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

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An evaluation of methods for predicting turbulent heat transfer in rough pipes has been made with the intention of obtaining a better understanding of the transfer processes involved and of providing a general design equation, valid for all types of roughness shapes and distributions. The equations of Martinelli, Nunner, and Mattioli, along with an empirical method suggested by Epstein, have been tested using the available experimental data. In addition, particular attention has been given to a proposed method which makes use of the velocity profile equations of Rouse and von Karman in Lyon's fundamental equation for the Nusselt number. The results indicate that the proposed method is not successful, largely because of ignorance of velocity conditions near the walls of rough pipes. Mattioli's equation also does not give a satisfactory correlation of experimental results. Epstein's empirical method, which, in the pertinent dimensionless groups, uses friction velocity and equivalent sand-roughness height of the roughness elements in place of the average fluid velocity and the pipe diameter, respectively, shows promise but requires further investigation. Nunner's equation and Martinelli's (simplified) equation give good prediction of the experimental results and are recommended for use at present, providing 0.5 < Pr < 1.0. The success of these latter equations gives support to the hypothesis that the fluid adjacent to a rough wall is probably in laminar motion. Using Nunner's model of the flow conditions in rough pipes, equations have been derived for predicting temperature profiles from velocity profile data. Generally, the absolute agreement between predicted profiles and Nunner’s experimental profiles is good, but the influences of Re and especially f are not too well accounted for. Nunner's conclusion that temperature and velocity profiles in rough pipes are not similar is substantiated by the results. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

LD2668 .T4 1940 H34 / Master of Science

published_or_final_version / Physics / Master / Master of Philosophy

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