Scaling group transformation for MHD boundary-layer flow of a nanofluid past a vertical stretching surface in the presence of suction/injection

The problem of laminar fluid flow which results from the stretching of a vertical surface with variable stream conditions in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of magnetic field. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz, scaling group of transformations. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. This solution depends on a Lewis number, magnetic field, Brownian motion parameter and thermophoretic parameter. The conclusion is drawn that the flow field and temperature and nanoparticle volume fraction profiles are significantly influenced by these parameters. (C) 2011 Elsevier B.V. All rights reserved.