Anisotropic porous penetrative convection for a local thermal non-equilibrium model with Brinkman effects

The intent of the present problem is to observe the effect of internal heat source on the onset of convection in a fluid saturated anisotropic porous medium. Brinkman model is employed to formulate the momentum equation and fluid and solid phases are considered to be at local thermal non-equilibrium. The linear and non-linear theories are implemented to analyze the stability by computing the critical Rayleigh number and corresponding wave number. Normal mode technique is used for linear analysis and energy method is used for non-linear 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, inter-phase heat transfer parameter, anisotropy parameter, porosity-modified conductivity ratio and internal heat parameter on critical Rayleigh number was analyzed numerically using Chebyshev pseudospectral method.