Classical Linear Stability Analysis of Energy Based Internally Heated Distributions on Bénard Porous Convection in a Micropolar Fluid Layer

Abstract

The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) and Free-Free (F-F). The RB convection models are distinguished by the three different temperature boundary conditions like: 1) RB1: lower and upper at fixed-temperature, 2) RB2: lower and upper with fixed-heat flux, or perfectly insulating and 3) RB3: bottom surface is fixed-temperature and top surface is fixed-heat flux. A Galerkin-type is based on the weighted residual method (WRM) which has been used to obtain the eigenvalue for gravity thermal Rayleigh number. It is noted that the porous medium of Darcy parameter and spin diffusion (couple stress) parameter N 3 is to hasten coupling parameter N 1 and micropolar heat conduction parameter N 5 is to delay the onset of convection. Further, increase in the value of N 1 , N 5 , and as well as decrease in N 3 is to diminish the size of convection cells.