Magnetic field effect on second order slip flow of nanofluid over a stretching/shrinking sheet with thermal radiation effect

The magnetic field effect on a steady two dimensional laminar radiative flow of an incompressible viscous water based nanofluid over a stretching/shrinking sheet with second order slip boundary condition is investigated both analytically and numerically. The governing partial differential equations are reduced to nonlinear ordinary differential equations by means of Lie symmetry group transformations. The dimensionless governing equations for this investigation are solved analytically using hyper-geometric Function and numerically by the fourth order Runge-Kutta method with the shooting technique. A unique exact solution exists for momentum equation in stretching sheet case and dual solutions are obtained for shrinking sheet case which has upper and lower branches. It is found that the lower branch solution vanishes in the presence of higher magnetic field. The velocity and temperature profiles, the local skin friction coefficient and the reduced Nusselt number are examined and discussed for different spherical nanoparticles such as Au, Ag, Cu, Al, Al2O3 and TiO2. A comparative study between the previously published results and the present analytical and numerical results for a special case is found to be in good agreement. (C) 2015 Elsevier B.V. All rights reserved.