Optimum Thermal Analysis of a Heat Sink with Various Fin Cross-Sections by Adjusting Fin Length and Cross-Section

A theoretical analysis of a heat sink is presented in this study to pursue the purpose of maximum thermal dissipation and the least material cost. Due to the general derivation, the longitudinal fin arrays on a heat sink can have either square, rectangular, equilaterally triangular, or cylindrical cross-section. By input of the Biot number, Bi, heat transfer coefficient ratio, H, and the shape parameter, γ, the heat transfer equation, which is expressed in implicit form, can be solved by iterative method to calculate the optimum fin length and fin thickness. Meanwhile, the thermal resistance of a heat sink can be obtained to illustrate the cooling performance under various design conditions.