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Theoretical and numerical analyses of convective instability in porous media with upward throughflow

✍ Scribed by Zhao, Chongbin; Hobbs, B. E.; Mühlhaus, H. B.

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
254 KB
Volume
23
Category
Article
ISSN
0363-9061

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✦ Synopsis

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward through#ow. 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 through#ow destabilizes the convective #ow in the horizontal layer. To con"rm these "ndings, the "nite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system.

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