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This paper presents a formal systematic optimization process to plate-fins heat sink design for dissipating the maximum heat generation from electronic component by applying the entropy generation rate to obtain the highest heat transfer efficiency. The design investigations demonstrate the thermal performance with horizontal inlet cooling stream is slightly superior to that with vertical inlet cooling stream. However, the design of vertical inlet stream model can yield to a less structural mass (volume) required than that of horizontal inlet stream model under the same amount of heat dissipation. In this paper, the constrained optimization of plate-fins heat sink design with vertical inlet stream model is developed to achieve enhanced thermal performance. The number of fins and the aspect ratio are the most responsive factors for influencing thermal performances. The heat sink used on AMD Thunderbird 1-GHz processor has been examined and redesigned by presenting optimization methodology. The optimal thermal analysis has a very good agreement to the both of vendors' announced information and using simulation of parabolic hyperbolic or elliptic numerical integration code series (PHOENICS). The optimum design that minimizes entropy generation rate in this paper primarily applied three criteria for plate-fins heat sink optimal design: formal constrained nonlinear programming to obtain the maximum heat dissipation; prescribed heat dissipation; prescribed surface temperature. As a result, the thermal performance can be notably improved; both the sink size and structural mass can apparently be reduced through the presented design method and process. This analysis and design methodology can be further applied to other finned type heat sink designs.