Numerical and Experimental Investigations on the ...

International Journal of Computation and Applied Sciences IJOCAAS, Volume 4, Issue 3, June 2018, ISSN: 2399-4509

330

Abstract— The impact of pin shape on the thermal performance

characteristics of pin fin heat sink is assessed numerically and

experimentally. Utilizing commercial ANSYS Fluent software,

three-dimensional numerical simulations, based on the standard

k-ε turbulence model with various parameters were studied on six

different pin shapes: circular, elliptical, drop - shaped, square,

hexagonal and triangular. In order to compare these various pin

shapes, in all pin fin shapes hydraulic diameter the same. The pin

fins were equidistantly arranged in a staggered manner. Six pin

fin heat sink shapes were researched in turbulent forced-

convection for Reynolds number 5165 to 41320 and heat flux 3000

to 24000 W/m2. To approve the numerical simulation and further

supporting study for the effect of pin shapes, experiments were

carried out for the same pin shapes with varying air velocities and

heat fluxes. A good agreement was observed between numerical

prediction and experimental data of heat transfer coefficient.

From the results, it is indicated that the round pin fins provide a

superior path for heat to transfer than sharp edges pin fins.

Additionally, during the optimization process for pin fin numbers

to be have varied, it is found that the Nf=46 can achieve the best

heat sink performance. Upon comparison analysis of various

shapes of pin fin heat sinks, the drop-shaped pin fin heat sink

demonstrated the best thermal performance indicated lowest

thermal resistance and heights Nusselt number.

Index Terms— Thermal performance, CFD, pin fin heat sink,

PIFHS, numerical simulation.

I. INTRODUCTION

Heat sinks are the most widely recognized for cooling the

hardware that utilized in electronics.

By increasing the surface area of the fins as well as fins

rearrangement, the thermal performance is improved to cooling

the electronic parts. Two basic sorts of heat sinks which are

generally utilized in the industry namely: pin-fin heat sinks

(PIFHSs) and plate-fin heat sinks (PLFHSs). PIFHSs consist of

littler volumes but larger exposure surfaces, so its thermal

performance is superior to that of the PIFHSs. Amid the most

recent couple of decades, for cooling of electronics,

applications utilizing PIFHSs have increased significantly

because of an increment in densities of heat flux and product

scaling down. Hung, et al., [2005] evaluated the thermal

performance of heat sinks with kept impingement cooling

utilizing infrared thermography. They investigated the impacts

of the type of the heat sinks, the height and the width of the fins,

impinging Reynolds number, the tip of the fins and the distance

between the nozzles on the thermal resistance.

1,2,3/ Department of Mechanical Engineering / Faculty of Engineering /Al-

Mustansiriyah University, Baghdad *E-mail address: jaffal. env @uomustansiriyah.edu.iq ,

Waqar, et al., [2008] developed analytical models for deciding

heat transfer from a staggered and in-line and cylindrical

PIFHSs. The forecasts of these models approve the past

numerical/experimental outcomes. Compared to the in-line

arrangement, lower thermal resistance and higher pressure drop

were obtained from the staggered arrangement. A numerical

investigation of heat transfer characteristics of an elliptical

PIFHS with and without metal foam embeds is directed

utilizing 3D conjugate heat transfer demonstrate by Hamid and

Mod [2010]. The impacts of metal foam porosity and air flow

Reynolds number on the overall pressure drop, efficiency and

Nusselt number of heat sink are examined. Significant effect of

the structural properties of metal foam insert was seen from the

results for both heat transfer and fluid flow in a PIFHS.

Utilizing Taguchi method Yang, et al., [2013] developed the

numerical simulation of an optimum PIFHS with air impinging

cooling. The target of this Taguchi method examination was to

inspect the impacts of the fin height and fin spacing on the

thermal resistance and to find the optimum gathering. It is

discovered that a sufficient inter-fin spacing arrangement could

expand the Nusselt number. The additions of the Nusselt

number diminishing step by step as as the Reynolds number

augmentations. The effects of geometries are spoiled at high

Reynolds numbers. Therisa, et al., [2014] introduced a modified

model of the heat sink with configurationally parameters

perforations in the Hyoid (U-shaped) PIFHS. Staggered and in-

line flow types with and without were considered. From this

examination, they gathered that the hyoid PIFHS is giving

superior thermal performance contrasted to the standard PIFHS.

