Analytical and numerical continuation methods for conductive temperature fields Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/7d278w930

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  • The continuation of conductive temperature fields is being considered. The continuation of a field involves the extrapolation of a field known over a limited domain to an adjacent domain in such a way that it satisfies the heat conduction differential equation and other imposed constraints. Continuations forward in time and toward the interior of the space from the constraining initial and boundary conditions are expressed analytically as convolution integrals. Solutions are approximated using linear filter methods in real and transform spaces. The inverse problems of continuation toward the constraining conditions are expressed in real space as power series of derivatives. Solutions are approximated as convolution filtering operations. Variational methods are also used to solve problems which do not yield to convolution filtering operations. The suitability of these approximation methods is shown in two ways: (1) the frequency response of the derived convolution coefficients are compared with the analytic transfer functions; and (2) the methods are applied to artificial test cases. These field continuation methods provide a tool for the interpretation of observational temperature data. Several examples of field data are treated using these techniques; (1) A case of the temperature inversion observed in a geothermal borehole is explained by a transient flow of thermal water along a narrow horizontal fracture; (2) Soil temperature data are treated to determine the in situ thermal diffusivity and show that departures from conductive conditions are accounted for by evaporative effects; (3) Shallow borehole temperature data which exhibit the nonstationary effects of the annual cycle are shown to be influenced by convective effects in the soil.
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