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

• Group classification for three-dimensional heat and mass transfer equations with variable physical parameters is performed.
• The Lie symmetries for every form of arbitrary elements are found.
• The exact solution for a simple configuration is constructed.
• The results are useful for modeling of heat and mass transfer processes in liquid binary systems.

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.