Heat conduction in eccentric annuli Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8c97kt64c

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  • Muitiregion annular geometry is a basic feature of energy removal systems ranging from advanced heat exchangers to fission reactor fuel rods. For the symmetric cases, the heat conduction through annular regions is well defined. However, for a shift of an annular region, analysis of the system must be made in two dimensions. The purpose of this study is to characterize the steady state heat conduction through eccentric annuli through a theoretical, numerical, and experimental investigation. In the theoretical study, the analytical solutions are sought for the governing heat conduction equations. Separate polar coordinate systems are used to describe the points in the inner tube, the annular region, and the outer tube. Particular attention is given to the interface conditions by explicitly retaining continuity of the components of the heat flux vector. Within the context of the specified assumptions, the resulting solutions are general, valid for any size annular regions and any degree of eccentricity. The boundary condition on the outer tube surface can be specified by either a prescribed temperature function of angle or a convective boundary condition. A computer program is developed to perform the calculations of the two-dimensional temperature profiles within the eccentric system. This program can be verified mathematically for the concentric condition. The experimental study is designed to verify the program for eccentric situations. The experiment is a straightforward determination of the two-dimensional temperature field within the eccentric annuli. An electrical heater rod is used in the experiment. A PVC pipe is chosen as the outer tube. For the intermediate annular region, standard hard lead shot is utilized. The thermal conductivity of the packed bed of lead shot is relatively insensitive over the temperature range of interest, and the thermal conductivity of the PVC pipe is constant over the temperature range used. The study of the results between the analytical solutions and the measurements indicate that the temperature profiles within the system can be accurately predicted if an appropriate boundary condition is used. In addition to the theoretical and experimental phases, numerical aspects of the problem are also studied. Four general approaches have been used to treat the problem. The first is to approximate the heater rod surface by a ratchet. This results in an increase in the number of radial node regions required and a subsequent loss of economy. The second approach utilizes concentric regions and defines a variable conductivity within the annulus region to account for the eccentric condition. This reduces the number of radial node regions and results in saving in both computation time and core space. To eliminate the common limitation in both approaches that the eccentric displacement must be smaller than the radius of heater rod, a third approach is developed. This approach utilizes a two-dimensional, cylindrical model in which the origin of the coordinate system is located at the center of the heater rod. However, if an existing general purpose finite difference code is used, an additional effort is required to translate the temperature profiles to a new coordinate system with the origin located at the center of outer tube. An existing finite element computer code is utilized as the fourth numerical approach. A relatively coarser grid system can be used in this code and less computer running time is required.
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