Abstract

The steady local temperature distribution has been determined for arbitrary prolate spheroidal systems with various boundary conditions. The temperature was derived for all possible systems, such as when the temperature was kept constant on the hyperbolic surfaces and variable on the prolate spheroidal surfaces, and vice versa. In'the latter case, roots with respect to the degree of the associated Legendre function for arguments larger than unity had to be determined. Some of the presented solutions have been evaluated numerically, and the isothermal surfaces have been presented.

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