Quasiclassical approximation of solutions of boundary convective-type problems of heat and mass transfer

The development of theoretical methods of analysis of heat and mass transfer processes requires involvement of mathematical physics apparatus first of all. And here there are some problems. In first, heat and mass transfer processes are described by very difficult differential equations. In second, practical difficulties are appeared with definition of parameters and calculation of turbulent heat and mass transfer. In this paper we suggest the approximate method of solving the internal convective heat and mass transfer problems based on the combined use of the Laplace transform and quasiclassical approximation. As an example of the method implementation, the boundary value turbulent heat and mass transfer problem under Dirichlet boundary condition for the motion of medium in a cylindrical channel is considered. The results of numerical analysis of the obtained solutions in smooth and rough channels are presented. The examples of determining the eigenvalues, eigenfunctions and solution constants are given.