2009 International Conference on Mechatronic System of Integration and Application

4-5 Dec, 2009, Tainan, TAIWAN

A numerical studyof jet coolingeffect on the pin fin heat sinks

Fang-Ming Tsai 1, I-Peng Chu2, HungYi Li3, Yuh-Chung Hu4, David T.W. Lin1,*

1Institute of Mechatronic System Engineering, National University of Tainan, No,33, Sec.2, Su-Lin St., Tainan City 700, Taiwan, R.O.C.

2Department of Mechanical Engineering, Far East University, Hsin-Shih, Tainan County 744, Taiwan, R.O.C.

3Department of Mechatronic Engineering, Huafan University, Shih Ting, Taipei 223, Taiwan, R.O.C.

4 Department of Mechanical and Electro-Mechanical Engineering, National Ilan University, I-Lan, 260, Taiwan, R.O.C

*corresponding author, E-mail:

ABSTRACT

The purpose of this study is to discuss the heat transfer phenomena of plate-fin heat sinks under high velocity jet cooling. The characteristic of impinging cooling is to increase the quantity of heat removal in the heated region. The finite element method is used to simulate, and the results are compared with the experiment to obtain the accuracy of this study. The parameters discuss in this study including the size of the fin, the Reynolds number and the impingement distance. Through the results of this study, we find that the effect of Reynolds number dominates to the heat removal. The heat removal increases as the Re increases obviously. In addition, the temperature profile of the surface of the fin is affected by the arrangement of the fin.

Keywords: Plate-fin heat sink; Impinging jet flow; Reynolds number; Impingement distance

INTERDUCTION

The operational speed of electronic components has been more quickly now, and the density of electronic circuits is also increasing relatively, they caused more larger heat in the chip per unit volume. Kraus et al. [1] point out that each 2 increasing of the temperature on electronic chips may cause reducing about 10% of stability and reliability. In 1995, Yeh [2] presented that the 55% of damage of electronic products caused by high temperature, so the electronic cooling is worth to study. The study of impinging jet cooling has four categories, single-nozzle cooling from a single plane, single-nozzle cooling the surface of the geometric shape, multi-nozzle nozzle cooling planar and multi-nozzle nozzle cooling geometric shape. In previous researches about single nozzle cooling plane, Guerra et al. [3] described the behavior of a semi-confined impinging jet over a heated flat plate. Experimental data for the pressure distribution, velocity and temperature fields were obtained. The presented research is particularly relevant due to its application for the development of methods that can be used for the determination of the local skin-friction and the local heat transfer coefficient. Hsieh et al. [4] study the unstable vortex flow and new inertia-driven vortex rolls resulted from an air jet impinging onto a confined heated horizontal disk. An experiment combined flow visualization and temperature measurement is carried out here to investigate. Hofmann et al. [5] measure the steady state heat transfer, flow structure and new correlations for heat and mass transfer in submerged impinging jets, which show the complex interaction of nozzle-to-plate spacing, radial distance from the stagnation point and the Reynolds number. The influence of Reynolds number and radial distance from the stagnation pointed on heat transfer coefficient are described by a new correlation.

