Symmetry analysis of nonlinear heat and mass transfer equations under Soret effect

Three-dimensional equations describing heat and mass transfer in fluid mixtures with variable transport coefficients are studied. Using Lie group theory the forms of unknown thermal diffusivity, diffusion and thermal diffusion coefficients are found. The symmetries of the governing equations are calculated. It is shown that cases of Lie symmetry extension arise when arbitrary elements have the power-law, logarithmic and exponential dependencies on temperature and concentration. An exact solution is constructed for the case of linear dependence of diffusion and thermodiffusion coefficients on temperature. The solution demonstrates differences in concentration distribution in comparison with the same distribution under constant transport coefficients in the governing equations.