in a Investigation of Hydraulic and Thermal Performances of Fin Array at Different Shield Positions without By-Pass

— In heat sinks, the flow within the core exhibits separation and hence does not lend itself to simple analytical boundary layer or duct flow analysis of the wall friction. In this paper, we present some findings from an experimental and numerical study aimed to obtain physical insight into the influence of the presence of the shield and its position on the hydraulic and thermal performance of square pin fin heat sink without top by-pass. The variations of the Nusselt number and friction factor are obtained under varied parameters, such as the Reynolds number and the shield position. The numerical code is validated by comparing the numerical results with the available experimental data. It is shown that, there is a good agreement between the temperature predictions based on the model and the experimental data. Results show that, as the presence of the shield, the heat transfer of fin array is enhanced and the flow resistance increased. The surface temperature distribution of the heat sink base is more uniform when the dimensionless shield position equals to 1/3 or 2/3. The comprehensive performance evaluation approach based on identical pumping power criteria is adopted and shows that the optimum shield position is at x/l=0.43.


I. INTRODUCTION
HE constant demand for speed and performance in electronics is unfortunately accompanied by ever increasing thermal dissipation. Air heat exchangers or heat sinks continue to be the most viable thermal solution for the electronics industry primarily because of low cost and high reliability. Heat sinks for electronics depend on conduction from the electronic package to the heat sink base, followed by conduction into the extended surfaces and convection to the flow. Hence, arrangement, shape, and orientation of extended surfaces play the main role in the thermal dissipation. Many authors have undertaken the characterization of parallel plate heat exchangers. Among research published on heat sinks to improve the cooling of electronic components, Knight et al. [1] analytically characterized the flow and heat transfer behavior of such heat exchangers as function of geometry and fluid characteristics, for developing and fully developed flow.
Teertstra et al. [2] similarly found analytical solutions for such configurations, and blended both regimes into a single solution for a wide range of Reynolds number.
Lee [3] studied the effects of flow by-pass, by allowing flow around the heat exchanger in a partially confined flow configuration. Butterbaugh and Kang [4] treated this case by constructing a nodal network of flow paths, and detailed the calculation of each network element. They accounted not only for flow by-pass, but also for that part of the flow that enters the heat sink and exits through the top, the so-called tip leakage.
Similarly, Shaukatullah et al. [5] measured the thermal performance for in-line square pin fins and plate heat sinks for different fin thickness, spacing, height, and angle of approach for velocities under 5 m/s, while allowing flow to partially bypass the exchanger. More recently, Jonsson and Moshfegh [6] experimentally characterized plate and circular, rectangular and strip pin fins, in both staggered and in-line configurations for different dimensions, allowing for variations on tip and side by-pass. Generally, most of the studies have not been especially useful for extracting local friction or heat transfer coefficients. Dogruoz et al. [7] investigated the hydraulic resistance and thermal performance of in-line square-pin fin heat sinks; their predictions based on a two-branch by pass model agreed satisfactorily with experimental data at large velocities of approach for tall heat sinks, but the discrepancy increased with decreasing approach velocity and height of the heat sink.
El-Sayed et al. [8] investigated the effects of the fin arrays geometries and also the fin tip-to-shroud clearance on the heat transfer, the fluid flow and the pressure drop characteristics of longitudinal rectangular-fin arrays. During the experiments, different geometrical parameters were varied such as the fin height, fin thickness, inter-fin space, fins number, and fin tipto-shroud clearance were varied parametrically; starting with the no-clearance case.
CFD approaches have been extensively applied to study flow and heat transfer in heat sinks, for example by Jonsson and Moshfegh [9], Biber and Belady [10], and Dvinsky et al. [11]. Dvinsky et al. [11] used CFD to study in detail flow and heat transfer behavior for in-line and staggered heat sinks for the approach velocities of 1, 3 and 5 m/s. Because their study allowed for both top and side flow by-pass, their results help to elucidate the deficiencies of a simple 2(or even 4) path model that does not allow for leakage from the heat sink, back to the channel. They found that, when allowing side and top clearance, up to half of the flow that enters the heat sink may leave it through the side and top. CFD simulations of Jonsson and Moshfegh [9] revealed that this leakage flow may be quite complex. They reported inward flow from the sides, to balance flow lost through the top. Li et al. [12] investigated numerically the hydraulic and thermal performance of a plate fin heat sink with a shield. The decrease of thermal resistance due to the shield diminishes with increasing increasing the width of the fins has a more radical effect. For a shield at a particular Reynolds number, the fin geometry should be selected carefully to fit the demands of enhanced effectiveness of heat transfer and decreased power consumption. Tsai et al. [13] investigated the effect of the inclination angle of a plate heat shield on thermal and hydraulic performance of a plate fin heat sink. It found that the minimum pressure drops for smaller fin heights appear for inclination angles of shield about 90° to 105°. The minimum pressure drops for the largest fin height are ambiguous. Zhang et al. [14] investigated experimentally the heat transfer performances of the fin array with shield in the bypass. Experimental results indicated that the heat transfer and flow performances of fin array were marginally influenced by the power input. Evaluated under the identical pressure drop and the identical pumping power criteria, the optimum position of shield was the position where the dimensionless position equaled 0, and the optimum shield height was half of the fin height. Finally, the correlations of mean Nusselt number and friction factor were fitted considering the influences of Reynolds number, the shield position and the shield height. The predicted values fitted the experimental data with the deviations less than ±15.0%.
As the previous literatures indicated, it was a feasible way to enhance the heat transfer of fin array by changing the bypass structure and shield inclination angle. Th an enhancement device for the fin array with/without bypass, and had a wide field of application with good prospects. The focus of the present work is to experimentally and numerically investigate the effect of a shield position on the hydraul thermal performance of pin fin heat sink. Comprehensive performance evaluation of fin array with different shield position is presented. Therefore, we try to find the optimum shield position where lowest thermal resistance is occurred.

