For various canonical forms (plane, cylinder, ball, etc.), a generalized mathematical model (MM) of a nonlinear steady-state process of molecular heat transfer (or moisture diffusion) through enclosing structures (ES) is proposed, taking into account infiltration or exfiltration of a vapor-air (gas) mixture and the presence of various internal or surface positive (moisture condensation) or negative (evaporation of moisture) of heat sources (HS). The mathematical formalization of the posed boundary value problem (BVP) of transfer and its general solution are given, on the basis of which, under various specified conditions of unambiguity, solutions of specific physical processes with constant or variable thermophysical characteristics and HS are constructed and analyzed. For large-scale transitions, the short-circuit problem is posed and solved under various boundary conditions (BVC), written in a criterion form as dependences of the dimensionless temperature T(R-, Pe, Po) on the dimensionless thermal resistance (R-) of the heat exchange criteria for the similarity of Pecle (Pe) and Pomerantsev (Po).
