Effects of temperature-dependent viscosity on Bénard convection in a porous medium using a non-Darcy model

Abstract

Temperature-dependent viscosity variation effect on Bénard convection, of a gas or a liquid, in an enclosure filled with a porous medium is studied numerically, based on the general model of momentum transfer in a porous medium. The exponential form of viscosity–temperature relation is applied to examine three cases of viscosity–temperature relation: constant ( μ = μ C ) , decreasing (down to 0.13 μ C ) and increasing (up to 7.39 μ C ). Effects of fluid viscosity variation on isotherms, streamlines, and the Nusselt number are studied. Application of the effective and average Rayleigh number is examined. Defining a reference temperature, which does not change with the Rayleigh number but increases with the Darcy number, is found to be a viable option to account for temperature-dependent viscosity variation.