A. Experimental Apparatus and Measurements
The experimental apparatus consists of the main supply duct, test section, tested models as shown in Fig. 1. The main duct which supplies air to the test section contains air blower, air gate to adjust the mass flow rate of the air through working section, a flow straighteners (screens) at the air inlet side of the wind tunnel, honeycombs to reduce the swirl motion of the air stream and to break up occasional large eddies that may reach the test section, and measure the air flow rate.
numerically the hydraulic and thermal performance of a plate fin heat sink with a shield. The decrease of thermal resistance due to the shield diminishes with increasing fin height, but increasing the width of the fins has a more radical effect. For a shield at a particular Reynolds number, the fin geometry should be selected carefully to fit the demands of enhanced effectiveness of heat transfer and decreased power mption. Tsai et al. [13] investigated the effect of the inclination angle of a plate heat shield on thermal and hydraulic performance of a plate fin heat sink. It found that the minimum pressure drops for smaller fin heights appear for f shield about 90° to 105°. The minimum pressure drops for the largest fin height are ambiguous. Zhang et al. [14] investigated experimentally the heat transfer performances of the fin array with shield in the bypass. e heat transfer and flow performances of fin array were marginally influenced by the power input. Evaluated under the identical pressure drop and the identical pumping power criteria, the optimum position of shield was the position where the dimensionless shield position equaled 0, and the optimum shield height was half of the fin height. Finally, the correlations of mean Nusselt number and friction factor were fitted considering the influences of Reynolds number, the shield position and the The predicted values fitted the experimental data As the previous literatures indicated, it was a feasible way to enhance the heat transfer of fin array by changing the bypass structure and shield inclination angle. The shield was an enhancement device for the fin array with/without bypass, and had a wide field of application with good prospects. The focus of the present work is to experimentally and numerically investigate the effect of a shield position on the hydraulic and thermal performance of pin fin heat sink. Comprehensive performance evaluation of fin array with different shield position is presented. Therefore, we try to find the optimum shield position where lowest thermal resistance is occurred.

