Abstract
The mathematical theory of integral transformations has been developed for finding analytical solutions of the generalized nonstationary heat conduction equation for a limited canonical-type region (infinite plate, solid cylinder, sphere) simultaneously in the Cartesian, cylindrical, and spherical coordinate systems. Improved solutions in the form of Fourier–Hankel′s series are suggested that absolutely and uniformly converge up to the boundary of the region and represent fundamentally new constructions of the analytical theory of thermal conductivity of solid bodies very convenient for conducting numerical experiments in the practical thermal physics. The Green′s function method has been developed: an integral relation is suggested for writing analytical solutions of boundary-value problems for the generalized equation of nonstationary heat conduction in terms of inhomogeneities in the equation and boundary-value conditions in the initial formulation of the problem, and the corresponding Green′s functions are presented.
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