Abstract
It is shown that the steady problem of heat conduction theory for regions bounded by cochleas of order 4m + 2 (m=1, 2, 3, ..., N), which emit heat from their surfaces according to Newton's law, is reduced by conformai mapping to the solution of certain equations in finite differences. For the case m=1 the solution of the equations is expressed in terms of Bessel functions, and formulas for the temperature distribution are obtained.
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Vasil'ev, B.A. Solution of a plane steady heat conduction problem with boundary conditions of the third kind for regions of special type. Journal of Engineering Physics 10, 428–433 (1966). https://doi.org/10.1007/BF00831066
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DOI: https://doi.org/10.1007/BF00831066