The optimum approach of a heat sink with the least material cost for maximum heat dissipation is presented in this study. The longitudinal fin arrays of a heat sink can have either cylindrical, square, equilateral triangular and rectangular cross section in the theoretical analysis of the cooling effect. In addition, the convection effect due to the fin tip loss has been incorporated into the derivation. By input the Biot number, Bi*, heat transfer ratios Hb* and He*, the optimum heat transfer equation can be derived in transcendental form which can be solved by iterative method to calculate the optimum fin length and fin cross section. Meanwhile, the thermal resistance of a heat sink can be obtained to illustrate the cooling performance under various design conditions. Finally, examples are provided to show the results for practical purpose.

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