Extract Optimized Solutions of q-Homotopy Analysis Method for Magneto-Hydrodynamic Nano-Fluid Flow in a Porous Medium

In this research, the magneto-hydrodynamic (MHD) flow of nano-fluids in a porous medium (PM) between two parallel plates was studied by q-homotopy analysis method (q-HAM). Similarity transformations are applied to convert the resulting system of partial differential equations into ordinary nonlinear differential equations. By forming a relationship between q-HAM with two transforms the Laplace transform (LT) and the EL-Zaki transform (ZT) in the presence of the convolution theory, the outcomes from the proposed method were improved. The resulting solutions from this problem were compared with numerical solutions from the Bvp4c method with the same values of physical parameters, which were shown to be highly accurate. The resulting solutions are represented in tables and graphs for the purpose of fully illustrating and explaining the flow behaviour under varying physical parameters such as pressure number, Casson fluid parameter and magnetic number.