analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field

in this paper, we examine the convective flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of a magnetic field. the governing partial differential equations with the auxiliary conditions are reduced to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. the analytical solutions of the resulting odes are obtained, and from which the analytical solutions of the original problem are presented. the influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, nusselt number and skin friction coefficient is discussed. comparison with published results is presented.