Viscous dissipation instability of non-Newtonian flow in a horizontal porous channel

The onset of thermal convection inside a horizontal porous layer is investigated. An Ostwald-de Waele non-Newtonian fluid is saturating the porous layer. The layer is impermeable with an adiabatic lower boundary and an isothermal upper boundary. A horizontal basic flow with uniform velocity and variable direction is imposed. The viscous dissipation contribution is included into the energy balance equation as internal heat source. A linear stability analysis of the basic state is performed employing the normal mode method. The problem is solved for high values of the Péclet number. The set of ordinary differential equations obtained are solved numerically as an eigenvalue problem by employing the Runge-Kutta method coupled with the shooting method. An accuracy test of the numerical solver is reported. The neutral stability curves are obtained for transverse, oblique, and longitudinal rolls. The threshold conditions of the governing parameters for the onset of thermal convection are reported.