Journal of Fluid Mechanics

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

J.  Gary a1p1, D. R.  Kassoy a2, H.  Tadjeran a2 and A.  Zebib a3
a1 Computer Science Department, University of Colorado. Boulder, Colorado 80309, U.S.A.
a2 Mechanical Engineering Department, University of Colorado, Boulder, Colorado 80309, U.S.A.
a3 Mechanical Engineering Department, Rutgers University, Piscataway, New Jersey 08854, U.S.A.

Article author query
gary j   [Google Scholar] 
kassoy dr   [Google Scholar] 
tadjeran h   [Google Scholar] 
zebib a   [Google Scholar] 


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.

(Published Online April 20 2006)
(Received November 10 1980)
(Revised September 1 1981)

p1 Present address: Mathematics Department, Colorado School of Mines, Golden, Colorado 80401, U.S.A.