Generalized stokes’ flow and radiative heat transfer model of a non-Newtonian fluid in a darcy porous medium subject to Navier’s slip conditions on the penetrable porous boundary: Group theoretical and compatibility analysis - Aziz, Taha (Applied mathematics and computation, 2021)
•We model unsteady flow of a third grade fluid filling the porous half space with suction/blowing.•The heat transfer analysis is also carried out under the influence of thermal radiation and internal heat source/sink.•We obtain all possible symmetries of the model equations using the classical Lie group approach.•The compatibility and generalized group approach is used.•A conditional symmetry approach is also employed.•We construct new class of group invariant solutions.•The graphs representing the solutions are plotted and discussed. In this work, the generalized Stokes’ model of a non-Newtonian fluid is discussed. The incompressible time-dependent flow and radiative heat transfer model of a non-Newtonian third grade fluid over a moving porous boundary is considered. The fluid flows into the porous region in the half space geometry. The flux disturbance caused by the impulsive movement of the porous boundary is studied. The energy equation is studied under the influence of internal heat source and thermal radiation. The flow and heat transfer model meets the Navier’s slip conditions at the boundary which allows the extremes of no-slipping at the penetrable surface. Lie symmetry analysis is carried out to calculate the complete Lie symmetry algebra associated with the modelled nonlinear partial differential equations. Symmetry operators are used to find self-similar transformations which help to perform reduction of the governing nonlinear partial differential equations to different classes of nonlinear ordinary differential equations. Reduced ordinary differential equations, as a result of the implication of symmetry reductions, are solved by employing the general compatibility approach. Furthermore, we have discussed the non-classical symmetry algebra, associated with the model, to classify all possible closed-form exact solutions of the flow model. The effect of various pertinent parameters on the flow and heat transfer model is studied in detail.