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Федеральный исследовательский центр 
«Красноярский научный центр
Сибирского отделения Российской академии наук»

Group analysis of variable coefficients heat and mass transfer equations with power nonlinearity of thermal diffusivity

2019 год

Stepanova, I. V.
Institute of Computational Modeling SB RAS, 50/44, Krasnoyarsk, Akademgorodok, Russian Federation
The paper presents symmetry analysis of three-dimensional equations of heat and mass transfer in a binary liquid. The system contains three unknown functions related to physical properties of liquid. Supposing thermal diffusivity to be depended on temperature with respect to power law, diffusion and thermal diffusion coefficients are found using of classical Lie symmetry approach. It is shown that the solution of the group classification problem consists of two parts. We obtain different results if we take into account that diffusion coefficient either has the same form as the thermal diffusivity coefficient or it depends on temperature and concentration essentially. Some reductions of the governing equations are constructed with the help of the obtained transformations of dependent and independent variables. New exact solutions of the reduced equations have been found in several cases. © 2018 Elsevier Inc.