numerical investigation of fluid flow and heat transfer

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cooling of trailing edge of turbine blades and electronic equipment cooling. However .... Flow across array of pin fins has fluid flow and heat transfer characteristics of both internal as well as external flows. A case ... Plate dimensions, Hp × Lp (mm×mm) 50 × 50. Approach ... Air flows from the bottom to the top of the chan- nel.
Proceedings of the 15th International Heat Transfer Conference, IHTC-15 August 10-15, 2014, Kyoto, Japan

IHTC15-8825

NUMERICAL INVESTIGATION OF FLUID FLOW AND HEAT TRANSFER CHARACTERISTICS OF PARTIAL LENGTH PIN FINS IN VERTICAL PARALLEL PLATE CHANNEL Ravi S. Jadhav,1 C. Balaji2,∗ 1 Research

Scholar, HTTP Laboratory, IIT Madras,Chennai-600036 2 Professor, IIT Madras, Chennai-600036

ABSTRACT This paper presents the results of a full three dimensional numerical investigation of forced convection heat transfer in a vertical parallel plate channel filled partially with a cluster of pin fins along its height. This novel approach of having pin fins on both vertically heated plates can be employed in applications like internal cooling of trailing edge of turbine blades and electronic equipment cooling. However, enhanced heat transfer is achieved at the cost of extra pressure drop. With increasing miniaturization and packaging of electronic components, there is a need to cool multiple electronic components but with space constraint. The axes of the pin fins are aligned horizontally with air flow from the bottom to the top. The pin fins on both the vertical plates are placed in an inline arrangement. A transitional flow regime with Re > 200 is considered. The vertical plates are maintained at 375K and conjugate heat transfer boundary condition is applied so as to c approximate realistic working conditions. Simulations are carried out with Ansys Fluent 13 to predict the fluid flow and temperature fields. The k −  turbulence model with enhanced wall treatment is applied to model turbulence closure. The vertical channel with no pin fins is used for the baseline comparisons. The pressure drop, Nusselt number and overall thermal performance in terms of two dimensionless parameters are obtained for the system. Dependency of Nusselt number on the Reynolds number and fin density is deduced.

KEY WORDS: Pin Fin, Electronic equipment cooling, Heat transfer enhancement, Turbulence, Conjugate Heat Transfer, Numerical Simulation and Super Computing

1. INTRODUCTION Information and communication technology industry has witnessed tremendous increase in processing power with advanced semi-conductor devices of today dissipating very high levels of power. Effective and efficient dissipation of high heat fluxes arising out of these pose considerable challenge to thermal engineers.. Although direct air cooling is still the most economical method for cooling of electronic equipments, in view of its poor heat transfer performance, secondary finned surfaces are usually provided to increase heat transfer. Among different configurations of finned surfaces, pin fins are regarded as one of the most effective method of heat transfer augmentation. Pin fins along with increasing the net surface area available for heat transfer enhance heat transfer by breaking the boundary layer of still air that is wrapped around its surface since still air is a good thermal insulator.



