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A new analytical solution is obtained for the first initial-boundary problem of heat transfer in an anisotropic plate with general anisotropy (non-zero off-diagonal components of thermal conductivity tensor) and given heat sources distributed over space and time. The tensorial character of heat transfer results in presence of mixed derivatives in the differential equation of thermal conductivity. The solution is obtained by constructing a source function and further use of the basic integral Green’s function. Convergence of the functional series of improper integrals is investigated. We analyze numerical results on the effect of principal components and orientation angles of principal axes of thermal conductivity tensor on nonstationary temperature fields. AMS Subject Classification: 80A20, 74E10, 74F05

ОN NON-STATIONARY HEAT TRANSFER IN ANISOTROPIC BODIES WITH GENERAL ANISOTROPY AND GIVEN DISTRIBUTED HEAT SOURCES