Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium

Abstract

Buoyancy opposed mixed convection is considered in a vertical channel filled with an isotropic, porous medium, in which the motion of an incompressible fluid is induced by external pressure gradients and buoyancy forces. The Brinkman-Wooding-extended Darcy model has been used to study the instability mechanisms of the basic flow and its dependence on the Prandtl number (Pr) of the fluid. The stability analysis indicated that for the same Reynolds number (Re), the fully developed base flow was highly unstable for a fluid with high Pr. For a porous medium with a Darcy number (Da) of 10−6 and Pr⩾0.7, two different types of instability, Rayleigh-Taylor (R-T) and buoyant instability, are observed. The R-T instability mode is observed for relatively small values of Re. Further, the results show that for Da=10−5 and Pr<1, the spectrum of the energy profile is abrupt and sudden, whereas the same is smooth when Da=10−6. In the case of R-T instability, the critical value of Ra at low Re is given by −2.47∕Da. Though the R-T mode of instability is independent of Pr, the range of Re that sustains the R-T mode is a function of Pr. It has been found that enhancement of Pr reduces the Re range mentioned above. In contrast to the case of a purely viscous fluid, where the effect of Pr is not significant, in isotropic porous media Pr plays a significant role in characterizing the flow stability. The instability characteristics of zero temperature flux perturbation (BC-I) and zero heat flux perturbation (BC-II) on the boundaries differ significantly in the case of the R-T stability mode. However, both conditions lead to similar results for buoyant stability, except at small values of Re.