Linear and Nonlinear Stability Analysis of a Horton–Rogers–Lapwood Problem with an Internal Heat Source and Brinkman Effects

Abstract

The effect of internal heat source on convection in a layer of fluid in a porous medium was analyzed using linear and nonlinear analysis, and boundaries are assumed to be stress-free and isothermal. Normal mode technique is used for linear analysis, and energy method is used for nonlinear stability analysis. The presence of heat generation leads to the possibility of the existence of a subcritical instability. Effects of increase of Darcy–Brinkman number and internal heat parameter on critical Rayleigh numbers were analyzed numerically using Chebyshev pseudospectral method.