The effect of viscous dissipation on the onset of convection in an inclined porous layer

The linear stability of a basic forced and free convection flow in an inclined porous channel is analysed by using the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of viscous dissipation, as well as by the boundary conditions. The boundary planes are assumed to be impermeable and isothermal, with a temperature of the lower boundary higher than that of the upper boundary. The instability against longitudinal rolls is studied by employing a second-order weighted residual solution and an accurate sixth-order Runge–Kutta solution of the disturbance equations. The instability against transverse rolls is also investigated. It is shown that these disturbances are in every case less unstable than the longitudinal rolls.