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

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 image, decreasing (down to image) and increasing (up to image). 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.