Effects of magnetic field and thermal radiation on stagnation flow and heat transfer of nanofluid over a shrinking surface

In this paper, the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow and heat transfer, with thermal radiation, of a nanofluid past a shrinking sheet is investigated numerically. Both the effects of Brownian motion and thermophoresis are considered simultaneously. A similarity transformation is used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations which are solved numerically using a shooting technique. A similarity solution is presented which depends on the magnetic parameter (M), radiation parameter (R), Brownian motion number (Nb), thermophoresis number (Nt), Prandtl number (Pr), Lewis number (Le) and the ratio of the rate constants of the shrinking velocity to the free stream velocity (α). Interesting solution behavior is observed with multiple solution branches for certain parameter domain. The results of the present paper show that the velocity, temperature, the wall shear stress, the Nusselt number and the Sherwood number are strongly influenced by the magnetic parameter. A comparative study between the previously published results and the present results for a special case is found to be in good agreement.