A convective instability analysis of a channel flow within a saturated porous medium

The influence of convection in a horizontal channel filled with a porous medium is examined to assess the stability of the fluid flow between the two walls that are held fixed at different temperatures. The flow is described by the Navier–Stokes equations, while heat transfer is captured through the energy equation. A coupled linear stability system is derived and solved using a Chebyshev spectral collocation method. The study focuses on the impact of the relevant nondimensional parameters on the development of the perturbations and the onset of instability within the flow. The onset of convection is advanced as the porous parameter (M) increases, while higher Prandtl numbers (Pr) and Reynolds numbers (Re) delay the onset of convection. The growth rate is unaffected by increases in Pr and the Rayleigh number (Ra); however, it increases as M decreases and as Re increases. The isocontours show that increasing Pr stabilizes temperature variations in the inner flow region.