Optimization of annular fins on a horizontal tube

A combination of uniform-thickness annular fins evenly spaced on a tube is a common extended-surface heat exchanger configuration. An analytical model is developed and is verified by comparing total heat transfer predicted by the model to available experimental data. A direct-pattern search technique is applied to the model to optimize the fin/ tube geometry. Optimum dimensions and spacing of fins are established to provide the maximum free convection heat transfer from a fin/tube combination. The optimum arrangement is dependent on fin thermal conductivity, tube diameter, volume of fin material per unit length of tube, and temperature difference between the tube and the surrounding air. Calculated results indicate that a fin in the optimum fin/tube system is shorter and thicker than an isolated fin optimized for minimum material (with no consideration of the effects of fin spacing).