The effects of significant viscosity variation on convective heat transport in water-saturated porous media

Abstract

Weakly nonlinear theory and finite-difference calculations are used to describe steadystate and oscillatory convective heat transport in water-saturated porous media. Two-dimensional rolls in a rectangular region are considered when the imposed temperature difference between the horizontal boundaries is as large as 200 K, corresponding to a viscosity ratio of about 6·5. The lowest-order weakly nonlinear results indicate that the variation of the Nusselt number with the ratio of the actual Rayleigh number to the corresponding critical value R / R c , is independent of the temperature difference for the range considered. Results for the Nusselt number obtained from finite-difference solutions contain a weak dependence on temperature difference which increases with the magnitude of R / R c . When R / R c = 8 the constantviscosity convection pattern is steady, while those with temperature differences of 100 and 200 K are found to oscillate.