio (đ??´đ?‘… H= The results presented in Figure 4 are for a heat sink equipped with three horizontal fins (n = 3) at ). The results presented in Figure 4 are for a heat sink equipped with three horizontal fins (đ?‘› = 3) length ratio of LR = 0.3. As can be seen in Figure 4, as the horizontal fins were incorporated to the at length of LR = 0.3. area As can be seen in Figure 4, as the horizontal incorporated to the PCM, theratio contact surface intensified which consequently improvedfins thewere conductive heat transfer, PCM, the contact surface area intensified which consequently improved the conductive heat transfer, hence SOT is improved. Therefore, it is desirable to add horizontal fins. To evaluate the effects of the hence SOT improved.

Therefore, it is desirable to add fins. To evaluate the effects of the number asiswell as the length of horizontal fins on heathorizontal sink performance, a heat sink at a constant number as well as the length of horizontal fins on heat sink performance, a heat sink at a constant height of (H = 10 mm) is selected. Some horizontal fins at length ratios of LR = 0.3, 0.5, 0.7 and 0.9 height of (đ??ť = mm) W is selected. Some horizontal fins at length ratios of LR = 0.3, 0.5, 0.7 and 0.9 were loaded at 10 5000 applied from the bottom surface. For the heat sink with three horizontal fins m2 were loaded at 5000 applied from surface.

For the (n = 3), the effects of length ratio on the SOTbottom are shown in Figure 5. heat sink with three horizontal fins (đ?‘› = 3), the effects of length ratio on SOT are shown in Figure 5.

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Figure4.4.The The variations in SOT owing the incorporation of horizontal into the PCM Figure variations in SOT owing to thetoincorporation of horizontal fins intofins the PCM filled heatfilled sink. heat sink.

Figure 4. 368 The variations in SOT owing to the incorporation of horizontal fins into the PCM filled heat sink.

368

366

SOT /s SOT /s

366

364 364

362 362

360 0.2 360 0.2

0.4

0.6

0.8

1.0

0.4

LR 0.6

0.8

1.0

Figure 5. The effect of increase in length ratio (LR) on SOT (H = 10 mm, three horizontal fins (n = 3), LR AR = 1).

Figure 5. The The effect effect of increase in length ratio (LR) on SOT (H == 10 10 mm, mm, three three horizontal horizontal fins fins (n (n ==3), 3), Figure = 1).

AR = 1).

As shown in Figure 5, with the rise in the length ratio (equivalent with the fins length growth),

SOT increases. In Figure 6, the streamlines are illustrated for both LR = 0.3 and LR = 0.9. As shown in As shown in Figure 5, with the rise in the length ratio (equivalent with the fins length growth), SOT increases. In Figure 6, the streamlines are illustrated for both LR = 0.3 and LR = 0.9. As shown in

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As shown in Figure 5, with the rise in the length ratio (equivalent with the fins length growth), 8 of 15 SOT increases. In Figure 6, the streamlines are illustrated for both LR = 0.3 and LR = 0.9. As shown in Figure 6, as the horizontal fin length rises, the contact area, as well as the convection intensity increased, Figure 6, as the horizontal fin length rises, the contact area, as well as the convection intensity which consequently SOT improves. increased, which consequently SOT improves.

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Symmetry Line

Symmetry Line

LR = 0.9

LR = 0.3

Figure 6. Comparison of the strength between LR =LR 0.3=and LR =LR 0.9=(n 3, = H3, =H 10=mm, AR =AR 1).= 1).

Figure 6. Comparison ofconvection the convection strength between 0.3 and 0.9= (n 10 mm,

Now, the the number of horizontal finsfins efficacy is examined.

By increasing the the horizontal finsfins from Now, number of horizontal efficacy is examined.

By increasing horizontal from for for a convenient understanding of of 3 to313, SOTSOT waswas recorded andand shown in Figure 7. However, to the 13, the recorded shown in Figure 7. However, a convenient understanding the the effect of the number of horizontal finsfins (n), (n), the the results were summarized for for n = n3,=5,3,115,and 13 as effect of the number of horizontal results were summarized 11 and 13 as illustrated in Figure 7. 7. illustrated in Figure When the the number of horizontal finsfins is five (n =(n5),=increasing the the fin length from the the LR LR = 0.3 When number of horizontal is five 5), increasing fin length from = to 0.3 to LR =LR 0.7=improves the SOT, but but more increase in LR, diminishes SOT.SOT. TheThe incorporation of horizontal 0.7 improves the SOT, more increase in LR, diminishes incorporation of horizontal finsfins has has a positive effect (thermal conductivity enhancement) as well as aas negative effect (latent heatheat a positive effect (thermal conductivity enhancement) as well a negative effect (latent reduction).

