The onset of convection in a porous layer induced by viscous dissipation: A linear stability analysis

The effect of viscous dissipation on parallel Darcy flow in a horizontal porous layer with an adiabatic lower boundary and an isothermal upper boundary is discussed. The presence of viscous dissipation serves to cause a nonlinear temperature profile within the layer. The linear stability of this nonisothermal base flow is then investigated with respect to the onset of convective rolls. The solution of the linear equations for the perturbation waves is determined analytically by a power series method, and the results are confirmed using a direct numerical approach using 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. The effect of an imperfect isothermal boundary condition at the upper boundary is investigated by considering finite values of the Biot number.