Lie Symmetry Analysis of Heat and Mass Transfer Equations with Cross-Diffusion Effects

We study the symmetry properties of heat and mass transfer equations. The group classification problem is solved with respect to two transport coefficients (diffusion and heat diffusivity) and two coefficients corresponding to the effects of thermal diffusion (Soret effect) and diffusion thermal conductivity (Dufour effect). These four parameters depend on temperature and concentration. In some cases, we determine all admissible forms of the classified functions. In the most complicated cases, we obtain relationships between the classified parameters and the corresponding admitted generators.