Group classification for equations of thermodiffusion in binary mixture

Group classification problem is solved for equations of motion of a binary mixture under the buoyancy force and thermodiffusion effect. These equations are parameterized by five arbitrary functions of two arguments. The admissible Lie symmetry algebras of generators are found depending on arbitrary elements. These results are useful for analytical and numerical modeling of the convection in binary mixtures.

► Group classification for physical parameters in the thermodiffusion equations is performed.
► The Lie symmetries for every form of arbitrary elements are found.
► The equivalence group admitted by the governing equations is calculated.
► The results are useful for modeling of convection in binary systems.