Senter and Solliec [6] analysis the flow field of a turbulent slot air jet impinging on a moving flat surface by using particle image velocimetry (PIV). The results show that surface-to-jet velocity ratio affect the flow field significantly. Astarita et al. [7] consider the flow visualizations and heat transfer measurements on a rotating disk with a relatively small centred jet perpendicularly impinging on it, which are accomplished by means of infrared (IR) thermography associated with the heated-thin-foil thermal sensor. Flow visualizations show a strong interaction between the turbulent jet and the laminar boundary layer over the rotating disk. A new governing similitude parameter is introduced and a heat transfer correlation for the Nusselt number at the disk centre is proposed. O’Donovan and Murray [8] employ particle image velocimetry to measure the fluid flow in a two-dimensional plane through a section of the impinging jet flow. In the study of cooling single-nozzle the geometric shape of the surface, Wang et al. [9] use a 3-D transient liquid crystal scheme on the flow and heat transfer problem of confined impinging jet cooling. The 1-D results of the local maximum heat reducing are higher than the 3-D results of the minimum heat reducing about 15–20%, and the overall heat transfer is 12% approximately. Yan et al. [10] measure the heat transfer along rib-roughened surface under arrays of impinging elliptic jets, and they find that the best heat transfer performance is obtained on a surface with 45and V-shape ribs. In addition, the heat transfer of continuous ribs is better than broken ribs. Graminho and Lemos [11] simulate the turbulent impinging jet into a cylindrical chamber with a porous layer at the bottom. Their results indicate that the permeability of the porous layer and the height of the fluid layer significantly affect the flow pattern. The effect of the porous layer thickness is less pronounced in affecting the flow behavior within the fluid layer. With the requirements of the high performance cooling technology, some scholars explore the cooling multi-nozzle plane. Thielen et al. [12] predict the flow and heat transfer phenomena in the multiple impinging jets with an elliptic-blending second-moment closure. Their computations are compared with the recent experimental results of Geers et al. [13-14].

More complex research about multi-nozzle cooling the surface of the geometric shape are studied further. Chang et al. [15] measure the heat transfer phenomena of impinging jet-array over convex-dimpled surface. Their analysis is performed to generate a set of heat transfer correlations. The recently researches on the impinging jet cooling can be seen from the literatures, of course, there are more researches to explore different parameters in this field. Li et al. [16-18] measure the thermal performance of heat sinks with confined impinging jet by infrared thermography. Their results show that the increasing of the Reynolds number of the impinging jet flow reduces the thermal resistance of the heat sinks consistently. In addition, the thermal resistance can be decreased by increasing the fin width combined with an appropriate Reynolds number. Increasing the fin height to enlarge the area of heat transfer also decreases the thermal resistance, but the effects are less conspicuous than those on altering the fin width. The experimental results show in their study and agree the numerical estimations. Lee et al. [19] investigate the fluid flow and heat transfer problem on the confined impinging slot jet with the low Reynolds number region for different channel heights. The numerical simulations are performed for different Reynolds numbers and different height ratios. The critical Reynolds number are beyond which the flow and thermal fields change their state from steady to unsteady state depending on the Reynolds number and height ratio.

The purpose of this study is to discuss the heat transfer phenomena of plate-fin heat sinks under high velocity jet cooling. The finite element method is used to simulate, and the results are compared with the experiment [18] to obtain the accuracy of this study.

Fig. 1 The schematic system.

Analysis

The finite element package-COMSOL 3.5 is used to analysis this study. The schematic diagram of this model is shown as Fig. 1. The governing equations of fluid is Reynolds averaged Naiver-Stoks equation and Energy equation as

(1)

(2)

(3)

where is density, is velocity component, is static pressure, is dynamic viscosity, is total energy per unit mass, is effective thermal conductivity, is volumetric heat source, T is temperature, is Reynolds stress and is deviatoric stress tensor.

The governing equations of heat conduction is Fourier law as

(4)

where is density, is specific enthalpy, is thermal conductivity, is temperature and is volumetric heat source.

Fig. 2 The schematic diagram of plate-fin heat sink.

Fig. 3 The flow field map.

The plate-fin heat sinks are designed as an array of 62 with a cut-off passage in the x-direction as shown in Fig. 2. The cut-off passage is noticed as the flow channel as Fig. 3. The material of the heat sinks is selected as aluminum alloy 6061. The length and width (L) of the base of the heat sinks are 80mm and the thickness (b) is 8mm. The height and width of the fins are varied as experimental parameters. There are 20 heat sink models in this study with 4 fin widths and 5 fin heights as shown in Fig.3. The heat transfer area of the plate-fin heat sink is given by

(5)

The thermal resistance of heat sink is defined as

(6)

where is the average temperature of the base of the heat sink, is the temperature of the impinging jet and is heating power.

