BOUNDARY VALUE PROBLEMS FOR WEDGES AND CONES UNDER HEAT CONDUCTION.
NORTH CAROLINA STATE UNIV RALEIGH APPLIED MATHEMATICS RESEARCH GROUP
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Mellin integral transforms and the Wiener-Hopf technique are used to obtain the temperature distribution in a semi-infinite wedge in which the temperature is specified on the boundary near the vertex and the remaining portion of the boundary is assumed to be insulated. Results are obtained in terms of infinite integrals. Several boundary value problems are considered for the semi-infinite cone. First, the temperature distribution is obtained for the problem where a constant temperature is specified for the portion of the surface of the cone near the vertex and the remaining surface is at zero temperature. Next, the problem is considered where a temperature, dependent only upon the radial distance r, is specified on the boundary. This latter problem was for the half space or cone of angle pi2 and was solved using the Legendre transform of odd order. Finally, the mixed boundary value problem for the cone, analogous to that of the wedge above, is considered with the method of solution including the Mellin integral transform and the Wiener-Hopf technique. The results for the cone of general angle, 0 alpha pi, is in the form of an inversion integral. The temperature distribution is obtained as a residue series for the special case of alpha pi2. Author