As shown in Figure 7, the7,optimal number of horizontal fins is five.

Asfive. the number of fins of reduction).

As shown in Figure the optimal number of horizontal fins is As the number risesfins uprises to five, the incremental effect effect of thermal conductivity improvement (positive effect) waswas up to five, the incremental of thermal conductivity improvement (positive effect) superior to the decremental effect of the latent heatheat reduction (negative effect), hence the the objective superior to the decremental effect of the latent reduction (negative effect), hence objective function (SOT) improved.

However, withwith a further increase in the number of fins upon five,five, the the function (SOT) improved.

However, a further increase in the number of fins upon negative effect prevailed over the the positive effect andand therefore thethe safesafe operation time diminished. negative effect prevailed over positive effect therefore operation time diminished.

In aIn study conducted

by Kalbasi and Salimpour [12], using theory, theory, it was shown a study conducted

by Kalbasi and Salimpour [12], constructal using constructal it was that shown under best the conditions, the number horizontal fins is equal thatthe under best conditions, the of number of horizontal finsto is four. equalInto[12], four.the Inheat [12],flux the input heat flux to the heattosink was considered to be constant.

Of course,Of with increasing the aspectthe ratio, the input input the heat sink was considered to be constant. course, with increasing aspect ratio, the energy also increases.

In this study, input for allfor heat was was considered constant. input energy also increases.

In thisthe study, theenergy input energy all sinks heat sinks considered constant.

However, in this study, as can be seen in Figure 7, the number of optimal horizontal finsfins is equal to to However, in this study, as can be seen in Figure 7, the number of optimal horizontal is equal five,five, which is very close to the corresponding value in [12]. which is very close to the corresponding value in [12].

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AR = 1 n=3 9 of 15 n=4 n=5 n=3n=6 n=4n=7 n=5 n=9 n=6 n=11 n=7 n=9n=13

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AR = 1

360 370 350 360 373

340

n=5

369 373

365

330 357 353

320

310 310

300 0.2 300

n=3

369

n=5

365

n=3

361

SOT/s

320

SOT/s

330

SOT/s

SOT/s

340 350

349 345

Exrta values of "n" have been removed Exrta values of "n" have been removed

361 n = 11

357 n = 11

353

n = 13

349

0.3

345

0.4 0.3

0.3

0.2

n=11 n=13

0.5 0.4

0.6 0.5

0.7 0.6

LR 0.5

0.4 0.3

LR

0.4

0.5

0.7

0.8 0.8

0.9

n = 13

0.9

0.6

LR 0.6

0.7

0.8

0.7

0.8

0.9 0.9

1.0 1.0

LR

Figure atat different 1010 mm).

Figure7.7.Effects Effectsofoflength lengthratio ratio(LR) (LR)ononSOT SOT differenthorizontal horizontalfins finsnumber number(H(H= = mm).

Figure 7. Effects of length ratio (LR) on SOT at different horizontal fins number (H = 10 mm).

Figure8 8the thestreamlines streamlinesfor forthe thethree threeLR LRvalues values(0.3, (0.3,0.7 0.7and and0.9) 0.9)are aredepicted. depicted.AsAs can seen, InInFigure can bebe seen, In Figure 8 the streamlines for the three LR values (0.3,places 0.7 and(between 0.9) are depicted.

As can be seen, at length ratio of LR = 0.7, the convection is formed in two the horizontal fins and the at length ratio of LR = 0.7, the convection is formed in two places (between the horizontal fins and the at length ratio of LR = 0.7, the convection is formed in two places (between the horizontal fins and the distancebetween betweenthe thehorizontal horizontalfin fintip tipand andthe theline lineofofsymmetry). symmetry).But ButatatLR LR= =0.5 0.5and andLR LR= =0.9 0.9the the distance distance between the horizontal fin tip and the line of symmetry). But at LR = 0.5 and LR = 0.9 the convection is formed only in one place.

