Classical symmetries for two special cases of unsteady flow in nanoporous rock

Abstract

In the present paper, we study two equations related to the theory of fluid and gas flow in nanoporous media. Both models are special cases of the basic equation of the unsteady flow in nanoporous rock, the first one is the case of weakly compressible fluid and the second one of the case of isothermic gas flow. Moreover, a generalization of the equations is presented to study thoroughly the physical phenomena. This new generalized equations involve arbitrary functions. Lie method is applied to the model of generalized unsteady flow and the model of generalized isothermic gas flow. Finally a classification in different cases depending on the arbitrary function is shown.