The paper presents the investigation of gas transfer in cylindrical channels in the presence of heterogeneous physicochemical conversions (filler evaporation in a channel, evaporation on the internal surface of a channel, catalytic reaction of the first order). With the use of the model kinetic equations for the gas molecule velocity distribution function, the solutions of the above problems have been obtained, suitable for the arbitrary ratios of free molecule path length to capillary radius, i.e. the Knudsen number. The comparison between the theoretical and experimental results on filler surface recession in a capillary during evaporation in the presence of a foreign gas is carried out. The applicability limits for the well-known phenomenological relations, used in the theory of drying, are established.