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. / Graduation date: 1976
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/29372 |
| Date | 17 July 1975 |
| Creators | Eggers, Dwight Edward |
| Contributors | Bodvarsson, Gunnar |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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