mhd boundary layer flow of a nanofluid over an exponentially permeable stretching sheet with radiation and heat source/sink

the problem of steady magnetohydrodynamic boundary layer flow of an electrically conducting nanofluid due to an exponentially permeable stretching sheet with heat source/sink in presence of thermal radiation is numerically investigated. the effect of transverse brownian motion and thermophoresis on heat transfer and nano particle volume fraction considered. the governing partial differential equations of mass, momentum, energy and nanoparticle volume fraction equations are reduced to ordinary differential equations by using suitable similarity transformation. these equations are solved numerically using an implicit finite difference scheme, for some values of flow parameters such as magnetic parameter (m), wall mass transfer parameter(s), prandtl number(pr), lewis number (le), thermophoresis parameter (nt), brownian motion parameter(nb), radiation parameter (r). the numerical values presented graphically and analized for velocity, temperature and nanoparticle volume fraction.