Khalil, et al., [2015] displayed simulation model for CPU

Processor utilizing COMSOL Multiphasic programming for

thermal performance of PIFHS with a various in-line

arrangement. The simulation result showed that different heat

thermal performance from variable in-line arrangement of pin

fin. The consequence of this survey in a perfect world can

uncover some understanding on how to improve in-line pin fin

arrangement heat sink design. Amer, et al., [2015] investigated

experimentally and numerically thermal performance of

circular PIFHSs for an in-line arrangement utilizing numerous

perforations For the conjugate heat transfer, the predictions

numerical data is found to agree well with experimental data

.The endorsed numerical model is utilized to complete a

parametric investigation of the effect of the situating and

number of circular perforations, which showed that, the Nusselt

augmentations relative to the quantity of pin perforations. It

demonstrated that to amplify the advantages from perforations

mind must be taken to guarantee that they are adjusted with the

https://orcid.org/0000-0002-3048-9623

Numerical and Experimental Investigations on the Performance

Characteristics for Different Shapes Pin Fin Heat Sink

Hayder Mohammad Jaffal*1, Hasan Salam Jebur2 and Abdullah Adil Hussein3

I


331

predominant flow direction and made with a decent finish

surfaces with high quality. Eaman [2015] numerically explored

the thermal performance PIFHSs with hexagonal shape to

compare with rectangular, square and circular PIFHSs in

laminar forced Convection. Fluid flow and heat transfer were

assumed to be two-dimensional, with identical pressure and

velocity distribution in the z-direction. For both staggered and

in-line arrangements, a comparison of hydraulic and thermal

performance are presented. For all PIFHSs, it can be noticed

that the thermal performance in the staggered arrangement

superior than in in-line arrangement. Amit [2016] proposed a

model of the modified PIFHS. The pins modification was

concentrated on extending pins outward. For free convection

for circular shape in in-line arrangement, thermal analyses of

the standard pin fin and the modified PIFHSs have been

evaluated numerically. It is clear from this numerical

examination, he concluded that the modified PIFHS will

perform superior better to the standard one. Muthukumarn, et

al., [2016] researched experimentally heat transfer and fluid

flow characteristics of cylindrical, perforated and horizontal

grooved cylindrical pin fins over inline pin fin arrangement.

The best enhancement in Nusselt number corresponds to the

grooved cylindrical pin fin. At higher inter fin space ratio, the

cylindrical pin fins have less pressure drops than grooved

cylindrical and perforated. Fatima, et al., [2016] performed a

numerical analysis of mixed convective modes of heat transfer

for solid fin arrays and new outline hollow/perforated elliptic

fins. Heat transfer characteristics of the new heat sinks under

few significant parameters such as Reynolds number and

geometrical position of the hole the contrasted to the standard

configuration. At all Reynolds number, the superior

augmentation in the heat transfer for perforated fins compare to

that with the solid fins. CFD investigation was directed to

explore the heat transfer coefficient of circular, elliptical,

square and triangular profile pin fins by Ravikumar and James

[2016]. The numerical parameters incorporate fin pitch in the

flow direction, fin arrangement and Reynolds number. All the

four heat sinks have equal wetted surface area of 0.00628m2, in

light of this; examination has been expert for the heat transfer

coefficient. The coefficient of heat transfer is most

extraordinary in the case of triangular fin contrasted to the other

fin profiles. Manikandan and Pachaiyappan [l2016]

numerically simulated hydraulic and thermal characteristics of

a perforated drop-shaped PIFHS in the staggered arrangement.

The drop-shaped pin fins results are contrasted with rectangular

and circular shapes. For the similar pressure drop

characteristics, the perforated drop -shaped pin fins give the

lower friction factor and better heat transfer when contrasted to

rectangular and circular pin fins. Chao, et al., [2017] researched

numerically the thermal and hydraulic characteristics of

turbulent forced convection of air flow through perforated

circular PIFHSs with constant heat flux. Numerical

computations are performed with a circular perforated pin fin

heat sink for the parameters contemplated including perforation

space, perforation diameter, circular pin fin diameter and

Reynolds number. Perforated pin fin has a higher averaged

Nusselt number compared with the solid pin fin, and the bigger

the pin fin diameter, the higher the friction factor and averaged

Nusselt number. The expanding trend of the averaged Nusselt

number is more prominent than that of the friction factor, so the

heat transfer augments while the pin fin diameter increments.