The presence of streamlines zone indicates that there is convection is formed only in one place.

The presence of streamlines in each indicates that there convection is formed only in one place. The presence of streamlines in each zone indicates that there a liquid phase motion which implies the possibility of the natural convection heat transfer. is a liquid phasephase motion which implies thethe possibility convectionheat heat transfer. is a liquid motion which implies possibilityof ofthe the natural natural convection transfer.

LR = 0.5

LR = 0.7

LR = 0.9

Figure 8. Convection strength at LR = 0.5, 0.7 and 0.9 (n = 5, H = 10 mm).

at LR = 0.5, 0.7 and 0.9 (n = 5, H =LR 10 = mm).

LRFigure = 0.5 8. Convection strength LR = 0.7 0.9

Figure 8. Convection strength at LR = 0.5, 0.7 and 0.9 (n = 5, H = 10 mm).

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It seems seems that that the the liquid liquid phase phase movement movement at at LR LR == 0.7 0.7 is is much much better better than than the the other other two two cases cases (LR (LR It = 0.5 and 0.9).

Because the streamlines are well distributed throughout the heat sink, hence that the = 0.5 and 0.9). Because the streamlines are well distributed throughout the heat sink, hence that the possibility of of the the liquid At LR LR == 0.5, 0.5, the the liquid liquid phase phase does does not not possibility liquid phase phase movement movement is is higher higher at at LR LR = = 0.7.

0.7. At move well in the space between the horizontal fins.

In the third case (LR = 0.9), due to the long length move well in the space between the horizontal fins. In the third case (LR = 0.9), due to the long length of the the horizontal horizontal fins, fins, it it is is difficult difficult to between the the space space of of each In other other of to establish establish aa connection connection between each fin. fin. In words, the it words, the liquid liquid phase phase movement movementisisblocked blockeddue duetotothe thelong longlength lengthofofthe thehorizontal horizontalfins. fins.Therefore, Therefore, seems that the convection strength for LR = 0.7 is superior to LR = 0.7 and LR = 0.7, which consequently it seems that the convection strength for LR = 0.7 is superior to LR = 0.7 and LR = 0.7, which leads to higher objective function. consequently leads to higher objective function.

As can be seen in Figure 9, for for heat heat sink sink with with 13 13 horizontal horizontal fins, fins, adding adding larger larger fins fins disrupt disrupt the the As can be seen in Figure 9, convection.

As shown in Figure 9, the liquid PCM movement is disturbed owing to an increase in convection. As shown in Figure 9, the liquid PCM movement is disturbed owing to an increase in fins length, length, hence hence the the convection convection intensity For this this reason, reduces with with increasing increasing fins fins fins intensity reduces. reduces. For reason, SOT SOT reduces length for heat sink with 13 horizontal fins as shown in Figure 7. length for heat sink with 13 horizontal fins as shown in Figure 7.

LR = 0.3

LR = 0.9

Figure9.

9. Comparison Comparison of of strength strength convection convection between betweenLR LR== 0.3 and LR = 0.9 (n ==13, Figure 13,H H==10 10mm). mm).

Considering the heat sink width grows, thethe aspect ratio AR(đ??´đ?‘… =W the constant constantheat heatsink sinkheight, height,asasthe the heat sink width grows, aspect ratio H= increases.

TheThe effects of increasing ARAR on SOT are shown in Figure 10. According to Figure 10, the ) increases. effects of increasing on ��� are shown in Figure 10. According to Figure 10, increase in AR does not affect the number of optimum fins.

That is, for H = 10 mm from AR = 1 to AR the increase in AR does not affect the number of optimum fins. That is, for H = 10 mm from AR = 1 to = 5, =the fin number is 5 (i.e., = 5). mentioned, addingadding fin has afin positive effect (thermal = 5).

As mentioned, has a positive effect AR 5, optimal the optimal fin number is 5nopt (i.e., noptAs conductivity enhancement) as well as a negative effect (latent heat reduction).

