Transient free convection from a vertical plate to a non-newtonian fluid in a porous medium

Abstract

An analysis of the transient, buoyancy-induced flow and heat transfer adjacent to a suddenly heated vertical wall, embedded in a porous medium saturated with a non-Newtonian fluid, is presented. It is shown that the governing equations, under boundary layer assumptions, are of a singular parabolic type and can be solved accurately in a semi-similar, finite domain using a successive relaxation method. The results show that during the initial stage, before effects of the leading edge become influential at a location, heat transfer and flow phenomena in porous media are governed by transient one-dimensional diffusion processes, for both pseudoplastic and dilatant fluids. Results are presented for the transition from this initial stage to a fully two-dimensional transient, which ultimately terminates in a steady convection. Non-Newtonian fluids which are pseudoplastic exhibit a significantly larger change in the heat transfer coefficient during the transition between the initial diffusive and final steady flow conditions, and unlike the free convection in homogeneous media neither dilatants nor pseudoplastics exhibit any undershoot in the heat transfer coefficient. Furthermore, it is shown that the time required to reach steady state increases and the heat transfer coefficient decreases with a decrease in the power law index.