Physically substantiated boundary conditions for problems of heat transfer in infiltrated granular beds based on the two-temperature model which allow for the absence of interphase heat transfer on boundaries are formulated. It is shown that classical Dankwerts conditions would be applicable for gas. The problem of porous cooling at the boundary conditions of the 2nd and 3rd kind on the outer boundary is solved in a new formulation. (c) 2005 Elsevier Ltd. All rights reserved.