As the number of (thermal conductivity enhancement) as well as a negative effect (latent heat reduction). As fins the rises up to seems effectthe of thermal conductivity (positive number of five, fins itrises upthat to the five,incremental it seems that incremental effect ofimprovement thermal conductivity effect) is superior to theeffect) decremental effect to of the the latent heat reduction hence the improvement (positive is superior decremental effect of(negative the latenteffect), heat reduction objective function improved.

However, by increasing the number by of fins from 5 the to 13, the negative (negative effect), hence the objective function improved.

However, increasing number of fins effect prevails over the positive effect and therefore the objective function will diminish.

As aspect from 5 to 13, the negative effect prevails over the positive effect and therefore the objectivethe function ratiodiminish. grows (AR , theaspect horizontal between vertical walls increases, hence conduction will As↑)the ratio distance grows (đ??´đ?‘… ↑), thethe horizontal distance between thethe vertical walls heat transfer diminished.

In this case, convection heat transfer has a larger role in SOT. In other increases, hence the conduction heat transfer diminished. In this case, convection heat transferwords, has a as AR role grows, the role of convection in the function larger in SOT. In other words, asheat AR transfer grows, the roleobjective of convection heatbecomes transfermore in theimportant objective and therefore the optimal length ratio should be reduced.

As shown in ratio Figure 10, thebe optimal length function becomes more important and therefore the optimal length should reduced.

As ratio LR decreases with increasing AR. shown in Figure 10, the optimal length ratio LR decreases with increasing AR.

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363

358

SOT/s

AR = 3

344 349

344 339

SOT/s

SOT/s

353

348

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349 354

358

353

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AR = 3

354

SOT/s

363

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339

334

348 334

343

338

n=3 n=5 343 n=11 n=13 0.3 338

329 n=3 n=5 n=11 0.4 n=13 0.3

329

324

0.5

0.6 0.5 LR 0.6 AR = 4 LR

0.4

350

0.8

324

0.9

0.3

n=11 n=13

0.3

0.4 0.4

0.5

0.6 0.6LR

0.5

AR = 5

0.7 0.7

0.8 0.8

0.9 0.9

LR AR = 5

350 350

337

SOT/s

SOT/s

340

SOT/s

SOT/s

310

0.7

0.9

337

340

320

0.8

AR = 4

350

330

0.7

n=3 n=5 n=11 n=3 n=5 n=13

330

311 311

320

n=3 n=5 n=11 310 n=13 0.3

324 324

n=3 n=5 n=11 n=13 0.3

0.4

0.4

0.5

0.5

0.6

LR

0.6

LR

0.7

0.7

0.8

0.8

0.9

0.9

298

298

n=3 n=3 n=5 n=5 n=11 n=11 n=13 n=13

0.3

0.3

0.4

0.4

0.5

0.5

0.6

0.6

0.7

LR

0.7

0.8

0.8

0.9

0.9

LR

Figure10.

10. Optimum Optimum fins at at different AR.AR. Figure finsnumber number different Figure 10. Optimum fins number at different AR.

Following Figure (AR==5), 5), the the objective objective function as the ratio (LR) (SOTdiminishes ) diminishes Following Figure 1010(AR function(SOT) as length the length ratio (LR) Following Figure (AR = 5),ratio the (AR), objective function diminishes theand length ratio (LR) grows. Because at 10 high aspect convection heat(SOT) transfer plays a keyas role, the shorter grows. Because at high aspect ratio (AR), convection heat transfer plays a key role, and the shorter the fin length, the greater intensity there will (Figure 11). grows.the Because at high aspectconvection ratio (AR), convection heatbetransfer plays a key role, and the shorter fin length, the greater convection intensity there will be (Figure 11). the fin length, the greater convection intensity there will be (Figure 11).

đ??żđ?‘… = 0.9

đ??żđ?‘… = 0.9

đ??żđ?‘… = 0.7

đ??żđ?‘… = 0.7 Figure 11. Streamlines at LR = 0.7 and LR = 0.9 (H = 10 mm, n = 5, AR = 5).

Figure 0.90.9 (H(H = 10 mm, n =n5,= AR = 5).

Figure11.

11.Streamlines StreamlinesatatLR LR= =0.7 0.7and andLR LR= = = 10 mm, 5, AR = 5).

