The stability of a cross rolls in a rayleigh-benard convection in a porous media of an infinite extent

Abstract

The process of flow through porous media is of interest to a wide range of engineers and scientists. The convective flow in porous media is one of the main topics of heat transfer which has been investigated in the last several decades. Porous medium is a material that contains the pores. It also has the skeletal portion of the material which is called the “matrix” or “frame”. The instability of a fluid layer which is confined between two thermally conducting plates, and is heated from below to produce a fixed temperature difference is called Rayleigh Benard convection. The aim of this study is to analyze small perturbation effects due to the leading convection term. The method of weakly nonlinear analysis is used to determine the convection threshold. The amplitude shows that the bifurcation is the stable branches and bifurcation of amplitude clearly shows similarity to linear distribution. The method of Runge-Kutta is used to determine the bifurcation of the cross rolls. The rolls with the higher amplitude will prevail.