Nonlinear Thermal Response Analysis of an Internally Heated Radiative-Convective Porous Fin subjected to Magnetic Fields using Method of Lines

Abstract

This paper demonstrated the computational efficiency and accuracy of method of lines for the nonlinear transient thermal response analysis of a radiative-radiative porous fin with temperature-dependent internal heat generation under the influence of magnetic fields.  To establish the computational accuracy of the method, the results of the solution are compared with the results of the developed exact analytical method. Also, the numerical solutions through the method of lines are adopted to explore the impacts of the model parameters on the performance of the passive device. It is found that as the conductive-convective, conductive-radiative, and magnetic field parameters increase, the fin temperature distribution in the fin decreases. The temperature distribution in the fin increases through the ?n as the nonlinear thermal conductivity parameter increases. It is hoped that the present study gives a good insight into the nonlinear analysis of the extended surface which will aid the proper design of the extended surfaces in thermal systems.