Apparatus and Measurements
The experimental apparatus consists of the main supply as shown in Fig. 1. The main duct which supplies air to the test section contains air blower, flow rate of the air through the working section, a flow straighteners (screens) at the air inlet side of the wind tunnel, honeycombs to reduce the swirl motion of the air stream and to break up occasional large eddies that may reach the test section, and flow orifice to The main supply duct runs from the blower discharge exit up to the inlet of the test channel. This duct consists of two parts: the first part is a U-shaped circular pipe of 75 diameter and connected to blower exit via a conical diffuser. The other end of the U-shape is connected to the second part of the main supply duct via a conical nozzle. The second part of the supply duct that precedes the test channel is 1.0 and consists of a diffuser, a settling length and a contraction. This part of the supply duct is fitted with honeycomb and mesh screens as flow straighteners. The test section is horizontal rectangular duct with cross height and 15cm width. Pressure taps are installed in the test section to measure the static pressure along the test section by using micro-manometer. In addition, pressure drop across orifice meter is measured by water U The tested heat sinks are located at 30 section entrance. All pin fin heat sinks are fabricat aluminum 7050-T7350 (kAl=155 W/m.K) and have base dimensions of 15cm x 15cm x 2mm. Each pin fin has cross section area of cm x1 cm and its height is 2cm.
Ni-Chrome foil heater is used to provide electrical heating as uniform heat flux. Power consu voltage drop and current across the foil or by Wattmeter with accuracy of 1%. Thermal insulation is also used on the other surface of the heater assembly. The insulation system consists of a 3mm thick amiant layer (k = 0.35 W/m 25mm thick glass wool layer (k = 0.041 W/m.K) and this is in turn followed by a 20mm thick wood board (k = 0.097 W/m.K).
In total, 12 copper-constantan (T type, 0.2 thermocouples are used. All the thermocouples are calibrated with the calibration device and the second mercury thermometer with an accuracy of 0.1 K. The fin array is instrumented with 7 thermocouples located on the middle and the root of fin along the flow direction. The other three are equipped on the insulation system, and other two on the inlet and outlet of the test section. The pressure drop is measured by pressure taps before and after heat sink.

B. Data Reduction
The thermal performance is measured at approach velocities of V= 2.4, 3.6, 4.8, and 7.2 m/ is from 10,000 to 25,000. In the experiments, it is assumed that the steady state conditions are achieved when the change in the base temperature of heat sink is less than 0.1oC in a time period about 3.5 hour. When these cond achieved, the base temperatures, the insulation system 1 Schematic diagram of test rig and instrumentation The main supply duct runs from the blower discharge exit up to the inlet of the test channel. This duct consists of two shaped circular pipe of 75mm inner diameter and connected to blower exit via a conical diffuser.
shape is connected to the second part of the main supply duct via a conical nozzle. The second part of the supply duct that precedes the test channel is 1.0m long and consists of a diffuser, a settling length and a contraction.
the supply duct is fitted with honeycomb and mesh screens as flow straighteners. The test section is horizontal rectangular duct with cross-sectional area of 4cm cm width. Pressure taps are installed in the test pressure along the test section by manometer. In addition, pressure drop across orifice meter is measured by water U-tube manometer.
The tested heat sinks are located at 30cm from the test section entrance. All pin fin heat sinks are fabricated from T7350 (kAl=155 W/m.K) and have base dimensions of 15cm x 15cm x 2mm. Each pin fin has cross section area of cm x1 cm and its height is 2cm.
Chrome foil heater is used to provide electrical heating as uniform heat flux. Power consumption is determined by the voltage drop and current across the foil or by Wattmeter with accuracy of 1%. Thermal insulation is also used on the other surface of the heater assembly. The insulation system consists mm thick amiant layer (k = 0.35 W/m.K) followed by a mm thick glass wool layer (k = 0.041 W/m.K) and this is in mm thick wood board (k = 0.097 constantan (T type, 0.2mm) thermocouples are used. All the thermocouples are calibrated he calibration device and the second-order standard mercury thermometer with an accuracy of 0.1 K. The fin array is instrumented with 7 thermocouples located on the middle and the root of fin along the flow direction. The other three are sulation system, and other two on the inlet and outlet of the test section. The pressure drop is measured by pressure taps before and after heat sink.
The thermal performance is measured at approach velocities of V= 2.4, 3.6, 4.8, and 7.2 m/s where Reynolds number range is from 10,000 to 25,000. In the experiments, it is assumed that the steady state conditions are achieved when the change in the base temperature of heat sink is less than 0.1oC in a time period about 3.5 hour. When these conditions are achieved, the base temperatures, the insulation system temperatures, the power delivered to the heat sink, the approach velocity, the pressure drop across orifice meter, and pressure taps are recorded.
The approach velocity is estimated as: where C d is discharge flow coefficient, ∆H is pressure drop across orifice (manometer head) in mm h2o, ρ is air density in kg/m3, and g is gravitational acceleration in m/s2. The temperature distribution along fin height can be neglected because of its small height so; the fin efficiency is not introduced. The total thermal resistance, Rth and the convective heat transfer rate, Qconv can be described as [7], [14]: where Tb is the mean base temperature of the heat sink, Ta is the ambient temperature, h is the convective heat transfer coefficient, As is the surface area of the heat sink, and Qconv is the convective heat transfer through the heat sink surfaces and is given by: Qtot is the total amount of power supplied to heat sink, Cp is the specific heat capacity of air, m is the air mass flow rate through the test section. Qloss is the total amount of heat loss through insulation system and can be estimated as: where ∆T is the temperature difference across the insulation system and ∑ Rins is the overall thermal resistance of the insulation system. Reynolds number and Nusselt number based on the hydraulic diameter of test section are defined as: where Dh= 0.06315 m, kf is the air conductivity in W/m.K, and ʋ is air viscosity at inlet air temperature in m2/s. The friction factor (f) is calculated as: where ∆P is the pressure drop across heat sink (Pa) and L is the distance between pressure taps (m).