Ho, et al., [2017] studied forced convective heat transfer

characteristics of novel airfoil heat sinks. Heat sinks of airfoil

shaped fins with staggered arrays were examined

experimentally and the results were contrasted with heat sinks

with circular and rounded rectangular fins. Examination of the

experimental results comes about demonstrated thermal

performance of the rounded rectangular and airfoil heat sinks

outperformed those of the circular heat sink.

In the paper, a comparative numerical and experimental

study was conducted on the thermal performance characteristics

in PIFHS different pin shapes. 3D Numerical simulation using

ANSYS FLUENT with various parameters were studied on six

different pin shapes with same hydraulic diameter: circular,

elliptical, drop - shaped, square, hexagonal and triangular. To

validate the numerical simulation and further supporting study

for the effect of pin shapes, experiments were carried out for the

same pin shapes with varying air velocities and heat fluxes.

II. NUMERICAL ANALYSIS

Steady state CFD detailing used to display this issue in ANSYS

FLUENT. In the CFD estimations, there are three principle

steps: Pre-Processing, Solver Execution, Post-Processing. Pre-

Processing is the demonstrating where the settled objective are

resolved and the computational mesh is made. Fins were

characterized as aluminum with a constant heat flux input at the

base surface of the array, utilizing fluid flow characteristics and

exhibit geometry, boundary conditions and numerical models

are set to start up the solver in the second step. Solver continues

running until the point when the meeting is come to. Right when

solver is finished, the results are reviewed which the post is

preparing part.

Governing equations: The forced convective fluid flow is

governed by the continuity equation, momentum equation and

energy equation. The steady state, turbulent, incompressible

fluid flow is considered. Also, the thermo-physical properties

of air are assumed to be constant. The radiation heat transfer

and bouncy impacts are immaterial. According to the above

suppositions, using standard k-ε model the three-dimensional

governing equations are:

Air Side

Continuity equation:

𝜕𝑢

𝜕𝑥+

𝜕𝑣

𝜕𝑦+

𝜕𝑤

𝜕𝑧= 0 (1)

x- momentum equations:

𝑢𝜕𝑢

𝜕𝑥+ 𝑣

𝜕𝑢

𝜕𝑦+ 𝑤

𝜕𝑢

𝜕𝑧= −

1

𝜌0

𝜕𝑝

𝜕𝑥+ 𝜗(

𝜕2𝑢

𝜕𝑥2 +𝜕2𝑢

𝜕𝑦2 +𝜕2𝑢

𝜕𝑧2) (2)

y- momentum equations:

𝑢𝜕𝑣

𝜕𝑥+ 𝑣

𝜕𝑣

𝜕𝑦+ 𝑤

𝜕𝑣

𝜕𝑧= −

1

𝜌0

𝜕𝑝

𝜕𝑦+ 𝜗(

𝜕2𝑣

𝜕𝑥2 +𝜕2𝑣

𝜕𝑦2 +𝜕2𝑣

𝜕𝑧2) (3)


332

z- momentum equations:

𝑢𝜕𝑤

𝜕𝑧+ 𝑣

𝜕𝑤

𝜕𝑦+ 𝑤

𝜕𝑤

𝜕𝑧= −

1

𝜌0

𝜕𝑝

𝜕𝑥+ 𝜗 (

𝜕2𝑤

𝜕𝑥2 +𝜕2𝑤

𝜕𝑦2 +𝜕2𝑤

𝜕𝑧2 ) (4)

Energy equation

𝑢𝜕𝑇

𝜕𝑥+ 𝑣

𝜕𝑇

𝜕𝑦+ 𝑤

𝜕𝑇

𝜕𝑧=

𝐾𝑓

𝜌0𝐶𝑝+ (

𝜕2𝑇

𝜕𝑥2 +𝜕2𝑇

𝜕𝑦2 +𝜕2𝑇

𝜕𝑧2) (5)

Solid Side

𝐾𝑠 (𝜕2𝑇

𝜕𝑥2 +𝜕2𝑇

𝜕𝑦2 +𝜕2𝑇

𝜕𝑧2) + �̇�𝑠 = 0 (6)

where Ks and Kf are the heat sink and fluid thermal

conductivity, T is the temperature within the eat sink, , u, v and

w are velocity components. q˙s is the heat generated per unit

volume.

