This paper presents analytical methods for investigating the processes of unsteady conjugate heat transfer complicated by the motion of the filtered sphere boundary. The investigations were carried out on the basis of formulation and solution of the following problems: conductive heating of an infinite rod connected to a variable heat flow on the combustion surface, which moves at a constant speed; convective heat transfer in a gasification channel connected to an increase in its length; filtration heat transfer of gas and coolant in an inhomogeneous medium with initial conditions on a moving boundary. Graphs of the acceptance dependences are presented.
