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. / Graduation date: 1979
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/29492 |
| Date | 26 April 1979 |
| Creators | Shyu, Chuen Tien |
| Contributors | Bodvarsson, Gunnar |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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