Computational Domain and Boundary conditions: A typical

mesh distribution and computational domain of the duct and the

PIFHS are shown in Fig. 1. In the computational domain, the

outlet (pressure outlet, inlet (velocity inlet), wall and symmetry

boundary conditions were applied. The boundary conditions

alluding to Fig. 1 are:

-inlet:

𝑝 = 𝑝𝑖𝑛, 𝑇 = 𝑇𝑖𝑛 = 300𝐾, 𝑤 = 𝑉𝑖𝑛, 𝑢 = 𝑣 = 0

-outlet:

𝑝 = 𝑝𝑜𝑢𝑡 , 𝑢 = 𝑣 = 0,𝜕𝑇

𝜕𝑧= 0

-adiabatic walls:

𝑢 = 𝑣 = 𝑤 = 0,𝜕𝑇

𝜕𝑦=

𝜕𝑇

𝜕𝑥= 0

-heated wall:

𝑢 = 𝑣 = 𝑤 = 0, 𝑞′′𝑤 = −𝑘𝜕𝑇

𝜕𝑥

III. EXPERIMENTAL ANALYSIS

In this segment, the test some portion of this examination led to

approve the proposed compact model is described. The

arrangement of the experimental system of a PIFHS was set up

and the details of test section are depicted.

Description of Test Rig: The test section is designed and

manufactured so that different parameters can be measured, in

the research facilities of Faculty of Engineering/Al-

Mustansiriyah University. The general arrangement of the

equipment is shown photographically in Fig. 2, and

schematically in Fig. 3. The experimental system consists of

wind tunnel, flow rate controller, blower, heat input unit power

supply, and a few thermocouples. The wind tunnel has an

interior cross-section of area 150 mm × 200 mm with a total

tunnel length of 800 mm. The tunnel is developed of galvanized

steel sheet of 1.5 mm thickness; the face of the wind conduit is

made of 4 mm thickness transparent Plexiglas glass sheet to

give a clear view of the within the test segment as appeared in

Fig.4. To give uniform heat flux transition to the PIFHS, heater

of plate type is led at power inputs of 300 W. With help of

bolts, the heat sink is fitted on a plate heater. The plate heater is

assigned inside protection box to insulate thermally by 30 mm

thickness glass wool. To control the electric power

commitment of the heating coil, the regular was utilized to get

reliable heat flux along the test segment. By a multi-meter, the

heater current and the voltage drops are measured. By single

stage centrifugal blower, air has been drawn through the duct.

By using the butterfly valve, the air flow rate is controlled.

Using an orifice plate with related ducting and differential

manometer, the air flow rate measured. Mercury thermometers

used to quantify air temperatures in the tunnel at inlet and outlet.

To gauge the base plate temperatures in the center area inside

heat sink, an outstanding the holes have been gathering to

implant three thermocouples type-K. In this work, to augment

the pin –fin performance, selection of PIFHS design depended

on fin shape; six different aluminum PIFHSs are fabricated by

using CNC machine namely: circular, elliptical, drop - shaped,

square, hexagonal and triangular. All pin fins with same

hydraulic diameter of 7 mm, base plate 114 mm long and

thickness of 18.5 mm, number of pin fins is 23. The height of

pin fins is 45 mm, fins arrays are in staggered arrangement with

equal pin spacing in streamwise and spanwise directions

(SL=ST=20 mm). The configurations of arrays of all PIFHSs

are shown in Fig. 5.

Fig.1. Mesh distribution and computational domain for the

heat sink.

Heat sink


333

Fig. 2. Photographic picture for the experimental test rig.

1

3

4

6 5 9

8

Inlet air

Fig. 3. Schematic diagram for experimental test rig.

1 Air blower 10 Holes for thermocouples

2 flanges 11 Heat sink

3 Butterfly valve 12 Plate heater

4 Air pipe 13 Insulated box

5 Orifice plate 14 Glass- wool insulation

6 U-Tube manometer 15 Thermocouple insertion point

7 Convergent section 16 Inlet air thermocouple

8 Flow straightener 17 Outlet air thermocouple

9 Wind tunnel 18 Base plate thermocouple

13

12

11

2 10 10

15

7

14

16 17 18


334

\

Fig. 4. Wind tunnel.

Fig. 5. The configurations of all heat sinks: a- circular, b- elliptical, c -drop - shaped,

d- square, e- hexagonal and f- triangular.

