Local thermal non-equilibrium flow with viscous dissipation in a plane horizontal porous layer

Darcy's flow in a horizontal porous layer with impermeable boundaries is studied. The viscous dissipation effect is taken into account and the local thermal non-equilibrium (LTNE) model for the energy balance is adopted. The upper boundary is assumed to be perfectly isothermal and the lower boundary is taken to be thermally insulated. The basic solution is expressed analytically. The case of a perfectly conducting solid phase is considered. The onset of convective roll instability is investigated by a linear analysis, with different values of the inter-phase heat transfer parameter. The eigenvalue problem is solved numerically by a Runge-Kutta method.