Nonlinear transient thermal analysis of a convective–radiative fin: A comparative study of two approximate analytical methods

Abstract

Developments of analytical solutions to nonlinear equations provide very good physical insights into the nonlinear phenomena. The nonlinear transient thermal responses of extended surfaces have been widely studied analytically with the aid of different methods based on power series solutions. Such solutions come with large numbers of terms that are not convenient for use in practice. In this work, a non-power series solution is presented for the nonlinear transient thermal analysis of the passive device. Also, a comparative study of two analytical methods, Laplace transform-Galerkin weighted residual and differential transformation methods is presented to analyze transient nonlinear thermal model of radiative–convective fin considering varying thermal conductivity. The obtained analytical solutions are verified analytically and numerically, and very good agreements are established. The symbolic results are employed to check the influences of model parameters on passive device’s thermal performance. It is found that as the conductive–convective, and conductive–radiative parameters increase, temperature distribution decreases since heat transfer becomes augmented and hence, the fin thermal efficiency is improved. The temperature distribution increases through the fin as thermal conductivity increases. At the different positions in the fin, the temperature increases with an increase in time. The time histories of the solution shows that transient solutions converge to a steady state and the fin tip temperature increases as time progresses. The developed approximate analytical solutions provide very good platforms for the nonlinear thermal analyses of fins and proper design of the extended surfaces in thermal systems.