The instability onset of generalized isoflux mean flow using Brinkman-Darcy-Benard model in a fluid saturated porous channel

Infinitely wide single-cell basic flow formation within a porous channel in the context of isoflux boundary conditions and its instability onset were determined in a recent work (Brandao et al., 2021). In the present analysis, the scope is to extend the latter work to incorporate the effective viscosity term within the transitional flow in the frame of Brinkman-Darcy-Benard convection. The accounted model entails a physical parameter, so-called as the Darcy number whose limiting values result in either the Darcy-Benard convection of Brandao et al. (2021) or the Rayleigh-Benard convection, which is the first time studied in the literature. Apart from the Darcy number, the Rayleigh number and the horizontal temperature parameter are the essential physical parameters. Neutral stability curves affected by these parameters are numerically simulated to explore the onset of instability within the linear stability analysis. The solution of eigenvalue problem fully conforms to the one in the above published in the absence of Darcy number. Comparatively larger Rayleigh numbers are derived within the Brinkman's model rather than the published Darcy model.