Onset of convective instabilities for Darcy-Forchheimer flow in a horizontal porous layer: the effect of viscous dissipation

Parallel Darcy-Forchheimer flow in a horizontal porous layer with an isothermal top boundary and a bottom boundary either isothermal or adiabatic is discussed by taking into account the effect of viscous dissipation. This effect causes a nonlinear temperature profile within the layer. The linear stability of this non-isothermal base flow is then investigated with respect to the onset of convective rolls. The isothermal/adiabatic condition on the bottom boundary is described by a third kind boundary condition such that the Biot number is either zero (adiabatic) or infinite (isothermal). The solution of the linear equations for the perturbation waves is determined by using a direct numerical approach, namely a fourth order Runge Kutta method. The neutral stability curve and the critical value of the governing parameter R = Ge*Pe^2 are obtained, where Ge is the Gebhart number and Pe is the P´eclet number. Different values of the tilt angle between the direction of the basic flow and and the propagation axis of the disturbances are considered.