On the computation of analytical solutions of an unsteady magnetohydrodynamics flow of a third grade fluid with Hall effects

In this article, a combination of Lie symmetry and homotopy analysis methods (HAM) are used to obtain solutions for the unsteady magnetohydrodynamics flow of an incompressible, electrically conducting third grade fluid, bounded by an infinite porous plate in the presence of Hall current. In particular, similarity reductions are performed on the governing equations in its complex scalar and corresponding vector system forms. Also, nontrivial conservation laws, using the multiplier approach, are constructed for the complex scalar equation. Furthermore, a comparison of the results with numerical results already existing in the literature is done. The analytical solutions are presented through graphs by choosing a range of the relevant physical parameters. The underlying calculations were obtained via a combination of software packages in Mathematica and Maple, in particular, for the Lie symmetry generators, Euler Lagrange operators and homotopy operators; the latter being towards the construction of the conserved flows.