Analytical solutions to models of local nonequilibrium heat transfer

A series of boundary-value problems of local nonequilibrium heat transfer is considered in terms of the theory of transient heat conduction for hyperbolic-type equations (wave equations). The mathematical models for the generalized equation are studied simultaneously in Cartesian, cylindrical (radial heat flux), and spherical (central symmetry) coordinate systems. The technique to determine analytical solutions to a broad class of practically important problems of transient heat conduction for canonical bodies (plate, solid cylinder, and solid sphere) and for partially bounded bodies (half-space bounded by a flat surface and spaces with an internal cylindrical cavity and an internal spherical cavity) is developed. The obtained, exact analytical solutions to a series of model problems can be considered as radically new results of analytical thermal physics.