Optimum thermal analysis of annular fin heat sink by adjusting outer radius and fin number

The theoretical exploration of the optimum cooling effect of a heat sink equipped with annular fins is presented in this study. The optimum equation is derived in transcendental form and the formula of the thermal resistance is also provided. With the input data of dimensionless parameter, C, heat transfer coefficient ratios, H and He, this optimum equation can be utilized to find the optimum outer radius of annular fins and fin number on a heat sink that affect the overall thermal effectiveness of a heat sink. Finally, examples are offered to illustrate the cooling performance of a heat sink including annular fins.