Corresponding C. Balaji: [email protected] 1

IHTC15-8825 2. LITERATURE SURVEY Research in the field of heat transfer enhancement by employing pin fins gained momentum when the temperature of the electronic devices like printed circuit boards started exceeding the critical limit(75◦ C). Till now, extensive research, both experimental and numerical, has been reported to investigate fluid flow and thermal characteristics of pin fin heat sink systems. Basic research in pin fin cooling has been done by several investigators as for example [1], [2] and [3]. [4] performed an experimental investigation on inline as well as staggered pin fin arrangement to study the effects of shroud clearance, optimum inter-fin spacing and missing pin on heat transfer. Authors formulated the correlation for heat transfer and concluded that the optimum inter fin spacing in both the directions is 2.5D regardless of the shroud clearance and type of array used. Heat transfer characteristics of cylindrical pin fins in a rectangular channel were studied experimentally by [5]. For in-line as well as staggered arrangement, they found that the Nusselt number increases with the Reynolds number and maximum heat transfer occurs at Sy/D = 2.94. A rectangular channel without fins was used for the baseline comparison. [6] experimentally studied steady state heat transfer from pin fin arrays for in-line and staggered arrangements of the pin fins. Air flow was orthogonal to the pin fins. For a Reynolds number range of 31386683, optimal spacings of the fins in the span wise and stream wise directions were determined. [7] studied experimentally pin fin heat sinks with pins having circular, elliptic and square cross section for in-line as well as staggered configurations. Authors concluded that for an in-line arrangement, the circular pin fin shows an appreciable effect of fin density on the heat transfer performance owing to unique deflection flow patterns. [8] performed an experimental study to investigate transitional fluid flow and heat transfer characteristics of a rectangular channel with staggered short pin fins. They concluded that, in the transitional flow regime, the pin fin channels lead to a 68% increase in the overall thermal performance. [9] numerically examined six kinds of pin shape, namely NACA, drop-form, lancet, elliptic, circular and square. Their simulations showed that the NACA profile offers little advantage. The first comparison criteria involving constraints as same hydraulic diameter, same coverage ratio and same pin length showed that an in-line circular pin fin configuration outperforms the other pin fin cross sections. The second comparison criterion with the constraints being the same blockage area, same distance between the pins and same pin length showed that a staggered elliptical form is the best one. [10] developed analytical models for determining heat transfer from inline and staggered pin fin heat sinks using integral method of boundary layer analysis. In this work, the effect of thermal conductivity on the thermal performance of heat sinks was also examined. From the aforementioned literature review, it is clear that while several numerical and experimental studies on pin fin heat sinks are available, studies on closely spaced pin fins protruding from the two surfaces of a channel, giving rise to a mesh like arrangement have not been considered in the literature. Such a type of arrangement of pin fins on vertical parallel plates is expected to augment the overall heat transfer rate considerably and can be employed in cooling multiple electronic equipments where space constraint is very critical.

2.1 Flow across array of pin fins Flow across array of pin fins has fluid flow and heat transfer characteristics of both internal as well as external flows. A case of cross flow over a pin fin array particularly depicts characteristics of external flow while pin fins in a channel resemble external as well as internal flow. Since the thermal boundary layer is continuously broken by the incoming air, heat transfer rate is higher than other finned configurations. Flow across long slender fins (L/D > 10) closely resembles the flow across tube banks. From [2], it is seen that for Re < 1000 flow across tube banks is laminar despite the presence of vortices in the wake region behind pin fins. However, [12] studied laminar and transition regime for flow across tube banks and suggested that for Re < 200, flow can be considered laminar and for 200 < Re < 5000 flow is in transition regime. In the present study, a vertical channel is formed by two vertical isothermal plates and pin fins protrude from both the plates. There will be a region in the channel where pin fins from both the plates will cross each other giving rise to dense, mesh like arrangement of pin fins. The objective of this study is to investigate fluid flow and heat transfer characteristics of the system.

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IHTC15-8825 Table 1 Value/Dimensions used for modeling the system Quantity Plate dimensions, Hp × Lp (mm×mm) Plate thickness, tp (mm) Pin diameter, D1 , D2 (mm) Height of pin fin 1, H1 (mm) Height of pin fin 2, H2 (mm) Pins for array 1 (Nt × Nl ) Pins for array 2 (Nt × Nl ) Distance between the plates, b (mm)

Value 50 × 50 5 4 30 30 6×6 5×5 45

Quantity Approach velocity, Uapp (m/s) k of Al (W/mK) k of air (W/mK) Density of air, ρ(kg/m3 ) Specific heat of air, Cp (J/kgK) Prandtl number, Pr(Air) Ambient temperature(◦ C)

Value 1 202 0.0242 1.1767 1007 0.71 27

3. MODEL AND GOVERNING EQUATIONS 3.1 Model Two vertical plates with dimensions 50mm × 50mm × 5mm (Hpt × Lpt × tpt ) are separated by a distance of 45mm. Pin fin arrangement on both the plates is in-line. Air flows from the bottom to the top of the channel. The backsides of the plates are kept at a constant temperature of 375K. The plate dimensions, pin fin dimensions and thermo-physical properties of air used for modeling the system are summarized in Table 1. The velocity range considered in the study is 0.5 − 5m/s for which the Reynolds number range turns out to be 200 − 2800 and this implies that the flow is in the transition regime. The Reynolds number is calculated on the basis of mean velocity in the minimum cross section which happens to be the region where fins from both the plates cross each other.

