Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.
机构:
Department of Mathematics, China University of Mining and Technology, BeijingDepartment of Mathematics, China University of Mining and Technology, Beijing
Cai W.
Su N.
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机构:
Department of Mathematical Sciences, Tsinghua University, BeijingDepartment of Mathematics, China University of Mining and Technology, Beijing
Su N.
He X.
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机构:
Department of Mathematical Sciences, Tsinghua University, BeijingDepartment of Mathematics, China University of Mining and Technology, Beijing
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Univ KwaZulu Natal, Sch Math Sci, Private Bag X01 Scottsville, ZA-3209 Pietermaritzburg, South Africa
Alneelain Univ, Fac Technol Math Sci & Stat, Khartoum, SudanUniv KwaZulu Natal, Sch Math Sci, Private Bag X01 Scottsville, ZA-3209 Pietermaritzburg, South Africa