C. Uncertainty Estimation
All instrumentations are independently calibrated. The uncertainty of the compound variables such as air density, thermal resistance, Reynolds number, Nusselt number, and friction factor can be calculated as follows [15], [16]: Assume that Y is a given function of the independent variables x1, x2... xn. Thus Y=f (x1, x2…... xn) Let UY is the uncertainty in Y and Ux1, Ux2… Uxn are the uncertainties in the independent variables. The uncertainty in Y can be put in the differential form as: The uncertainty of the compound variables can be estimated from this principle and the results of this analysis are summarized in Table I.

III. NUMERICAL ANALYSIS
The geometry of the theoretical model and the boundary conditions are illustrated in Fig. 2 where i is a tensor indicating 1, 2, 3 and τij is the viscous shear tensor.
In order to calculate the turbulent flow, standard k-ε turbulence model is selected and its equations is added to the governing equations and solved by CFD software.

Fig. 2 Computational domain and boundary conditions
A. Mesh Sensitivity Several unstructured grids are performed with different mesh sizes for heat sink without shield with approach velocity of 3.6 m/s in order to guarantee the grid independence of the results. The mesh is intensified between the fins to refine the numerical solution Fig. 3 shows the therma 200,000, 400,000, 500,000, 800,000 and 1,000,000 grid sizes. According to this figure, the obtained results with 800,000 and 1,000,000 are very close where the maximum percentage error is about 0.3%. Therefore, the results from 1,000,000 g can be considered to be grid independence.

B. Code Validation
One case of heat sink without shield with approach velocity of 3.6 m/s and heating power of 40 W is selected to establish the validation process. A comparison between the predicted results by the numerical code and the present experimental data is performed in Fig. 4. This figure shows a good agreement between the predicted thermal resistance numerically and the present experimental measu this numerical code is validated by comparing its predicted data with the experimental data measured by Zhang et al. [14] and obtains the same trend. Therefore, the present numerical code is valid to simulate the heat sinks. performed with different mesh sizes for heat sink without shield with approach velocity of 3.6 m/s in order to guarantee the grid independence of the results. The mesh is intensified between the fins to refine the numerical solution Fig. 3 shows the thermal resistance for 200,000, 400,000, 500,000, 800,000 and 1,000,000 grid sizes. According to this figure, the obtained results with 800,000 and 1,000,000 are very close where the maximum percentage error is about 0.3%. Therefore, the results from 1,000,000 grid size can be considered to be grid independence.
Thermal resistance at different grid sizes One case of heat sink without shield with approach velocity of 3.6 m/s and heating power of 40 W is selected to establish n process. A comparison between the predicted results by the numerical code and the present experimental data is performed in Fig. 4. This figure shows a good agreement between the predicted thermal resistance numerically and the present experimental measurements. Also, this numerical code is validated by comparing its predicted data with the experimental data measured by Zhang et al. [14] and obtains the same trend. Therefore, the present numerical

