Group theoretical analysis for unsteady magnetohydrodynamics flow and radiative heat transfer of power-law nanofluid subject to Navier’s slip conditions

The present work covers the flow and heat transfer model for the Power-law nanofluid in the presence of a porous medium over a penetrable plate. The flow is caused by the impulsive movement of the plate embedded in Darcy’s porous medium. The flow and heat transfer models are examined with the effect of linear thermal radiation in the flow regime. The Rosseland approximation is utilized for the optically thick nanofluid. The governing partial differential equations are solved using Lie symmetry analysis to find the reductions and invariants for the closed-form solutions. These invariants are then utilized to obtain the exact solutions for the shear-thinning, Newtonian, and shear-thickening nanofluids. In the end, all solutions are plotted for the Cu-water nanofluid to observe the effect of different emerging flow and heat transfer parameters.