Nonlinear stability analysis of a fluid saturated anisotropic Darcy–Brinkman medium with internal heat source

Abstract

In the present study, the effect of mechanical anisotropy on the onset of convection is observed when the fluid layer is influenced by internal heat generation and heat extraction through the boundary. The extended Darcy model is employed to establish the momentum equation. Particularly, the emphasis is laid upon that how these factors alter the criteria of onset of convection. The variation in certain parameters affects the stability of the system. Linear instability and nonlinear stability analysis are performed to predict the stability of the system, however; it is found that the linear and nonlinear analyses are not in agreement with the substantial change in internal heat generation. All numerical and graphical results of the subsequent analysis are obtained by using the Chebyshev-pseudospectral method.