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Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media(Ⅱ)

Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 422-430页

作者： cai {1.1. gou {1.1. 2 & ZHANG Na1.1. institute of engineering thermophysics, Chinese Academy of Sciences, beijing 1.0080, china 2. Graduate School, Chinese Academy of Sciences, beijing 1.0080, china 1. institute of{1. thermophysics Chinese Academy of Sciences 100080 Beijing China 2. Graduate School Chinese Academy of Sciences 10080 Beijing China

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.

关键词： explicit analytical solution, porous medium, natural convection, Brinkman model, anisotropic.

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Algebraically explicit analytical solu-tions for the unsteady non-Newtonian swirling flow in an annular pipe

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Science china(Physics,Mechanics & Astronomy) 2006年第4期49卷 396-400页

作者： cai ruixian1.& gou chenhua1.2 1. institute of engineering thermophysics, Chinese Academy of Sciences,{1., china 2. Graduate School, Chinese Academy of Sciences,{1., china 1. institute of{1. thermophysics Chinese Academy of Sciences Beijing 100080 China 2. Graduate School Chinese Academy of Sciences Beijing 100080 China

This paper presents two algebraically explicit analytical solutions for the incompressible unsteady rotational flow of Oldroyd-B type in an annular pipe. The first solution is derived with the common method of separation of variables. The second one is deduced with the method of separation of variables with addition developed in recent years. The first analytical solution is of clear physical meaning and both of them are fairly simple and valuable for the newly developing computational fluid dynamics. They can be used as the benchmark solutions to verify the applicability of the existing numerical computational methods and to inspire new differencing schemes, grid generation ways, etc. Moreover, a steady solution for the generalized second grade rheologic fluid flow is also presented. The correctness of these solutions can be easily proven by substituting them into the original governing equation.

关键词： analytical solution, Oldroyd-B type fluid, swirling flow, non-Newtonian.

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Explicit analytical solutions fof transport equations considering non-Fourier and non-Fick effects in porous media

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Progress in Natural Science:Materials International 2005年第6期 545-549页

作者： gou {1. 1.2 , cai {1.1.* and ZHANG Na1.1. institute of engineering thermophysics, Chinese Academy of Sciences, beijing 1.0080, china 2. Graduate School, Chinese Academy of Sciences, beijing 1.0080, china)

Based on the method of separation variables with addition developed in recent years, new methods of separation variables are proposed, and two algebraically explicit analytical solutions to the general partial differential equation set of non-Fourier and non-Fick heat and mass transfer in porous media drying are derived. The physical meaning of these solutions is simple and clear, and they are valuable for computational heat and mass transfer as benchmark solutions.

关键词： non-Fourier effects non-Fick effects porous media heat and mass transfer analytical solution.

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