We analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet with a heat source/sink, under the action of a uniform magnetic field, orientated normally to the plate. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of local similarity transformations. The differential equations are solved by the variational finite element method (FEM). We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, uniform magnetic field, viscoelastic parameter, Prandtl number, heat source/sink parameter, Lewis number, and the slip parameter on the flow field and heat transfer characteristics. Graphical display of the numerical examination is performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, and Nusselt and Sherwood numbers distributions. The present study has many applications in coating and suspensions, cooling of metallic plate, paper production, heat exchangers technology, and materials processing exploiting. 1. Introduction Due to enormous industrial, transportation, electronics, biomedical applications, such as in advanced nuclear systems, cylindrical heat pipes, automobiles, fuel cells, drug delivery, biological sensors, and hybrid-powered engines, the convective heat transfer in nanofluids has become a topic of great interest. Nanofluids are engineered by suspending nanoparticles with average sizes of 1–100？nm. Choi et al. [1] and Masuda et al. [2] have shown that a very small amount of nanoparticles (usually less than 5%), when dispersed uniformly and suspended stably in base fluids, can provide dramatic improvements in the thermal conductivity and in the heat transfer coefficient of the base fluid. The term nanofluids (nanoparticle fluid suspensions) was coined by Choi [3] in 1995 to describe this new class of nanotechnology-based heat transfer fluids that exhibit thermal properties superior to those of their base fluids or conventional particle fluid suspensions. The nanoparticles are typically made of oxides such as alumina, silica, titania and copper oxide, carbides, and metals such as copper and gold. Carbon nanotubes and diamond nanoparticles have also been used in nanofluids. The base fluid is usually a conventional heat transfer fluid, such as oil, water, and ethylene glycol.
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