PROBLEMS OF HEAT CONDUCTION FOR AN
ANGULAR REGION WITH AN INTERNAL SOURCE

A. D. Chernyshov

UDC 536

Exact solutions of nonstationary problems of heat conduction 
have been obtained for an unbounded rectangular region when the opening 
angle is equal to  /(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 0 
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 0   / 2, while for the right or obtuse angles 
0   / 2 the stationary regime is impossible, 
since the temperature increases without bound at internal points.

Voronezh State Technological Academy, Voronezh, Russia. 
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 4, pp. 
150-155, July-August, 2003. Original article submitted January 
3, 2002; revision submitted November 27, 2002.