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/Rc, 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/Rc. When R/Rc = 8 the constantviscosity convection pattern is steady, while those with temperature differences of 100 and 200 K are found to oscillate.

Numerical study on a vertical plate with variable viscosity and thermal conductivity

“…Gary et al [9] studied the effects of significant viscosity variation on convective heat transport in water-saturated porus media. Elbashbesy and Ibrahim [10] analyzed the flow of a viscous incompressible fluids along a heated vertical plate, taking into account the variation of the viscosity and thermal diffusivity with temperature.…”

The Effect of Radiation on MHD Natural Convection Flow of Fluid with Variable Viscosity from a Porous Vertical Plate

“…Molla et al [11] studied the Magnetohydrodynamic natural convection flow on a sphere with uniform heat flux in presence of heat generation. Accordingly, Gary et al [12] and Mehta and Sood [13] have concluded that when this effect is included, the flow characteristics substantially change compared to the constant viscosity case. Recently, Kafoussius and Williams [14] and Kafoussias and Rees [15] have investigated the effect of the temperature-dependent viscosity on the mixed convection flow past a vertical flat plate in the region near the leading edge using the local nonsimilarity method.…”

MHD Natural Convection Flow of Fluid From a Vertical Flat Plate Considering Temperature Dependent Viscosity

“…Following Gray at al. [23], Mehta and Sood [24], Kafoussias and Williams [25] and Kafoussias et al [26], we assume the temperature dependent viscosity μ can be of the form…”