(a) (b) (c)

(d) (e) (f)


335

Test Procedure: In order to evaluate the thermal performance

of PIFHS, a series of experiments was done at various heat

fluxes (1544 - 25088 W/m2) and air velocities (Reynolds

number range is 4965- 24421) to measure heat dissipation for

various heat sinks. By changing the heat sinks with various pin

fin shapes, the relating qualities are measured. A typical test

procedure is as per the following: Air velocity is first controlled

by a butterfly valve. The heater is then powered up and allowed

to. Exactly when the modules temperature does not change

with time (steady state condition was accomplished), the local

temperatures of the modules were then recorded. At consistent

state condition, the temperature estimations of the two modules

were recorded. Comparable systems were taken after to repeat

the test for the diverse fan speeds. Thermocouples were placed

at different modules and test procedures were repeated again.

To reach the steady state, the system usually takes around 25

minutes.

Data Reduction: From electrically heated test surface, the

convective heat transfer rate is computed by using a relation:

𝑄𝑁 = 𝑄(𝑒𝑙𝑒𝑐𝑙𝑟) + 𝑄(𝑐𝑜𝑛𝑑) + 𝑄(𝑟𝑎𝑑) = 𝑚𝑎∙ 𝐶𝑝𝑎(𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛) (7)

From the electrical current and potential provided to the

surface, the electrical heat input is computed. In similar

examinations, specialists detailed that total conduction and

radiation heat losses from a comparable test surface would be

around 1.1% and 0.5% of the total electrical heat input and

consequently Qcond and Qrad are dismissed in the present work.

The convection heat transfer from the test segment can be

figured as:

𝑄𝑁 = ℎ𝑎𝑣𝐴𝑇 [𝑇𝑠 − (𝑇𝑜𝑢𝑡+𝑇𝑖𝑛

2)] (8)

The area AT in eEq. 8 is total area of fin that touches fluid going

through the conduit; it is equivalent to the entirety of aggregate

surface zone and projected area commitment from the blocks

Kavita, et al., 2014.

For circular PIFHS:

𝐴𝑇 = 𝑊𝐿 + 𝜋𝐷𝑁𝑡𝑜𝑡𝑎𝑙𝐻 + 2𝐵[𝐿 + 𝑊] (9)

The maximum base plate temperature (TS) can be calculated

from three reading of thermocouples measured heat sink

temperatures as:

𝑇𝑆 =𝑇1+𝑇2+𝑇3

3 (10)

The average convection heat transfer coefficient can be

registered as Kavita, et al., 2014:

ℎ𝑎𝑣 =𝑄𝑁

𝐴𝑇[𝑇𝑠−(𝑇𝑜𝑢𝑡+𝑇𝑖𝑛

2)]

(11)

Presently, the thermal resistance is ascertained as Mehedi, et

al., 2015:

𝑅𝑡ℎ =1

ℎ𝑎𝑣𝐴𝑇 (12)

The dimensionless groups are computed as takes after:

The Nusselt number is characterized as:

𝑁𝑢 =ℎ𝑎𝑣𝐷ℎ

𝑘𝑎 (13)

Keeping in mind the end goal to better reflect the actual

genuine velocity at the estimation area in the test segment, the

average velocity is computed utilizing volumetric volume flow

rate; V° and the free fluid flow area; Afree, such as:

𝑉𝑎𝑣 =𝑉°

𝐴𝑓𝑟𝑒𝑒 (14)

The free flow area Afree for circular pin fin is calculated as:

𝐴𝑓𝑟𝑒𝑒 = 𝐴𝑤 − [(𝑊𝐵) + 𝑁𝑥𝐻𝐷] (15)

The air Reynolds number based on the duct dimension is

defined as:

𝑅𝑒 =𝜌𝑎𝑉𝑎𝑣𝐷ℎ

𝜇𝑎 (16)

The hydraulic diameter of the rectangular area of the passage is

characterized as:

𝐷ℎ = 4𝐴𝑤

𝑃𝑤 (17)

where Aw is the cross-sectional area of tunnel, and Pw the

perimeter of tunnel.

The values of air thermophysical properties are gotten in all

calculations at the bulk mean temperature, which is:

𝑇𝑚𝑒𝑎𝑛 = (𝑇𝑜𝑢𝑡+𝑇𝑖𝑛

2) (18)

III. RESULTS AND DISCUSSION

Experimental verification of a numerical simulation: By

keeping up the same operating conditions, an experimental

study is conducted to validate the CFD simulation results. Good

agreement between the experimental and simulation results

with maximum deviation of 10% as shown in the Fig.6 and

Fig.7. The variety of convection heat transfer coefficient with

heat flux was presented in Fig.6. As the heat flux increases, the

convection heat transfer coefficient increases, in light of fact

that the heat sink gets warmed up progressively in view of

conduction heat transfer from the heat source. Convection heat

transfer coefficient as a function of Reynolds number was

presented in Fig.7. Heat transfer coefficient increasing in


336

proportional relation with Reynolds number because of the

fluid is progressively heated due to convection heat transfer.