The Reynolds number of the impinging jet is calculated by

(7)

where is jet velocity and is the kinematic viscosity of air.

Fig. 4 The temperature profiles of the plate-fin surface with various X, at (, and and ).

Fig. 5 The pressure profiles of the plate-fin surface with various X, at (, and and ).

Results and Discussions

In this study, the numerical results is calculated as , , and , and compared with Li et al. [18], as shown in Fig.4. The numerical simulation is compared with Li et al. [18], maximum error is 2.077, and relative error is 6.51%. The numerical results of this study is closer the experimental results than the ones of Li et al. [18].

The pressure profiles are shown in Fig. 5 and compared with the Ref. [18]. We find that the biggest difference is happened at the center of the heat sink. In addition, the same phenomena are shown in Fig. 4. This is the reason of the complex heat and mass transfer at the center of the heat sink resulted from the impinging flow.

As for the effects of jet flow velocity, the variation of the thermal resistance with Reynolds number and in the conditions , are shown in Fig. 6.

Fig. 6 The influence of the Reynolds number on the thermal resistance for various fin widths with and .

The thermal resistance decreases about 32.71% under the two kinds of of the heat sink as is from to . This shows that the dominate effect of the thermal resistance decreasing is the increasing of the jet velocity as the Re is low. However, the average decline of the thermal resistance is reduced to 16.61%, 8.13%, and 6.19% as the Reynolds number increases from , to , respectively. But, the increasing of the jet velocity for the thermal efficiency still has the benefit in the cooling process.

Further, the influences of the impinging distance are shown in Fig.7. Discloses the Fig. 7, we can observe clearly the profiles of the thermal resistance with impinging distance and Re at , . As the impinging distance is too small, the cooling flow cannot flow into the channel of the heat sink thoroughly. For the reason of the complex flow field above the heat sink resulted from the small spacing between the impinging jet and the heat sink. But, the thermal resistance will be increased as the impinging distance is too large. Therefore, we find that the impinging distance exists a optimal value the make the thermal resistance to approach the minimum value.

The thermal resistance profiles with the fin width are shown in Fig.8 and compared with the Ref. [18]. Under the condition of impinging distance of and the Reynolds number, ,,, we find that the thermal resistance decreases as the Re and the width of heat sink increases, respectively.

As the discussion concluded above, we notice that the Re, impinging distance, size of the heat sink are the important parameters in the optimal process to find the best thermal efficiency. We will use the optimal method to tune these parameters to approach the optimal design of the impinging cooling in future.

Fig. 7 The influence of the impinging distance on the thermal resistance with and .

Fig. 8 The influence of the fin width on the thermal resistance for various fin heights with .

Conclusion

For the reason of increasing of power density resulted from the size reduction of electronics, the method of heat removal becomes an important topic in the heat transfer field. In this study, to discuss the heat transfer phenomena of plate-fin heat sinks under high velocity jet cooling is our purpose. The results of this paper are compared with the experiment of Ref. [18] to obtain the accuracy of this study. The variations of the size of the fin, the Reynolds number and the impingement distance are discussed in this study. We notice that the heat removal increases as the Re, , and increases obviously. In addition, the impinging distance must have a optima value to obtain the best thermal efficiency. We summarize some conclusions and list as below.

(1) The increasing of Reynolds number of jet flow can increase the cooling efficiency, and a great benefit will be happened on the low Re region.

(2) As the impinging distance is too small or large, the thermal resistance will be increased. Therefore, we find that the impinging distance exists an optimal value the make the thermal resistance to approach the minimum value. In this study we find the optimal distance () is about 20.

The advantage of this cooling process will be expected to use on the power saving, high power electronics cooling, etc.. In addition, the design of the impinging jet cooling can be achieved through the optimal method in future.

References

[1] Cohen, A.B., Kraus, A.D., and Davidson, S.F., (1983): “Thermal frontiers in the design and packaging of microelectronic equipment,” J. Mechanical Engineering, Vol. 105, pp. 53-59.