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It was mentioned that the optimal fin number for H = 10 mm is five (i.e., nopt = 5). Now, the effects It was mentioned that the optimal fin number for H = 10 mm is five (i.e., nopt = 5). Now, the effects of increase in the heat sink height on the number of optimal fins are investigated. The sensitivity of the of increase in the heat sink height on the number of optimal fins are investigated. The sensitivity of objective function (SOT) to n and LR at different heat sink height of 12.5, 15, 17.5 and 20 mm was the objective function (SOT) to n and LR at different heat sink height of 12.5, 15, 17.5 and 20 mm was illustrated in Figure 12. 12.

According to to Figure 12,12,the of 12.5, 12.5,15, 15,17.5 17.5 and illustrated in Figure According Figure theoptimal optimalfins finsnumber number at at heights heights of 20 mm is also five (i.e., n = 5).

It seems that by increasing the number of fins up to five, the positive opt(i.e., nopt = 5). It seems that by increasing the number of fins up to five, the and 20 mm is also five effectpositive of fin installation superior its negative buteffect, by increasing the number of finsoffrom 5 effect of fin was installation wastosuperior to its effect, negative but by increasing the number 5 to 13, the negative effect (decreasing the phase change enthalpy the overcomes positive to 13,fins thefrom negative effect (decreasing the phase change enthalpy overcomes positivethe effect (increase effect (increase in thermal conductivity), hence SOT decreases.

Focusing on Figure 12 revealed that in thermal conductivity), hence SOT decreases. Focusing on Figure 12 revealed that the optimum theratio optimum (LRopt) is thetorange of 0.3 that to 0.7.

Noteisthat opt is the LR which maximize length (LRoptlength ) is inratio the range ofin0.3 0.7. Note LR theLR LR which maximize the SOT. opt the SOT.

H = 12.5 mm

370

H = 15 mm

362.5

359.0

365

SOT/s

SOT/s

355.5

360

352.0

355

350 0.2

348.5

n=3 n=5 n=11 n=13 0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

345.0 0.2

n=3 n=5 n=11 n=13 0.3

0.4

0.5

H = 17.5 mm

355

0.6

0.7

0.8

0.9

1.0

0.7

0.8

0.9

1.0

LR

LR

H = 20 mm

340

335

345

330

SOT/s

SOT/s

350

325

340

335

330 0.2

320

n=3 n=5 n=11 n=13 0.3

0.4

0.5

0.6

LR

0.7

0.8

0.9

1.0

315 0.2

n=3 n=5 n=11 n=13 0.3

0.4

0.5

0.6

LR

Figure The variationin inSOT SOT with with respect at at different heat sinksink height.

Figure 12.12.

The variation respecttotoLR LR different heat height.

Volume Fraction Variations PCMPCM Volume Fraction Variations As the horizontal fins installed,the the PCM PCM volume volume decreases.

ForFor thethe basebase heatheat sink sink (without As the horizontal fins installed, decreases. (without ) variations in terms of AR are shown in Figure 13. horizontal fins), the PCM volume fraction (đ?œ‘ horizontal fins), the PCM volume fraction (Ď•PCM ) variations in terms of AR are shown in Figure 13.

As the aspect ratio increases from 1 to 5, the PCM volume fraction (for base heat sink) rises from 0.926 As the aspect ratio increases from 1 to 5, the PCM volume fraction (for base heat sink) rises from 0.926 to 0.965. To evaluate the variation in PCM volume fraction for heat sink equipped with the horizontal to 0.965.

To evaluate the variation in PCM volume fraction for heat sink equipped with the horizontal fins, the optimal number of fins along with appropriate length ratio (LR) must be determined from fins, Figure the optimal fins along appropriate ratioconsidering (LR) must Equation be determined 10 andnumber then theofoptimal PCMwith volume fraction islength calculated (1). As from Figure 10 and then the optimal PCM volume fraction is calculated considering Equation (1).

As shown shown in Figure 13, đ?œ‘ for heat sink with optimal fins number increases as the heat sink becomes in Figure wider.13, Ď•PCM for heat sink with optimal fins number increases as the heat sink becomes wider.

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1.00

PCM volume fraction for base heat sink (without horizontal fins)

PCM Volume Fraction

0.95

0.90

0.85

PCM volume fraction for heat sink equipped with optimal number of fins 0.80

1

2

3

4

5

AR Figure Figure13.