Numerical Results: By using commercial FLUENT 15

software utilized Standard k-ε model for turbulence model, the

conjugate heat transfer investigation of PIFHS have been

finished. Conjugate heat transfer simulation work comprises of

the analysis of both convection and conduction heat transfer

forms.

The air flows over the fins at the interface locales of fluid and

solid. The principal equations solved for fluid flows are the

turbulence-modeling and momentum equations. In the fluid

flow region, the solution of the Navier-Stokes equations gives

the pressures and velocity vectors. Navier-Stokes equations

with standard k-ε applied turbulence model have the

successfully solved using FLUENT 15. By applying the

interface boundary conditions at the coupled locale,

temperature distribution along the length of the fin acquire by

solved the energy equation for both solid (aluminum) and fluid

(air) regions. Through series of numerical calculations, the

impacts of heat flux, Reynolds number and fins number on the

thermal performance in the PIFHS have been presented.

The results are focused to the local static temperature

distribution in heat sinks. the filled contour of temperature of

the heat sink at the heat flux of 23000 W/m2 and an air velocity

of 3 m/s in a wind tunnel for various pin shapes presents in

Fig.8. The extreme temperature is observed for all of the pin

shapes in the base plate, which is phenomenal for any heat fin-

based thermal system. The temperature at the base of the fin is

high contrast to that at the top surface of the fin indicates the

cooling effect of air at the top surface. Also, since the level

intensity of heat transfer between the air and the aluminum is

crest close to the heat source at the bottom surface, the centers

are the hottest spots for all pin shapes of heat sinks. The least

base plate temperatures observed for hexagonal, drop - shaped

and elliptical PIFHSs models.

Fig. 9 shows the turbulence kinetic energy contour for all

simulated PIFHSs for an air velocity of 3 m/s inside a wind

tunnel and heat flux of 23000 W/m2 and. It is clearly noticed

that the higher turbulence kinetic energy existing on the top

surfaces of all fines and the wall of surrounding fins around the

heat sink. This normal phenomenon for all PIFHSs was

observed because the mechanical energy of the flow is

converted into turbulence at the interface. It likewise be noticed

that the maximum turbulence kinetic energy at the highest point

of PIFHS causes changes in temperature at the height of fin.

From the comparison between a various cross-sectional

geometry of PIFHSs, it is also noticed that the increment rates

of turbulence kinetic energy in the heat sinks with cross-

sections of elliptical and drop-shaped are much higher than

other heat sinks.

The variety of Nusselt number with heat flux for Reynolds

number 20660 is presented in Fig.10. For all pin shapes, it can

be seen that the Nusselt number is increased as the heat flux

increased. The reason for this increase increases in the Nusselt

number is a direct result of the increment in the quantity of heat

transfer. For example, for drop-shaped PIFHS, and at the het

flux of 3000 and 24000 W/m2, the Nusselt number is calculated

as 470.569 and 790.294 respectively. The effect of the

Reynolds number on the Nusselt number with for a heat flux of

20000 W/m2 is represented in Fig.11. For each pin shapes, the

Nusselt number is expanding as the Reynolds number extended.

It is clearly noticed that the increments of the Nusselt number

0

20

40

60

80

100

120

140

0 5000 10000 15000 20000 25000 30000

Experimental

CFD simulation

He

at t

ran

sfe

r co

eff

icie

nt

[W/m

² °C

]

Heat Flux [W/m²]

Fig. 6. Comparison of experiments and modeling: heat

transfer coefficient as a function of heat flux for elliptical

pin fin heat sink.

0

10

20

30

40

50

60

70

80

90

100

0 5000 10000 15000 20000 25000 30000

Experimental

CFD simulation

He

attr

ansf

er

coe

ffic

ien

t [W

/m²

°C]

Reynolds Number [-]

Fig. 7. Comparison of experiments and modeling: heat

transfer coefficient as a function of Reynolds number

for elliptical pin fin heat sink.


337

are because of the expansion in heat transfer that was caused by

expanded an air flow rate. For example, for drop-shaped

PIFHS, as air the Reynolds number of 5165 and 41320, the

Nusselt number is found as 386.0634 and 899.1398

respectively.

