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A three-dimensional analysis procedure for the thermal performance of a manifold microchannel heat sink has been developed and applied to optimize the heat-sink design. The system of fully elliptic equations, that govern the flow and thermal fields, are solved by a SIMPLE-type finite volume method, while the optimal geometric shape is traced by a steepest descent technique. For a given pumping power, the optimal design variables that minimize the thermal resistance are obtained iteratively. The procedure is robust and the optimal state is reached within six global iterations. Comparing with the comparable traditional microchannel heat sink, the thermal resistance is reduced by more than a half while the temperature uniformity on the heated wall is improved by tenfold. The sensitivity of the thermal performance on each design variable is also examined and presented in the paper. Among various design variables, the channel width and depth are more crucial than others to the heat-sink performance. The optimal dimensions and corresponding thermal resistance have a power-law dependence on the pumping power.

The recent trend in the electronic equipment industry toward denser and more powerful products requires higher thermal performance from a cooling technique. Many ideas for innovative cooling methods have been proposed including a microchannel heat sink. Two representative types of the microchannel heat sink are (1) the traditional microchannel (TMC) type and (2) the manifold microchannel (MMC) type. A TMC heat sink, which was proposed first by Tuckerman and Pease [1], is characterized by the long microchannels that run in one direction parallel to the heat-sink base. It has been successfully investigated by using a simple one-dimensional model [2] or more sophisticated three-dimensional numerical methods [3] and [4]. Even though the TMC heat sink has brought substantial improvements in the cooling performance, it has two disadvantages: the relatively high pressure loss and the significant temperature variation within the heat source. An MMC heat sink, on the other hand, differs from a TMC type in that the coolant flows through the alternating inlet and outlet manifolds in the direction normal to the heat-sink base to and from the segmented microchannels as shown in Fig. 1(a). The flow path is greatly reduced to a small fraction of the total length of a heat sink; the shortened flow path is expected to reduce the pressure drop and restrain the growth of the thermal boundary layer along the streamwise direction.Harpole and Eninger [5] proposed an MMC system having between 10 and 30 manifold channels and reported that, for constant flow rate or pumping power, the maximum temperature and the temperature variation within the heat source were substantially reduced from that of a TMC heat sink. Copeland et al. [6] tested a variety of MMCs experimentally and reported that the thermal resistance was inversely proportional to the volume flow rate in a log–log scale. Copeland et al. [7] also found in a comparative study of an MMC heat sink that the simple analytical model based on correlations for a straight channel is not satisfactory in predicting the performance. The purpose of the present study is to develop a three-dimensional analysis procedure for the thermal performance of an MMC heat sink and apply it to optimize the geometric shape and the operating condition. The SIMPLE-type finite volume method is coupled with an optimization scheme based on the steepest descent method [8]. The geometric parameters that minimize the thermal resistance are obtained. The effects of the channel number and the pumping power on the performance of a heat sink are examined.

A three-dimensional analysis procedure for the thermal performance of an MMC heat sink has been developed and coupled with the steepest descent algorithm to obtain the optimal geometric dimensions. For a given pumping power and a specified number of manifolds, the optimal channel depth, channel width, fin thickness, and inlet/outlet width ratio that yield the lowest thermal resistance are numerically calculated. The convergence is robust and the optimal state has been reached within six global iterations. It was found that 95% of the heat is removed through the fin surface and that the lowest temperature on the floor is attained in the vicinity of the channel entrance point while the hottest spots are near the inlet and outlet stagnation points in the channel floor. Comparing to the TMC heat sink for the identical heat load and pumping power, the thermal resistance is lowered by more than 50% while the maximum temperature variation on the heated wall is improved by tenfold. Among various design variables, the channel width and depth appear to be more critical than others in dictating the heat-sink performance. When the channel number is allowed to vary, the optimal channel shape and flow rate change widely: the aspect ratio of the channel cross-section and the inlet to outlet width ratio are both low, and carries a larger flow rate when the channel density is relatively sparse while the opposite is true when the channel number exceeds 200. The optimal dimensions and corresponding thermal resistance have a power-law dependence on the pumping power. The optimal aspect ratio of the channel cross-section remains unchanged as the Reynolds number of the pumping power varies.