Group theoretical analysis for magnetohydrodynamic generalized Stokes’ flow and radiative heat transfer model of a non-Newtonian nanofluid with heat generation/absorption

Abstract

The fully developed boundary layer flow and heat transfer model of an unsteady, incompressible, electrically conducting, optically thick and thermodynamically compatible third-grade nanofluid are investigated from the viewpoint of Lie symmetry approach. We have studied the Stokes’ model in which flow is generated due to motion of the bounding surface with an impulsive time-dependent velocity. The mathematical model also includes the effect of thermal radiation and internal heat source or sink in the flow regime. Lie symmetry approach is employed to obtain the symmetry algebra of the governing nonlinear partial differential equations for both flow and heat transfer models. The governing nonlinear partial differential equations describing the flow and heat transfer model are reduced to different classes of nonlinear ordinary differential equations under the implication of symmetry generators. The reduced ordinary differential equations are investigated using the compatibility and generalized group theoretical method. The exact closed-form solutions for nanofluid motion and temperature distribution within the boundary layer are obtained. The effect of various thermophysical parameters on the characteristics of flow and heat transfer for Cu-water nanofluid model is explored from a physical point of view.