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Theoretical and numerical analyses of convective instability in porous media with upward throughflow
Author(s) -
Zhao Chongbin,
Hobbs B. E.,
Mühlhaus H. B.
Publication year - 1999
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/(sici)1096-9853(199906)23:7<629::aid-nag986>3.0.co;2-k
Subject(s) - throughflow , convective instability , mechanics , constant (computer programming) , péclet number , instability , rayleigh number , galerkin method , convection , porous medium , mathematics , materials science , geology , thermodynamics , physics , porosity , finite element method , geotechnical engineering , natural convection , computer science , programming language
Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers ( Pe ⩽ 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright © 1999 John Wiley & Sons, Ltd.