Preliminary group classification for the flow of a thermodependent fluid in porous medium

In this work, we perform preliminary group classification of equations governing the flow of a thermo-dependent fluid in a porous medium. The detailed model is a coupled system of nonlinear partial differential equations containing two arbitrary functions. The principal Lie algebra admitted by the coupled system is given. The study also demonstrates that the forms of arbitrary functions provide an extension of this algebra via an optimal system of one-dimensional Lie subalgebras.