Exact and numerical solutions of MHD nano boundary-layer flows over stretching surfaces in a porous medium

Two dimensional and axisymmetric flows over stretching surfaces in a porous medium in the presence of a magnetic field with second order slip condition are investigated. Using suitable similarity transformations, the governing partial differential equations are reduced to non-linear ordinary differential equations. The resulting system is solved analytically in the case of 2D, and numerically, in the axisymmteric case, by the Chebyshev pseudospectral differentiation matrix (ChPDM) technique. It is found that the second order slip has a considerable effect in reducing the physical property along the stretching sheet for increasing values of the magnetic parameter and for decreasing values of the porosity parameter. In addition, the presence of the magnetic and permeability parameters, and the first and second order slip parameters lead to a decrease in the nano boundary-layer thickness. Furthermore, for fluid flows at nano scales, the shear stress at the wall decrease (in an absolute sense) with an increase in the first and second order slip parameters, the magnetic parameter, and the permeability parameters. For the special cases, comparisons with previously published results are also made, and the results are found to be in very good agreements. (C) 2014 Elsevier Inc. All rights reserved.