Legendre wavelet operational matrix method for the analysis of thermal radiation effect on natural convection of a vertical plate embedded in a saturated porous medium

Abstract

In this paper, the heat transfer characteristics of natural convection around a vertical flat surface embedded in a saturated porous medium are studied by taking into account the thermal radiation effect. With the aid of the similarity transformations, the governing equations of the problem are reduced to the system of ordinary differential equations over the infinite domain. Moreover, the Legendre wavelet operational matrix method (LWOMM) is hired to find the numerical solution to the considered problem. Initially, to ensure the efficiency of the proposed strategy, a third-order nonlinear boundary value problem having the exact solution is considered a test problem. The numerical findings elucidate that the solutions obtained by the LWOMM are in good agreement with the exact solution as compared with the solution obtained by the Haar wavelet operational matrix method, with the consumption of less computational CPU time. Also, the temperature and velocity profiles are discussed graphically.