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The article calculates the temperature field in an elliptical body with internal heat dissipation. In this case, the boundary conditions are boundary conditions of the third kind. The solution is located at the transition to the elliptic coordinate system. The author has obtained an analytical solution for the distribution of the temperature field in a body with an elliptical cross-section of infinite length with zero ambient temperature with partial adiabatic isolation in the form of a functional series using hypergeometric functions.

Temperature distribution in an elliptical body with an internal heat source with partial adiabatic isolation