Influence of anisotropy on the stability of mixed convection in a porous channel ASME

This paper addresses the stability of mixed convective buoyancy assisted flow due to external pressure gradient and buoyancy force in a vertical fluid saturated porous channel with linearly varying wall temperature. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. Two different types of temperature perturbations, (i) zero temperature and (ii) zero heat flux, have been considered to study the effect of anisotropic permeability and thermal diffusivity on the flow stability. The stability analysis indicated that the least stable mode is two-dimensional. Furthermore, the results show that for the same Reynolds number, the fully developed base flow is highly unstable (stable) for high (low) permeable porous media as well as for a porous medium with small (large) thermal diffusivity ratio. Depending on the magnitude of all parameters studied, three types of instabilities (shear, thermal, and mixed instability) occurred. The transition of instability from one type to another took place smoothly, except when the permeability ratio exceeded 6. Based on the value of the permeability ratio, the flow in an anisotropic medium for a specific Reynolds number may be either more or less stable than the flow in an isotropic medium. In addition, the fully developed flow is more stable for relatively small values of the modified Darcy number than for larger values. The effect of Brinkman as well as Forchheimer terms are negligible for the set of other parameters studied here. In contrast to a pure viscous fluid or an isotropic porous medium, which are characterized by unicellular convective cells, in anisotropic porous media convective cells may be unicellular or bicellular. The stability analysis of mixed convection in channels filled either with a viscous fluid or with an isotropic saturated porous medium may be obtained as special cases of the general study presented here