Onset of Instability in Hadley-Prats Flow in an Anisotropic Porous Media with Viscous Dissipation

The stability of a Hadley-type flow in a horizontal porous medium under an inclined temperature gradient is investigated when a fundamental horizontal mass flow (Prats flow) is present. Consequently, the Hadley-prats flow is the name given to the basic flow. We consider anisotropic thermal diffusivity and weak vertical heterogeneity in permeability. It is believed that viscous dissipation has a significant impact. The Rayleigh number associated with the vertical thermal gradient Ra is one of the eigenvalues. The other parameters include the thermal diffusivity (𝜉), the Gebhart number (𝐺𝑒) for viscous dissipation, the horizontal Rayleigh number (Rah) for the horizontal through flow, and the parameter 𝜆 for changes in permeability. A linear stability analysis is executed, wherein the governing equations are numerically solved to determine the critical Rayleigh and wave numbers. The discussion pertains to longitudinal and transverse rolls. Longitudinal rolls are generally considered the most effective means of characterizing instability in most scenarios.