3.2 Governing equations Governing equations for the problem under consideration are the continuity equation, Navier-Stokes equations and energy equation. For the current study, simulations are performed for a three dimensional transition flow of air through a vertical channel with cluster of pin fins along its height. Turbulence is handled by the Reynolds Averaged Navier Stokes (RANS) equations along with an appropriate turbulence model to handle closure. For a three dimensional, steady, incompressible flow with heat transfer, governing equations are as follows: Continuity equation: ∂u ∂v ∂w + + =0 ∂x ∂y ∂z

(1)

∂u ∂u ∂u 1 ∂P ∂ 02 ∂ 0 0 ∂ 0 0 +v +w =− + ν∇2 u − (u ) − (u v ) − (u w ) ∂x ∂y ∂z ρ ∂x ∂x ∂y ∂z

(2)

∂v ∂v ∂v 1 ∂P ∂ 02 ∂ 0 0 ∂ 0 0 +v +w =− + ν∇2 v − (v ) − (u v ) − (v w ) ∂x ∂y ∂z ρ ∂y ∂x ∂y ∂z

(3)

∂w ∂w ∂w 1 ∂P ∂ ∂ 0 0 ∂ 0 0 +v +w =− + ν∇2 w − (w0 2 ) − (u w ) − (v w ) ∂x ∂y ∂z ρ ∂z ∂x ∂y ∂z

(4)

Momentum equation: u

u

u

3

IHTC15-8825 Energy equation: u

∂T ∂T ∂T ∂ 0 0 ∂ 0 0 ∂ +v +w = α∇2 T − (u T ) − (v T ) − (w0 T 0 ) ∂x ∂y ∂z ∂x ∂y ∂z

(5)

Turbulence closure is handled with the low Re number standard k- model known for its robustness to solve wide variety of problems with reasonable accuracy. The turbulent kinetic energy, k and its rate of dissipation,  are obtained from the following transport equations: ∂ ∂ ∂ ∂ h µt  ∂k i ∂ h µt  ∂k i (ρku) + (ρkv) + (ρkw) = µ+ + µ+ + ∂x ∂y ∂z ∂x σk ∂x ∂y σk ∂y ∂ h µt  ∂k i µ+ + Pk + Pb − ρ ∂z σk ∂z

(6)

∂ ∂ ∂ h µt  ∂ i ∂ h µt  ∂ i ∂ (ρu) + (ρv) + (ρw) = µ+ + µ+ + ∂x ∂y ∂z ∂x σ ∂x ∂y σ ∂y µt  ∂ i  2 ∂ h µ+ + C1 (Pk + C3 Pb ) − C2 ρ ∂z σ ∂z k k

(7)

and

where, Pk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Pb is the generation of turbulence kinetic energy due to buoyancy, C1 , C2 , C3 are constants and σk , σ are the turbulent Prandtl numbers for k and  respectively. The constants used in the above equations are given by C1 = 1.44, C2 = 1.92, Cµ = 0.09, σk = 1, σ = 1.3 Conduction through the pin fins is given by the energy equation in the solid which is given by, ∂ 2 Ts =0 ∂x2i

(8)

3.3 Boundary Conditions Since the system is symmetric about the vertical XY plane, only one half of the system is modeled. Fig. 1 represents the core computational domain of the physical problem along with appropriate boundary conditions. Appropriate boundary conditions at the inlet, outlet and plates are applied to represent actual flow of air through the system. These boundary conditions can be summarized as follows: • For inlet section 5-6-7-8, U (x, 0, z) = 0, V (x, 0, z) = Uapp , W (x, 0, z) = 0 and T (x, 0, z) = Tin

(9)

• No slip and constant temperature boundary condition is applied for wall 11-12-14-13 and 9-15-16-10. U (0, y, z) = V (0, y, z) = W (0, y, z) = 0 and T (0, y, z) = Tw f or wall 9 − 15 − 16 − 10

(10)

U (b, y, z) = V (b, y, z) = W (b, y, z) = 0 and T (b, y, z) = Tw f or wall 11 − 12 − 14 − 13

(11)

• For face 1-4-6-5, symmetry boundary condition is applied. ∂V ∂U ∂T = = 0 and V (x, y, 0) = 0 =0 ∂z ∂z x,y,0 ∂z x,y,0

4

(12)

IHTC15-8825

Fig. 1 Core computation domain with boundary conditions

• For the remaining walls, adiabatic wall boundary condition is assigned.

