About one boundary value problem for the equations of heat and mass transfer with normal derivatives of the third order in the boundary condition

Abstract

A boundary value problem is considered for the equations of heat and  mass transfer when one of the boundary conditions contains normal derivatives of the third order, to which a certain problem of heat and mass transfer in drying processes is reduced. The solution of the boundary value problem is sought in the form of the thermal potential of a double layer. A lemma on finding the limits of the third order normal derivatives is given. Using the boundary conditions, a system of the integro-differential equations (SIDE) with various heat conduction operators is obtained. A characteristic part of SIDE is solved by the method of integrated transformations of Fourier-Laplace when performing a condition of solvability. By the method of regularization of SIDE it is reduced to the system of the integrated equations of Volterra-Fredholm. A theorem of solvability of a boundary value problem is given under the condition of solvability of the heat and mass transfer equations with normal derivatives in the boundary conditions.