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 = GePe2 are obtained, where Ge is the Gebhart number and Pe is the Péclet number. Different values of the tilt angle between the direction of the basic flow and and the propagation axis of the disturbances are considered