Non-linear time-dependent flow models of third grade fluids: A conditional symmetry approach

In this communication some non-linear flow problems dealing with the unsteady flow of a third grade fluid in porous half-space are analyzed. A new class of closed-form conditionally invariant solutions for these flow models are constructed by using the conditional or non-classical symmetry approach. All possible non-classical symmetries of the model equations are obtained and various new classically invariant solutions have been constructed. The solutions are valid for a half-space and also satisfy the physically relevant initial and the boundary conditions.