Analysis of heat transfer between an inert gas and a porous structure with ultralow thermal conductivity using the Sumudu transform method

Abstract

The relatively new integral transform called the Sumudu transform method can be used to solve partial differential equations with variable coefficients and as well as intricate problems in engineering and applied mathematics without resorting to a new frequency domain. Unlike the other integral transforms, the Sumudu transform has scale and unit-preserving properties. However, the method is still not widely known or used for solving differential equations especially in the area of applied mathematics and engineering. As a means of demonstrating the potency of the method, the paper applied the Sumudu transform to present analytical solutions of a one-dimensional problem of heat transfer between an inert gas and an ultralow thermal conductivity porous medium. The developed analytical solutions are used to investigate the heat propagation in the porous medium. Depending on the initial temperature, it is established from the study that there are snapshots of the heat wave propagating and a sharp heat front propagation through the medium during its heating or cooling. This sharp front is difficult to detect and quantify by numerical methods. Hence, exact analytical solutions are presented in this study. As it is demonstrated in this study, it is hoped that the Sumudu transform method will be applied to other various complex engineering problems.