Linear Heat- and Mass-Transfer Problems: General Formulas and Results

One-, two-, and three-dimensional linear unsteady-state inhomogeneous boundary-value heat- and mass-transfer problems with arbitrary dependences of the equation coefficients on time and on the spatial coordinates are considered. General formulas are obtained that enable one to express the solutions of these problems in terms of the Green function under boundary conditions of all the main types. Integral relations (of the Duhamel integral type) are presented, which allow one to construct the solutions of complex problems on the basis of the solutions of simpler problems. The results obtained can be used in the study of heat and mass transfer in motionless and moving media in the isotropic and anisotropic cases (when bulk and surface chemical reactions occur).