4. SOLUTION PROCEDURE c The mesh for the system is generated in Ansys 13 Meshing software using unstructured tetrahedron elements. Since the gradients of velocity and temperature are critical near the surface area of pin fins, inflation technique with ten layers of prism elements is applied which makes the mesh near wall surface extremely fine. Fig. 2 shows the mesh generated with the inflation layers. The pressure-velocity coupling is handled using the SIMPLE scheme. Second order upwind scheme is used for the interpolation of velocity and temperature gradients. Finally, the discretized governing equations [1]-[8] are solved using the commercially available Fluc ent 13 software. Since standard k- model does not capture near wall gradients, enhanced wall treatment is employed in that region. Inflation layers generated helps to keep the y + values near the wall region of the order of 1. Computations were carried out on the Virgo Cluster populated with 2XIntel E5-2670 eight core 2.6 GHz processor, High Performance Computing Facility available at IIT Madras. Pin fins were considered to be aluminium with constant and isotropic properties and air was selected as fluid

Fig. 2 Mesh with inflation layers for a cut section

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IHTC15-8825 8

Nusselt number, Nu

7

6

5

4

3

2 0 10

Experimental Results[13] Present Results 1

2

10

3

10

10 −3

Grashof Number, Gr × 10

Fig. 3 Validation with experimental results from the literature with constant specific heat and thermal conductivity.The Sutherland model is used to calculate molecular viscosity as,  T  1 273.15 + C 2 s µ= µ0 (13) 273.15 T + Cs where, µ0 =dynamic viscosity at 273.15K and 101.325kPa, Cs =Sutherland constant and T=Absolute temperature

4.1 Validation of the solution For validation of the solution, numerical simulations are performed for a smooth vertical channel without pin fins. [13] performed experimental studies on multi-mode heat transfer between vertical parallel plates. Authors approximated the vertical plates as isothermal and the average Nusselt numbers based on the hot wall were calculated for a wide range of Grashof numbers and aspect ratios. For an aspect ratio of five, the Nusselt number for five Grashof number values are obtained numerically and compared with the experimental values of [13]. From fig.3, it is clear that present results are in good agreement with literature and this serves as a validation for the numerical methodology employed in the present study.

4.2 Grid Independence Study A convergence criterion of 10−4 is set on residuals of all equations for all computations and solution is said to be converged only if all the residuals satisfy this convergence criteria. Attention is given to conservation of mass and energy. Initially, laminar model is switched on and the solution is converged for Uapp upto 0.5m/s. However, for Uapp = 1m/s (Reynolds number comes out to be 550), convergence criteria could not be met Table 2 Results of the grid independence study Mesh Coarse Normal Fine

Cells(in million) 2.28 3.4 4.1

6

To (K) 324.72 324.18 324.16

Nu 37.14 36.91 36.85

IHTC15-8825 which indicates that the flow is in transition regime. Hence, for further computations k −  turbulence model is switched on. Ansys Meshing software is highly flexible and automatic which gives users the choice to generate coarse mesh, normal mesh and fine mesh. In addition, mesh relevance factor (range -100 to +100) helps refine the mesh further. Hence, for grid independence check, three meshes were generated with the number of cells ranging from 2 million to 4 million cells. By comparing the results for the three meshes, the difference in Nusselt Numbers between the fine mesh and normal mesh comes out to be less than 1% Hence, a normal mesh with a relevance factor equal to 50 is selected for further computations. It should be duly noted that unique number of cells cannot be generated for all the models. However, the cell count for all the models comes out to be anywhere between 2.5 million and 4 million (for a velocity of 1.5m/s).

4.3 Analysis In order to simplify the calculation of heat transfer from the pin fin arrays, overall heat transfer co-efficient of the system corresponding to the wetted area is proposed which is calculated as, Qtotal = havg × Awetted × 4Tm

(14)

The logarithmic temperature difference, 4Tm is calculated as, 4Tm =

(Tw − Tin ) − (Tw − Tout ) (Tw − Tin ) ln (Tw − Tout )

(15)

