REVIEW
On the 275th Anniversary of the Russian Academy of Sciences

ANALYTICAL METHODS OF SOLUTION OF BOUNDARY-VALUE PROBLEMS
OF NONSTATIONARY HEAT CONDUCTION IN REGIONS WITH MOVING BOUNDARIES
E. M. Kartashov

UDC 536.2.001

Classical linear problems of nonstationary heat conduction 
(and of related phenomena) for canonical regions and standard boundary 
conditions can be solved using well-developed analytical methods yielding 
an exact solution of the problem [1-19]. For a bounded 
region, its analytical solution in the form of a Fourier series where 
conjugation conditions for the functions in the boundary conditions 
of the problem at angular points of the phase region of determination 
of the equation of nonstationary heat conduction are not fulfilled 
[17] makes it possible to improve the convergence to an absolute and 
uniform one up to the boundary of the region [20-22]. 
The improved solutions become very convenient in consideration of 
many practical issues of thermophysics: calculations of thermophysical 
constants based on solution of inverse problems; determination of 
the time of heating of a canonically shaped workpiece; calculation 
of the time in which the process reaches the stationary phase, etc. 
In these and other cases, it becomes possible to investigate the kinetics 
of the processes based on calculational analytical relations of a 
parametric character.

L. M. Lomonosov Moscow Institute of Fine Chemical Technology, 
Moscow, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 
74, No. 2, pp. 171-195, March-April, 2001. Original article submitted 
January 5, 2000; revision submitted August 4, 2000.

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