Lie symmetry analysis of thermodiffusion equations

Abstract:
The differential equations describing convection in binary mixture with the Soret effect are considered. We assume that the mixture density is an arbitrary function of temperature T and concentration C. The transformation, which reduces the diffusion equation to a homogeneous one, is employed. The group classification of equations with respect to the function of density is performed. Different specializations of this function and the corresponding generators admitted by the governing equations are found. The equivalence group of the system is calculated. Using this group, the representation of density function can be simplified.