The inlet and the outlet bulk fluid temperatures Tin and Tout are the temperatures at the inlet and the outlet of the control volume. The inlet bulk temperature is taken as 300K for all the numerical models while the outlet bulk temperature is calculated as R U T dAout Tout = RAout (16) Aout U dAout where, U=Velocity in flow direction and Aout =Outlet cross section of control volume. To present the results in dimensionless form, a pin array Nusselt number(N ua ) is used which is given as, N ua =

havg dh kf

(17)

where, dh is the hydraulic diameter of pin fin and kf is the thermal conductivity of air. To describe the pressure drop of air across the inlet and outlet cross section in dimensionless terms, a friction factor is calculated as, f=

2 × 4P × dh 2 ρ × Vmax ×L

(18)

The enhancement in convective heat transfer rates at higher velocities is achieved but at the cost of energy spent to overcome the friction experienced by the air as it flows across the pin fin array. For an assessment of the heat transfer enhancement afforded by the pin fins, smooth channel without pin fins on both the plates is used as the baseline case for purpose of comparison. In order to present the performance of the system, two dimensionless parameters namely γ and ε are defined. The first performance parameter γ is the ratio of heat transfer of the system with pin fins to that without pin fins. It gives the overall heat transfer enhancement of the system afforded by the pin fins. Qwith pinf ins (19) γ= Qsmooth channel The second performance parameter ε evaluates the performance of the system by including both heat transfer

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IHTC15-8825 Table 3 Pin fin arrangement on two vertical plates Pin Fin Array 1(Nl × Nt ) Pin Fin Array 2(Nl × Nt ) Sy D (mm) 8×6 7×5 6 4 7×6 6×5 7.2 4 6×6 5×6 8.4 4 5×6 4×6 10.4 4

Sy /D 1.5 1.8 2.1 2.625

and pressure drop terms and is defined as, ε=

[Q/4P ]with pin f ins [Q/4P ]smooth channel

(20)

5. RESULTS AND DISCUSSION The fluid flow and the heat transfer performance of the channel with pin fins for four different ratios of Sy /D namely 1.5, 1.8, 2.1 and 2.625 are studied. The diameter of the pin fins is kept constant at 4mm and the number of pin fins on both the plates is changed to obtain the desired ratios. Details of the pin fin arrangement on both the plates for these four Sy /D ratios is shown in Table3. Fig. 4 shows the variation of the outlet air temperature with Reynolds number for four Sy /D ratios mentioned above. When the inlet air temperature is kept constant, the outlet air temperature decreases with increasing Reynolds number. This happens because heat transfer rate increases as incoming air velocity is increased. Fig.5 shows the variation of pressure drop across the system for different Sy /D ratios. It can be noted that at lower Reynolds number, pressure drop is more or less the same for all the four SyD / ratios. However, at higher Reynolds number, air experiences more friction as the density of the pin fins increases and higher pressure drop is observed for higher Reynolds number and denser pin fin configurations. The variation of friction factor with the Reynolds number is shown in fig.6. From this figure, it is seen that the friction factor decreases as the Reynolds number increases, however it tends to reach the asymptotic value at higher Reynolds number which one can safely say in the turbulent region.

350 S /D=1.5 y

Bulk Outlet Temperature, To (K)

345

Sy/D=1.8 Sy/D=2.1

340

Sy/D=2.6 335 330 325 320 315 310 305 300

0

500

1000

1500

2000

2500

3000

Reynolds Number, Re

Fig. 4 Bulk Outlet Temperature as a function of Reynolds number

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IHTC15-8825 0

90

10

Sy/D=1.5 80

Sy/D=1.8 Sy/D=2.1 Sy/D=2.6

60

Friction Factor, f

Pressure drop (Pa)

70

50 40 30

Sy/D=1.5 −1

Sy/D=1.8

20

10

Sy/D=2.1 10 0

Sy/D=2.6 0

500

1000

1500

2000

2500

3000

0

500

Reynolds Number, Re

1000

1500

2000

2500

3000

Reynolds Number, Re

16

9

14

8.5 First Performance Parameter, γ

Average Nusselt number, Nu

Fig. 5 Pressure drop as a function of Reynolds number Fig. 6 Friction factor as a function of Reynolds number

12 10 8 6 Sy/D=1.5

4

Sy/D=1.8

7.5

7

6.5

Sy/D=1.5 Sy/D=1.8

6

Sy/D=2.1

2

8

Sy/D=2.1

Sy/D=2.6 0

0

500

1000

1500

2000

2500

Sy/D=2.6 5.5

3000

Reynolds number, Re

0

500

1000

1500

2000

2500

3000

Reynolds number, Re

Fig. 7 Average Nusselt number as a function of Fig. 8 First Performance Parameter, γ as a function of Reynolds number Reynolds number

