Other
Scientific paper
Nov 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980mnras.193..345m&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 193, Nov. 1980, p. 345-351. Research supported by the Shirley Farr Fund
Other
3
Flow Equations, Flow Geometry, Heat Transfer, Sunspots, Anisotropy, Free Convection, Radiative Heat Transfer, Surface Temperature, Thermal Conductivity, Thermal Diffusion
Scientific paper
The geometry of sunspots has been used to suggest a problem in heat flow. The equation of heat transport is solved for the case of a cylinder with a given thermal conductivity imbedded in an otherwise uniform medium with different conductivity. The surface of this region radiates heat with flux proportional to temperature. At a lower surface, either in heat flux or temperature is held constant. The cylinder can have an anisotropic thermal conductivity. The variations in temperature along the radiating surface have been determined. A simple approximation is noted which has been found to give a general solution with acceptable accuracy. This method may be of some use in other situations requiring the solution of Laplace's equation with a free surface. The analysis is used to set limits on the ratio of diameter to depth for cases which preserve the sharp surface temperature transition across the cylinder.
Knobloch Eberhard
Margolis Steven H.
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