A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger. 1. Introduction The term “nanofluid” was proposed by Choi [1], referring to dispersions of nanoparticles in the base fluids such as water, ethylene glycol, and propylene glycol. The thermal conductivity enhancement characteristic of nanofluid was observed by Masuda et al. [2]. Buongiorno [3] discussed the reasons behind the enhancement in heat transfer for nanofluid and he found that Brownian diffusion and thermophoresis are the main causes. Later, Nield and Kuznetsov [4] and Kuznetsov and Nield [5] investigated the natural convective boundary layer flow of a nanofluid employing Buongiorno model. The study of boundary layer flow and heat transfer due to stretching surface has numerous applications in industry and technology, such as in polymer extrusion, drawing of copper wires, artificial fibers, paper production, hot rolling, wire drawing, glass fiber, metal extrusion and metal spinning, and continuous stretching of plastic films. Crane [6] first studied the boundary layer flow due to linearly stretching sheet. Many researchers [7–17] extended the work of Crane, whereas Magyari and Keller [18] considered the boundary layer flow and heat transfer due to an exponentially stretching sheet. The flow and heat transfer over an exponentially stretching surface were investigated by Elbashbeshy [19] taking wall mass suction. Khan and Sanjayanand [20] presented the boundary layer flow of viscoelastic fluid and heat transfer over an exponentially stretching sheet with viscous
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