Boundary conditions in the calculation of transient heat- and mass-transfer processes

It is shown that error estimation by order of approximation alone is not sufficient for the difference analogs of boundary conditions. It is necessary to consider the degree of correspondence of the difference schemes to the physical substance of the processes described by them. Difference analogs are proposed for the Neumann and Cauchy boundary conditions, yielding an error of approximation lower than that in the common schemes of Schmidt and Dusinberg. To obtain improved accuracy difference analogs of the boundary conditions in combined heat- and mass-transfer calculations, it is necessary to express the derivatives in the same form as in the proposed schemes. Results are given from a comparative calculation of the heat transfer in semi-infinite body according to one of the proposed schemes, a Schmidt scheme, a Dusinberg scheme, and a rigorous analytical solution.