Lie symmetry reductions and exact solutions for magnetohydrodynamic flow and heat transfer of third grade nanofluid with thermal radiation

Abstract

Nanofluids are fundamental building blocks of nanotechnology. The movement of heat due to nanofluid motion opened new stream of research by including the effect of nano-sized solid particles (nanoparticles) in the flow field. In this work, Lie symmetry method is adopted to present exact closed form solutions for unsteady, laminar, flow and heat transfer of electrically conducting, optically thick third grade nanofluid. Nanofluid occupies the space over a penetrable surface in a Darcy’s type porous medium. The flow is generated due to the arbitrary motion of bounding surface. Within optically thick nanofluid, effects of thermal radiation are also considered in the present mathematical analysis. Lie symmetry approach is utilized to find symmetries of modelled nonlinear partial differential equations. Obtained symmetries are then used for reduction of governing equations to linear ordinary differential equations. The reduced equations are then solved using compatibility and generalized group theoretic method to form exact closed form solutions for velocity and temperature profiles. Obtained solutions are also depicted graphically for Cu–water nanofluid for various governing parameters and present their effect on velocity and temperature characteristics of nanofluid.