Problems of Heat Conduction for an Angular Region with an Internal Source

Abstract

Exact solutions of nonstationary problems of heat conduction have been obtained for an unbounded rectangular region when the opening angle is equal to π/(2n + 1), where n is any natural number. By passage to the limit it has been shown that no stationary regime is possible for the rectangular region in the case of action of a constant internal source. The exact solution of the stationary problem for an angular region with an arbitrary opening angle κ₀ has been given. It has been proved that in the presence of a constant heat source the stationary regime is possible just for the acute angle κ₀ ≤ π/2, while for the right or obtuse angles κ₀ ≥ π/2 the stationary regime is impossible, since the temperature increases without bound at internal points.