The extraction of heat from a bulk medium through a thin, highly-conducting disc
Abstract
The steady conduction of heat is examined as it flows from an infinite medium into a slender highly-conducting disk and then into a line sink at the disk center. The temperature distribution is affected by the ratio of thermal conductivities in the bulk medium and disk, and by the shape of the disk. An analytical solution is obtained for the first perturbation approximation to the temperature when both the ratio of thermal conductivities in bulk medium and disk, and the ratio of disk thickness-to-diameter are small parameters of similar magnitude. The disk shape is arbitrary within the general constraints of the perturbation scheme. Singular perturbation solutions are required at the disk center and rim. An example application of the results is included.
- Publication:
-
International Journal of Engineering Science
- Pub Date:
- 1976
- Bibcode:
- 1976IJES...14..869W
- Keywords:
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- Boundary Value Problems;
- Conductive Heat Transfer;
- Disks (Shapes);
- Perturbation Theory;
- Temperature Distribution;
- Asymptotic Methods;
- Differential Equations;
- Heat Flux;
- Fluid Mechanics and Heat Transfer