Linear stability of horizontal throughflow in a Brinkman porous medium with mixed thermal boundary conditions

The onset of convective instability in a horizontal throughflow due to external heating and viscous dissipation is investigated. The flow is considered along a porous layer with high permeability, bounded by two impermeable surfaces subjected to external heating. Hence, the third kind of thermal boundary conditions are used at the two boundaries. The Brinkman extended Darcy's law is adopted for the equations governing flow through the layer. The base flow is assumed to be inclined to the horizontal axis at an angle gamma. An average mass flow along the horizontal direction is considered, the magnitude of which is given by Pe (Peclet number). The disturbances in the flow are assumed in the form of two-dimensional oblique rolls inclined to the base flow at an angle gamma(0 <= gamma <= pi/2) The four limiting cases with different combinations of B-0, B-1 -> 0, infinity, are also discussed. The effect of viscous dissipation and external heating at the two boundaries, on the instability of the flow is discussed. The instability remains unaffected by the direction of the throughflow. However, the instability is affected by the magnitude of the throughflow. Viscous dissipation has a stabilizing effect on the flow, as long as the external heating at the bottom boundary is higher than that at the upper boundary. The longitudinal rolls (at gamma = pi/2) are the preferred mode of instabilities.