Analytical Treatment to Find Stability of the System of Partial Equations Arising from Heat Transfer on A porous Plate

Abstract

This paper presents the analytical solution for a mathematical model of heat transfer by free convection which arises from the flowing of fluid on a porous plate. The plate is laid on a horizontal position with temperature source at the surface of the plate that is different from the surrounding atmosphere temperature. The governing mathematical equations, which have been established, consist of partial differential equations with some boundary conditions. The model has been converted into a boundary value problem, and in this case, an analytical solution was adopted by using a perturbation of the functions which are playing the important role in the solution of the system like temperature, velocity. These functions help to find the necessary factor that controls the stability of the problem. The outcome results showed that the wave number has the significant effect in the stability.