A. Thermal and Hydraulic Performance
After validation of the CFD code, either experimental or numerical data can be used to investigate the effect of Reynolds number and dimensionless shield position on the hydraulic and thermal performance of pin fin heat sink. Distribution of the velocity b is clear that, the maximum value of air velocity occurs under the shield where the smallest effective flow area at the shield cross-section. Therefore, the heat transfer performance of fin array is enhanced as the influence of shield as shown in Fig. 6. The effect of Reynolds numbers on the thermal resistance is depicted in Fig. 7 for various position of the shield. The thermal resistance decreases as the Reynolds number increases and dimensionless shield position increases until x/l = 1/3 and then this behavior reverses. Therefore, the shield plays an important role in increasing the heat transfer around it. The effects of Reynolds numbers on the Nusselt numbers are depicted in Fig. 8 for various shield position. The Nusselt number increases as the Reynolds number increases and dimensionless shield position increases until x/l = 1/3 and then this behavior reverses. The reason of such behavior is that the air before the shield at the entrance of the heat sink has low temperature and sinks and absorbs the heat from the heat sink. At the shield, the velocity increases and the heat transfer coefficient increases. As results, the region around the shield becomes cooler than any point on the base. Therefore, the

Re
Therefore, the heat transfer performance of fin array is hield as shown in Fig. 6.
Temperature distribution over heat sink base at various shield position for Re = 25000 The effect of Reynolds numbers on the thermal resistance is depicted in Fig. 7 for various position of the shield. The resistance decreases as the Reynolds number increases and dimensionless shield position increases until x/l = 1/3 and then this behavior reverses. Therefore, the shield plays an important role in increasing the heat transfer around it. sistance versus Reynolds numbers at different shield The effects of Reynolds numbers on the Nusselt numbers are depicted in Fig. 8 for various shield position. The Nusselt number increases as the Reynolds number increases and d position increases until x/l = 1/3 and then this behavior reverses. The reason of such behavior is that the air before the shield at the entrance of the heat sink has low temperature and sinks and absorbs the heat from the heat sink. elocity increases and the heat transfer coefficient increases. As results, the region around the shield becomes cooler than any point on the base. Therefore, the impact of shield on the heat transfer performance is more significant at higher Reynolds numbe becomes the maximum value when dimensionless shield position is about 1/3.  Fig. 9, the friction factors increases due to the rise of the dimensionless shield position x/l. It is also found that the change of the friction factor is nearly same for x/l = 1/3 and 2/3 or x/l = 0.0 and 1.0. The maximum value of friction factor occurs at x/l = 1/3 and 2/3 where the shield at the middle region of the heat sink. The air in the inter-fin channel is gradually heated and leaked upward after the shield because of its lower density. Along the flow direction, the velocity of air increased gradually. Thus, the larger the dimensionless sh disturbance caused by shield is. Consequently, the flow resistance in the test section increased with the dimensionless shield position.  Fig. 9, the friction to the rise of the dimensionless shield position x/l. It is also found that the change of the friction factor is nearly same for x/l = 1/3 and 2/3 or x/l = 0.0 and 1.0. The maximum value of friction factor occurs at x/l = 1/3 and e middle region of the heat sink. The fin channel is gradually heated and leaked upward after the shield because of its lower density. Along the flow direction, the velocity of air increased gradually. Thus, the larger the dimensionless shield position is, the sharper the disturbance caused by shield is. Consequently, the flow resistance in the test section increased with the dimensionless  Fig. 10 illustrates the effect of dimensionless shield position on the thermal resistance at different Reynolds numbers. From this figure, it is found that, the thermal resi the dimensionless shield position increases. This trend continues until x/l reaches to about 0.43. After this value, the thermal resistance increases as x/l increases. As results, the optimal value of dimensionless shield position is 0. view point of thermal performance in the present study range of Reynolds numbers.

