Thermal Analysis of Semicircular Fins Considering Temperature-dependent Thermal Conductivity and Heat Transfer Coefficient

Abstract

This paper investigates the semicircular fin efficiency considering the fact that both thermal conductivity of the fin material and the heat transfer coefficient for dissipation of heat from the fin surface are temperature dependent and can render changes in fin efficiency for large temperature differences. Based on a steady-state two-dimensional thermal analysis, the non-linear differential equation of semicircular fin model has been solved using finite-difference method. Two-dimensional temperature distribution of the fin surface has been successfully correlated to a third-degree polynomial. Results show that for a cooling fin with increase in tube size fin efficiency remains nearly the same or decreases for a given number of fin depending on whether fin number is large or small and whether tube size is slightly large or much larger. With increase in fin number for a given tube size, efficiency remains nearly the same or increases depending on whether fin numbers are a few more or many more and whether tube size is small or large. The efficiency range is 0.2875–0.311 for aluminium and 0.295–0.308 for copper corresponding to tube size from 0.01 m to 0.09 m and fin number ranging from 4 to 24. As expected, fin efficiency has been found to increase with enhancement in base temperature and reduction in ambient temperature. Results mentioned above are consistent for both copper and aluminium as fin material.