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

Published online by Cambridge University Press:  20 April 2006

J. Gary ,
D. R. Kassoy ,
H. Tadjeran  and
A. Zebib
J. Gary
Affiliation:
Computer Science Department, University of Colorado. Boulder, Colorado 80309, U.S.A. Present address: Mathematics Department, Colorado School of Mines, Golden, Colorado 80401, U.S.A.
D. R. Kassoy
Affiliation:
Mechanical Engineering Department, University of Colorado, Boulder, Colorado 80309, U.S.A.
H. Tadjeran
Affiliation:
Mechanical Engineering Department, University of Colorado, Boulder, Colorado 80309, U.S.A.
A. Zebib
Affiliation:
Mechanical Engineering Department, Rutgers University, Piscataway, New Jersey 08854, U.S.A.
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 117 , April 1982 , pp. 233 - 249
Copyright
© 1982 Cambridge University Press

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