Numerical analysis of critical field functions for thermal convection in vertical or quasi-vertical Darcy flow slabs Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8c97ks980

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  • The numerical analysis of thermal convection in porous media, heated from below, and assuming Darcy flow conditions, involves the solving of a set of non-linear equations for the temperature and flow fields. The condition of criticality determining the onset of convection is obtained by linearization and the solving of an eigenvalue problem of the fourth order. The smallest eigenvalue represents the critical Rayleigh number. The shape of the critical temperature and flow fields is then obtained from the linear set. In most practical cases, the problem setting is such that closed analytical solutions cannot be derived. The difficulties of solving the convection equations can be overcome by using the Galerkin finite-element method. The method allows the solution of both the linear set and also the more complete non-linear set of equations at various boundary conditions and taking variations in the material parameters into account. In this thesis, the Galerkin method is used to solve the convection equations for infinitely long porous vertical or semi-vertical slabs with prescribed temperatures at the top and bottom surfaces. The first set of models investigated involve boundary walls that are impermeable to the fluid but perfectly conducting to heat. The critical Rayleigh numbers and critical temperature and flow fields are obtained for such slabs with various aspect ratios. The results show that the critical number is raised by 200 to 400% as compared with published data for similar slabs with thermally non-conducting walls. The results are generalized by investigating cases of slabs with (1) three types of vertically varying permeability, (2) by taking the temperature dependence of the fluid properties into account, (3) by including non-linear terms, and finally, (4) a few cases of slabs with boundary walls of finite thermal conductivity are investigated. The results are applicable to a number of situations in geothermal areas. A brief discussion of two such cases is given, that is, (1) the estimating of the critical permeability profile for the East geothermal field in the Imperial Valley and (2) the computation of a temperature cross section in the Cumali geothermal field in Turkey.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2012-06-01T15:59:44Z (GMT) No. of bitstreams: 1 ShyuChuenTien1979.pdf: 1869321 bytes, checksum: 33f00de48fde5706b4d395d0a86ed360 (MD5)
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2012-06-01T15:54:05Z (GMT) No. of bitstreams: 1 ShyuChuenTien1979.pdf: 1869321 bytes, checksum: 33f00de48fde5706b4d395d0a86ed360 (MD5)

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