To show the impact of the fins number on the thermal

performance of PIFHS, three geometries for elliptical pin fin

chosen for this reason. The values of fins number are 46, 33 and

23 and corresponding space between fins are 15 mm, 16 mm

and 20 mm respectively. Heat transfer characteristics for the

three configurations have appeared in Figs. 12 to 14. Fig. 12

illustrates the results of computing the effect of the heat flux on

the thermal resistance for inlet velocity of 2 m/s. It is clearly

noticed that for all geometries, the thermal resistance is slightly

decreased as the heat flux increased. This decrease of thermal

resistance is the direct result of the increase in the quantity of

heat transfer. Then again, it is demonstrated from this figure as

the number of fins increases, the thermal resistance tend to

decreases. The effect of Reynolds number on the thermal

resistance for a heat flux of 20000 W/m2 is represented in

Fig.13. The thermal resistance is diminished as the Reynolds

number expanded for each configuration. In the computational

domain, as the number of fins is increased (i.e. by decreasing

the spacing between fins) the heat transfer increases and this is

joined by a comparing ascend in the flow velocity inside heat

sink. By increasing the inlet velocity, a larger rate of heat

transfer is accomplished. At high velocity, the distinction of

heat transfer at various fin spacing is extensive. Figure 14

demonstrates the static temperature contours for the three fin

number at heat flux of 12000 W/m2 and air velocity of 0.5 m/s.

The temperature at the lower of the fin is higher contrasted with

that at the top surface of the fin indicates the cooling impact of

air at the top surface. On the other hand, the base plate

temperature tends to increment transcend the exit of heat sink.

With abatement the spacing between the pin-fin, the flow is

quickened between the pin fins. This increases the velocity

between the pins and it improving heat transfer characteristics

of PIFHS. Compared with that for the other two cases, It has

been seen that for Nf=23, the heat transfer from the fins to the

bulk of the fluid is fewer. This is because of little area for heat

transfer available in this situation for the same volume of the

heat sink.

Experimental Results: Figs.15 and 16 demonstrates the

impacts of heat flux and Reynolds on the convection heat

transfer coefficient for all manufactured PIFHSs. The variety of

the heat transfer coefficient with the heat flux upon for various

heat sinks for Re = 24421 is represented in Fig.15. It is indicated

from this figure that the heat transfer coefficient increments as

heat flux increments for all PIFHSs. Additionally, it is shown

that the biggest heat transfer coefficient can be accomplished in

the drop-shaped PIFHS as a result of the deferral in thermal

flow detachment from drop-shaped pin fin and expanded the

wetted surface area contrasted with other sorts. The heat

transfer coefficient comparing to various Reynolds number for

various PIFHSs for heat flux=16892 W/m2 is appeared in

Fig.16. The heat transfer coefficient increments as the Reynolds

number increment for each PIFHS. The most vital explanation

behind expanding heat transfer coefficient with Reynolds

number while expanding the quantity of air, the flow capability

of heat expelled will augment and caused an extended the heat

transfer coefficient. It is additionally shown that the biggest

heat transfer coefficient is accomplished in the drop-shaped

PIFHS due to higher heat removal compared with other sorts.

Figs. 17 to 18 demonstrate the impacts of the heat flux and

Reynolds number on the on the thermal resistance for all

manufactured PIFHSs. The variety of the thermal resistance

with the heat flux for constant Reynolds number is appeared in

Fig.17. For all heat sinks, the thermal resistance decreases with

the increasing of heat flux because of expanding in heat transfer

between the air and the heat sink. The effect of Reynolds

number on the thermal resistance for constant heat flux is

outlined in Fig.18. For all PIFHSs, it can be seen that the

thermal resistance is contrarily proportional with Reynolds

number.

IV. CONCLUSION

In this study, turbulent forced convection performances of

various pin-fins geometries have been numerically and

experimentally investigated. For this examination, it is found

that a good agreement between the predicted numerical and

experimental results for the same working conditions that was

considered. Thermal performances characteristics for PIFHSs

were evaluated by studying the effects of both geometrical and

operational parameters. By analyzing the present work results,

the most important conclusions can be summarized as follows:

- A round pin fins provides a better path for heat to transfer than

sharp edges pin fins.

- For a given heat flux, inlet air Reynolds number has an

effective impacts on the Nusselt number.

- The drop-shaped pin-fins array has a higher Nusselt number

compared to the all pin-fins arrays.

