Inertia effects on non-parallel thermal instability of natural convection flow over horizontal and inclined plates in porous media (Q1614557)

This paper considers the inertia effects on the onset of thermal instability in free convection flow over heated horizontal and inclined flat plates embedded in fluid-saturated porous media. It is assumed that the temperature of the plate varies as a power-law function of the distance measured along the plate. The linear non-parallel flow model is used in the instability analysis, which takes into account the streamwise variation as well as the transverse variation of the disturbance amplitude function. Such an assumption leads to a system of nonlinear equations for the disturbance amplitude functions. In the basic flow, the boundary-layer approximations are invoked and the resulting governing equations are transformed into a system of non-similar dimensionless equations that are then solved by an implicit finite difference method. The resulting governing equations for the disturbance amplitude function are partial differential equations that are converted into a system of homogeneous linear ordinary differential equations with homogeneous boundary conditions by the local similarity method. The resulting eigenvalue problem is then solved by an implicit finite difference method. Representative neutral stability curves and critical Rayleigh numbers are presented. Some of the principal results of this paper are: (i) the onset of vortex instability can be predicted for all positive angles of inclination relative to the horizontal; (ii) the non-parallel flow model predicts a higher critical Rayleigh number than the parallel flow model; (iii) the flow becomes more stable to the vortex mode of instability as the angle of inclination increases; (iv) the flow becomes more stable with an increasing value of the power-law exponent of the wall temperature. The paper is carefully prepared and presented. Those interested in thermal stability in porous media will find the results interesting.