Thermophoresis and Brownian motion effects on MHD boundary-layer flow of a nanofluid in the presence of thermal stratification due to solar radiation

The problem of laminar fluid flow which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar radiation has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis with thermal stratification 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, thermal stratification 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.