Unsteady magnetohydrodynamic flow of a fourth grade fluid caused by an impulsively moving plate in a Darcy porous medium: A group-theoretical analysis

The effects of non-Newtonian fluids are investigated by means of an appropriate model studying the flow of a fourth grade fluid. The geometry of this model is described by the unsteady unidirectional flow of an incompressible fluid over an infinite flat plate within a porous medium. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The classical Lie symmetry approach is utilized in order to construct group invariant solutions to the governing higher-order nonlinear partial differential equation (PDE). The conditional symmetry approach has also been utilized to solve the governing model. Some new classes of conditional symmetry solutions have been obtained for the model equation in the form of closed-form exponential functions. The invariant solution corresponding to the nontraveling wave type is considered to be the most significant solution for the fluid flow model under investigation since it directly incorporates the physical behavior of the flow model.