The average Nusselt number is evaluated for each Sy /D ratio for the velocity range 0.5 − 5m/s. The Reynolds number is calculated on the basis of maximum velocity which occurs in the minimum cross section. The variation of average Nusselt number with respect to Reynolds number for four Sy /D ratio is shown in fig.7. From the figure, it is clear that as the velocity of the incoming air is increased, more is the heat transfer from the pin fin surface, hence Nusselt number increases. From the literature, researchers have proved that Nusselt number is maximum when Sy /D ratio is close to 2.5 Among the four Sy /D ratios, a pin fin arrangement with Sy /D = 2.625 gives the highest Nusselt number at a given Reynolds number. The variation of first performance parameter with respect to Reynolds number is shown in fig.8. From the figure, it is seen that γ increases as the Reynolds number is increased, becomes maximum and then tends to approach asymptotic value at higher Reynolds number. Maximum heat transfer enhancement achieved is about

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Second Performance Parameter, ε

Second Performance Parameter, ε

IHTC15-8825

1.2

1.1

1

0.9 Sy/D=1.5 Sy/D=1.8

0.8

Sy/D=2.1

1.2

1.1

1 Uapp=1

0.9

Uapp=2 Uapp=3

0.8

Uapp=4 Uapp=5

Sy/D=2.6 0.7

0

500

1000

1500

2000

2500

0.7 1.4

3000

1.6

1.8

Reynolds number, Re

2

2.2

2.4

2.6

2.8

Sy/D

Fig. 9 Second performance parameter, ε as a function Fig. 10 Variation of second performance parameter, ε of Reynolds number with Sy /D 8.5 times that obtained with smooth channel.At lower Reynolds number, γ is same for all the four Sy /D ratios, however higher values of γ are observed for denser pin fin configurations. Fig.9 shows the variation of second performance paramter, ε with respect to Reynolds number for different Sy /D ratios. It is clear from the figure that ε initially increases with Reynolds number, attains the maximum value and then decreases. This general trend is observed for all the four Sy /D ratios. One can also note that for each Sy /D ratio, the value of ε becomes highest at Re = 1200. However, among the four Sy /D ratios, overall performance of the system with Sy /D ratio equal to 2.625 is better than the remaining configurations. It can also be noted that at higher Reynolds number, the performance of all the configurations is more or less similar. Fig.10 gives the change in ε for four Sy /D ratios against different approach velocities. It can be seen that higher values of ε are observed for Uapp = 1m/s.

16

Nusselt number (correlation), Nucorr

Correlation Coefficient=0.9963 14 12 10 8 6 4 2 0

0

2

4

6

8

10

12

14

16

Nusselt number (data), Nudata

Fig. 11 Parity plot between the fit and numerical Nusselt number values

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IHTC15-8825 Based on the forty data points, a correlation for Nusselt number in terms of Reynolds number and Sy /D ratio is deduced by multiple linear regression technique in the form as, N u = 0.108Re0.5524

 S 0.514 y

(21)

D

Fig. 11 shows the parity between the correlation and numerical data from which it is clear that the correlation fits the data well giving the correlation coefficient as 0.9963 with an RMS error of 0.2637.

6. CONCLUSIONS In this study, the fluid flow and heat transfer characteristics of a vertical channel with a cluster of pin fins along its height is investigated numerically using the high resolution full three dimensional conjugate heat transfer model using the RANS approach. Four different arrangement of pin fins on both the plates with 4mm diameter and 30mm length is studied. The presence of the pin fins on the second plate increases the complexity of the study significantly. The variation of the Nusselt number with respect to Reynolds number and fin density on both the plates is examined and a correlation is derived. It can be concluded that highest Nusselt number is reported for Sy /D = 2.625 which gives 5 × 6 pin fin configuration on plate 1 and 4 × 5 pin fin configuration on plate 2. Two dimensionless parameters γ and ε are defined to evaluate the performance of the system. Although more pressure drop is observed by employing pin fins, at the same time heat transfer enhancement achieved is significantly large (upto 8.5 times) and pressure drop in comparison is very small. Higher values of γ are observed for denser pin fin configurations at higher Reynolds number. The variation of second performance parameter, ε with Reynolds number gives the velocity range of air as 1.5 − 2.5m/s at which the performance will be optimum in terms of heat transfer and pressure drop. For all the four Sy /D ratios, the variation of ε is similar. However, higher ε is observed for Sy /D = 2.625 which again proves that 5×6 pin fin configuration on plate 1 and 4 × 5 pin fin configuration on plate 2 is the optimum configuration for Re range 200 ≤ Re ≤ 2800.

