SOLUTION OF STATIONARY HEAT-CONDUCTION PROBLEMS FOR CURVILINEAR REGIONS
USING EIGENFUNCTION EXPANSIONS(FUNDAMENTAL SOLUTIONS)

A. D. Chernyshov

UDC 536;539;517.946

Formulas for solution of stationary problems of heat conduction 
in bodies of a curvilinear shape have been obtained in explicit form 
using eigenfunction expansions; an analogous solution has been constructed 
for temperature fluctuations. An algorithm of computation of the boundary 
functions for classical regions has been proposed; these functions 
make it possible to reduce the boundary conditions of the problem 
to a homogeneous form. The exact fundamental solutions in the region 
of a rectangle with arbitrary smooth boundary conditions of the 1st 
kind have been constructed using them. These solutions are fundamental, 
since they can be used when boundary-value problems and inverse problems 
with unknown boundary conditions are considered for a wide range of 
curvilinear regions.

Keywords: heat-conduction equation, curvilinear regions, 
eigenfunctions, exact solutions. 

Voronezh State Technological Academy, 19 Revolyutsiya 
Ave., Voronezh, 394000, Russia; email: chernyshovad@mail.ru. Translated 
from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 163-169, 
January-February, 2009. Original article submitted August 30, 
2007; revision submitted March 27, 2008.