Significance of fin tip temperature on the heat transfer rate and thermal efficiency of a convective-radiative rectangular fin with variable thermal conductivity

Abstract

In this work, effect of fin tip temperature on the rate of heat transfer and thermal efficiency of a rectangular convective-radiative fin with temperature-dependent thermal conductivity is analyzed using differential transformation method. The results of the power series solutions are verified numerically, and very good agreements are established. Also, the symbolic solutions are used to examine the effects of the conductive-convective and nonlinear thermal conductivity parameters on the thermal performance of the passive device. It is found that when the nonlinear thermal conductivity parameter increases, the fin tip temperature increases. However, the temperature at the tip of the fin decreases as the conductive-convective parameter increases. The thermal efficiency of the fin increases as the fin tip temperature and nonlinear thermal conductivity parameters are augmented but an increase conductive-convective parameter causes the fin tip temperature and the thermal efficiency of the extended surface to reduce. An increase in the conductive-convective parameter causes decrease the temperature distribution and thermal efficiency in the passive device. However, the efficiency of the fin increases as the nonlinear thermal conductivity parameter increases. When nonlinear thermal conductivity and conductive-convective parameters increase, the rate of heat transfer at the fin base increases. The developed analytical solutions provide a good platform for the nonlinear thermal analysis of the fin and proper design of the extended surfaces in thermal systems.