Mathematical Model of Interrelated Heat and Mass Transfer with Account for the Two-Phase Lag

A system of differential equations of interrelated heat and mass transfer under the conditions of nonlocal equilibrium has been obtained that accounts for the velocities and accelerations of driving forces (of the gradients of corresponding values and of heat and mass fluxes caused by them) in the course of the joint occurrence of nonisothermal diffusion and heat conduction. The system of equations includes second order derivatives with respect to time and mixed derivatives in the product with corresponding relaxation coefficients of interacting flows and of their driving forces (double lag). An analysis of the numerical solution of the resulting system has shown that the boundary values for the temperature and concentration cannot be adopted instantly, since the process of determining them takes some time, during which they increase from zero to the values assigned by the boundary conditions of the boundary-value problem. From comparison of the solutions with and without account for double lag, it follows that their maximum difference is observed over the initial segment of time, in the course of which the establishment of boundary conditions and concentrations occurs. Consequently, the solutions of the classical equations of interrelated heat and mass transfer obtained without taking into account relaxation phenomena within the range of the time of establishment of boundary conditions cannot be used because of the inadequate description by them of the real physical processes.