Unsteady state heat transfer analysis of a convective-radiative rectangular fin using Laplace Transform-Galerkin weighted residual method

Abstract

The present investigation is concerned with the development of non-power series solutions for the unsteady state nonlinear thermal model of a radiative-convective fin having temperature-variant thermal conductivity using Laplace transform-Galerkin weighted residual method. In the study, it is demonstrated that the symbolic solutions do not involve a large number of terms, complex mathematical analysis, high computational cost, and time as compared to the power series solutions in previous studies. The solutions allow effective predictions of the extended surface thermal performance over a large domain and time. The results of the non-power series solutions are verified numerically, and very good agreements are established. Parametric studies are carried out with the aid of the symbolic non-power solutions. It is found that as the conductive-convective and conductive-radiative increase, temperature distribution decreases since the rate of heat transfer becomes augmented and hence, the fin thermal efficiency is improved. Additionally, when the thermal conductivity of the fin increases, the temperature distribution in the passive device increases. The temperature increases with time at the different positions in the fin. Following the time histories of the solution, it is shown that unsteady state solutions converge to a steady state as time progresses. It could therefore be stated the developed non-power series analytical solutions provide a good platform for comparison of the nonlinear thermal analyses of fins in thermal systems.