- During the optimization process for pin fin numbers to be have

varied, it is found that the Nf=46 can achieve the best heat sink

performance.


338

Fig. 8. Temperature contour of the pin fin heat sinks: a- circular, b- elliptical, c- drop-shaped, d- square, e-

hexagonal and f- triangular.

(f) (c)

(b) (e)

(a) (d)


339

Fig. 9. Turbulence kinetic energy contour of the pin fin heat sinks: a- circular, b- elliptical, c- drop-shaped, d-

square, e- hexagonal and f- triangular.

(a) (d)

(c) (f)

(b) (e)


340

Fig. 10. Numerical variation of Nusselt number with

different heat fluxes for all heat sinks.

200

300

400

500

600

700

800

900

0 5000 10000 15000 20000 25000

circular

elliptical

drop - shaped

square

hexagonal

triangular

Nu

ssle

t N

um

be

r [-

]

Heat Flux [W/m²]

Fig. 11. Numerical variation of Nusselt number with

Reynolds number for all heat sinks.

200

300

400

500

600

700

800

900

1000

1100

0 10000 20000 30000 40000 50000

circular

elliptical

drop - shaped

square

hexagonal

triangular

Nu

ssle

t N

um

be

r [-

]Reynolds Number [-]

0.15

0.2

0.25

0.3

0.35

0.4

0 5000 10000 15000 20000 25000

Nf=23

Nf=33

Nf=46

The

rmal

Re

sist

ance

[K

/W]

Heat Flux [W/m²]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 10000 20000 30000 40000 50000

Nf=23

Nf=33

Nf=46

The

rmal

Re

sist

ance

[K

/W]

Reynolds Number [-]

Fig. 12. Numerical variation of thermal resistance with

different heat fluxes for different fins number of

elliptical pin fin heat sink.

Fig. 13. Numerical variation of thermal resistance

with Reynolds number for different fins number of

elliptical pin fin heat sink.


341

Fig. 14. Temperature contour of the different fins number of elliptical pin

fin heat sink: a- Nf=46, b- Nf=33 and c- Nf=23

(a)

(b)

(c)


342

30

40

50

60

70

80

90

100

110

0 5000 10000 15000 20000 25000 30000

circular

elliptical

drop - shaped

square

hexagonal

triangular

He

at T

ran

sfe

r C

oe

ffic

ien

t [W

/m2.K

]Reynolds Number [-]

30

40

50

60

70

80

90

100

110

120

130

0 5000 10000 15000 20000 25000 30000

circular

elliptical

drop - shaped

square

hexagonal

triangular

He

at T

ran

sfe

r C

oe

ffic

ien

t [W

/m2.K

]

Heat Flux [W/m2]

Fig. 15. Experimental variation of heat transfer coefficient

with heat flux for all pin fin heat sinks.

Fig. 16. Experimental variation of heat transfer coefficient with

Reynolds number for all pin fin heat sinks.

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 5000 10000 15000 20000 25000 30000

circular

elliptical

drop - shaped

square

hexagonal

triangular

The

rmal

Re

sist

ance

[K

/W]

Heat Flux [W/m2]

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0 5000 10000 15000 20000 25000 30000

circular

elliptical

drop - shaped

square

hexagonal

triangular

The

rmal

Re

sist

ance

[K

/W]

Reynolds Number [-]

Fig. 17. Experimental variation of thermal resistance with

heat flux for all pin fin heat sinks.

Fig. 18. Experimental variation of thermal resistance with

Reynolds number for all pin fin heat sinks.


343

NOMENCLATURE

A heat transfer area [=m2]

B base height [=m]

D fin diameter [=m]

Dh hydraulic diameter [=m]

H height of fins [=m]

h convection heat transfer coefficient [=W/m2 oC]

k thermal conductivity [=W/m oC]

L length of heat sink [=m]

�̇� mass flow rate [= kg/s]

Nu Nusselt number

Nf number of fins

Nx number of fins in row

Re Reynolds number

Rth thermal resistance [= oC/W]

SL pin spacing in streamwise direction

ST pin spacing in spanwise direction

T temperature [= oC]

t fin thickness [= m]

V velocity [=m/s]

W width of heat sink [= m]

GREEK SYMBOLS

Ρ density [=kg/m3]

μ dynamic viscosity [=N s/m2]

SUBSCRIPTS

a air

av average

in inlet

N convection

out outlet

S base

T total

w win tunnel

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