Nomenclature 

Second performance parameter

(-)

kf

thermal conductivity of air

γ

First performance parameter

(-)

Lp

length of the plate

µ ρ

absolute viscosity density

Awetted wetted area

(W/mK) (m)

2

Nusselt number

3

pressure

2

Prandtl number

(-)

Reynolds number

(-)

(N s/m ) N u (kg/m ) P (m ) P r (m) Re

b

distance between the plates

Cp

specific heat

D

pin diameter

f

friction factor

(-)

Gr

Grashof number

(-)

H

pin height

havg

average heat transfer coefficient

k

thermal conductivity of aluminium

(J/kgK) Sy

(-) (P a)

Inter fin spacing in stream-wise direction

(m)

plate thickness

(m)

Tin

bulk inlet temperature

(K)

Tout

bulk outlet temperature

(K)

(m) Tw

base plate temperature

(K)

2

approach Velocity

(m) t

(W/m K) Uapp (W/mK)

11

(m/s)

IHTC15-8825 REFERENCES [1] E. Sparrow and J. Ramsey, “Heat transfer and pressure drop for a staggered wall-attached array of cylinders with tip clearance,” International Journal of Heat and Mass Transfer, vol. 21, no. 11, pp. 1369 – 1378, 1978. [2] A.Zukauskas and J.Ziugzda, “Heat transfer of a cylinder in cross flow,” New York: Hemisphere, 1985. [3] M. Tahat, R. Babus’Haq, and S. Probert, “Forced steady-state convections from pin-fin arrays,” Applied Energy, vol. 48, no. 4, pp. 335 – 351, 1994. [4] M. A. R. M. Jubran, B. A.Hamdan, “Enhanced heat transfer, missing pin, and optimization for cylindrical pin fin arrays,” Journal of Heat Transfer, ASME, 1993. [5] K. Bilen, U. Akyol, and S. Yapici, “Heat transfer and friction correlations and thermal performance analysis for a finned surface,” Energy Conversion and Management, 2001. [6] M. Tahat, Z. Kodah, B. Jarrah, and S. Probert, “Heat transfers from pin-fin arrays experiencing forced convection,” Applied Energy, vol. 67, pp. 419 – 442, 2000. [7] K. Yang, W. Chu, I. Chen, and C. Wang, “A comparative study of the airside performance of heat sinks having pin fin configurations,” International Journal of Heat and Mass Transfer, vol. 50, 2007. [8] R. Yu, W. Chaoyi, and Z. Shusheng, “Transitional flow and heat transfer characteristics in a rectangular duct with stagger-arrayed short pin fins,” Chinese Journal of Aeronautics, vol. 22, no. 3, pp. 237 – 242, 2009. [9] N. Sahiti, A. Lemouedda, D. Stojkovic, F. Durst, and E. Franz, “Performance comparison of pin fin in-duct flow arrays with various pin cross-sections,” Applied Thermal Engineering, vol. 26, no. 1112, pp. 1176 – 1192, 2006. [10] W. Khan, J. Culham, and M. Yovanovich, “Modeling of cylindrical pin-fin heat sinks for electronic packaging,” Components and Packaging Technologies, IEEE Transactions on, vol. 31, no. 3, pp. 536–545, 2008. [11] Ansys Fluent Theory Guide. Ansys Inc, 14, 2011. [12] S. D. O.P. Bergelin, G.A. Brown, “Heat transfer and fluid friction during flow across banks of tubes,” Trans. ASME 74, pp. 953–960, 1952. [13] A. Krishnan, B. Premachandran, C. Balaji, and S. Venkateshan, “Combined experimental and numerical approaches to multi-mode heat transfer between vertical parallel plates,” Experimental Thermal and Fluid Science, vol. 29, no. 1, pp. 75 – 86, 2004. [14] A. Bejan, Heat Transfer. John Wiley and Sons, 1993.

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