Onset of convection in LTNE Darcy–Brinkman anisotropic porous layer: Cattaneo effect in the solid

The onset of convection in anisotropic porous medium in local thermal non-equilibrium regime is studied. The Cattaneo's law to describe heat propagation in solid phase is allowed, while the Fourier's law in fluid phase is employed. Linear and nonlinear stability of the conduction solution are performed and the critical Rayleigh numbers in a closed form are obtained. The influence of second sound effect, inter-phase heat transfer and anisotropy of the medium on the onset of instability have been analysed via numerical simulations, too