13.Variations Variationsin inPCM PCMvolume volumefraction fractionfor forbase baseheat heatsink sinkand andheat heatsink sinkequipped equippedwith withoptimal optimal number numberof ofhorizontal horizontalfins. fins.

Note that that with with increasing increasing đ?œ‘Ď•PCM, , the the fin fin volume volume fraction fraction đ?œ‘ Ď• f in decreases.

As mentioned mentioned in in Note decreases. As Figure 11, 11, with with the the increase increase in in AR, AR, the the intensity intensity of of the the convection convection heat heat transfer transfer isis amplified amplified and and Figure therefore the the presence presence of of horizontal horizontal fins fins may may disturb disturb the the liquid liquid phase movement. movement. Therefore Therefore with with therefore increasing AR, shorter therefore it isit expected thatthat withwith increasing aspect ratio, increasing shorter fins finsperform performbetter betterand and therefore is expected increasing aspect the finthe volume fraction Ď• f in forđ?œ‘the heat sinkheat equipped with the optimal fins diminishes. ratio, fin volume fraction for the sink equipped with thenumber optimalofnumber of fins Figure 13 shows AR rises, theAR optimal PCM volume fraction increases, which corresponds diminishes.

Figurethat 13 as shows that as rises, the optimal PCM volume fraction increases, which to a decreasetoina Ď• .

This means that as the heat well widens, less fin volume fraction is required. corresponds decrease in đ?œ‘ .

This means that as the heat well widens, less fin volume fraction f in 13 shows that the PCM volume fraction of the studied basestudied heat sinks changed in the range isFigure required.

Figure 13 shows that the PCM volume fraction of the basehas heat sinks has changed of the 0.92range to 0.97. installing horizontal fins reduces Ď•PCM that the đ?œ‘ optimal varies in the in ofHowever, 0.92 to 0.97.

However, installing horizontal finssoreduces soĎ•that optimal PCM the range of 0.83 to 0.93. đ?œ‘ varies in the range of 0.83 to 0.93.

Conclusions 6.6.Conclusions Inthis thisstudy, study, the the thermal thermal behavior behaviorof ofaa PCM-based PCM-basedheat heatsink sinkin inthe thepresence presenceof ofhorizontal horizontalfins fins In was numerically investigated.

The sensitivity of the objective function (SOT) to the input variables of was numerically investigated. The sensitivity of the objective function (SOT) to the input variables of theaspect aspectratio ratio (AR), (AR), number number of of horizontal horizontal fins fins (n) (n) and and length length ratio ratio (LR) (LR) was was evaluated. evaluated. The Themost most the important results are as follows: important results are as follows:

••

• •

Based on on the the results, results, the number ofof fins rises up Based the optimal optimalnumber numberof ofhorizontal horizontalfins finswas wasfive. five.As Asthe the number fins rises to five, the incremental effecteffect of thermal conductivity improvement (positive effect) was superior up to five, the incremental of thermal conductivity improvement (positive effect) was to the decremental effect of the latent heat reduction (negative effect), hence the objective function superior to the decremental effect of the latent heat reduction (negative effect), hence the improved.function However, for the increase in number fins from to 13, theofnegative effect objective improved.

However, for the of increase in 5number fins from 5 toprevailed 13, the over the positive effect and over therefore safe operation timetherefore diminished. negative effect prevailed the the positive effect and the safe operation time The optimum length ratio for the horizontal fins depends on the aspect ratio. As the aspect ratio diminished. increases, it is length recommended use horizontalfins finsdepends with a lower length ratio.

However, the optimal The optimum ratio fortothe horizontal on the aspect ratio.

As the aspect ratio value of the ratio variedtoinuse the horizontal range of 0.3fins to 0.7. increases, it length is recommended with a lower length ratio. However, the optimal value of the length ratio varied in the range of 0.3 to 0.7.

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Author Contributions: A.M.: Writing, Methodology; H.M.: Writing, Methodology, Introduction, Investigating; S.A.-N.: Methodology, Data curation; R.K.: Writing, Conceptualization, Software, Validation; A.K.: Writing, Formal analysis; G.C.: Writing—review & editing, Formal analysis. All authors have read and agreed to the published version of the manuscript.

Funding: This research received no external funding.

Conflicts of Interest: There is no conflict of interest.

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[CrossRef] © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).