B. Comprehensive Performance Evaluation of Shield Position
As mentioned above, all of these heat transfer promoters caused an increase of pressure loss. To comprehensively survey the influence of shield on the fin array performance, the evaluation approach based on identical pumping p criteria is adopted. The identical pumping power criterion is based on that the pressure drop is inversely proportional to the cubic of the air velocity, and measured by the value (Nu/ Nu0)/(f/f0)1/3. When the value is greater than 1, it means that under the same pump power, the heat transfer rate of the enhanced heat transfer surface is larger than that of the reference surface. Fig. 11 presents the comprehensive performance evaluation of fin array with different shield position, under identical pumping power criterion. It is noted that the ratio of (Nu/Nu0)/(f/f0)1/3 increased as the dimensionless shield position increased. In the present experimental range, the ratio is lower than 1 only when the shield position x/l = 0. Accordingly, the shield at the position x/l = 0 caused a decrease of fin array performance with the same pump power consumption. The fin array performance is improved as the shield installed in other positions. As the above discussion, the inlet section of fin array is not the optimum And, the middle section at x/l = 0.43 is the optimum position of the shield as previously mentioned in Fig. 10.  Fig. 10 illustrates the effect of dimensionless shield position on the thermal resistance at different Reynolds numbers. From this figure, it is found that, the thermal resistance decreases as the dimensionless shield position increases. This trend continues until x/l reaches to about 0.43. After this value, the thermal resistance increases as x/l increases. As results, the optimal value of dimensionless shield position is 0.43 from view point of thermal performance in the present study range Distribution of thermal resistance with shield position at different Reynolds numbers

Evaluation of Shield
As mentioned above, all of these heat transfer promoters caused an increase of pressure loss. To comprehensively survey the influence of shield on the fin array performance, the evaluation approach based on identical pumping power criteria is adopted. The identical pumping power criterion is based on that the pressure drop is inversely proportional to the cubic of the air velocity, and measured by the value (Nu/ Nu0)/(f/f0)1/3. When the value is greater than 1, it means that der the same pump power, the heat transfer rate of the enhanced heat transfer surface is larger than that of the Fig. 11 presents the comprehensive performance evaluation different shield position, under identical ng power criterion. It is noted that the ratio of (Nu/Nu0)/(f/f0)1/3 increased as the dimensionless shield position increased. In the present experimental range, the ratio is lower than 1 only when the shield position x/l = 0. position x/l = 0 caused a decrease of fin array performance with the same pump power performance is improved as the shield installed in other positions. As the above discussion, the inlet section of fin array is not the optimum position for shield. And, the middle section at x/l = 0.43 is the optimum position of the shield as previously mentioned in Fig. 10. The effects of shield position without by transfer and flow performances of fin array are experimentally and numerically investigated. These investigations have been reported and showed that CFD, an important tool in thermal engineering, is used to analyze the data generated by models representing the complexity of the flow patterns that evolve inter-fins. The standard k -ε turbulence model with enhanced wall treatment and viscous heating can be used to simulate this type of problems. This result is also considered in other paper [17].
The thermal resistance and the fiction factor decreases as the Reynolds number increases. The increase of the dimensionless shield position, the increase of Nusselt number until x/l reaches to 0.43. When x/l goes beyond this value, the Nusselt number decreases.
As the presence of the shield, the temperature gradient over the base of the heat sink is approximately diminished. The surface temperature distribution of the heat sink with shield at x/l = 1/3 or 2/3 is more uniform. This distribution is similar to the performance and behavior of the vapor chamber heat sink as mentioned in other papers [18 Under the identical pumping power criterion, the shield at the inlet section of fin array cau performance in present experimental and numerical range. The results show that the optimum shield position is at x/l = 0.43. gineering, is used to analyze the data generated by models representing the complexity of the flow patterns that evolve ε turbulence model with enhanced wall treatment and viscous heating can be used to simulate this oblems. This result is also considered in other paper The thermal resistance and the fiction factor decreases as the Reynolds number increases. The increase of the dimensionless shield position, the increase of Nusselt number 3. When x/l goes beyond this value, the As the presence of the shield, the temperature gradient over the base of the heat sink is approximately diminished. The surface temperature distribution of the heat sink with shield at = 1/3 or 2/3 is more uniform. This distribution is similar to the performance and behavior of the vapor chamber heat sink as mentioned in other papers [18], [19].
Under the identical pumping power criterion, the shield at the inlet section of fin array caused a decrease of fin array performance in present experimental and numerical range. The results show that the optimum shield position is at x/l = 0.43.