Magnetohydrodynamics Marangoni boundary-layer copper/water nanofluid flow driven by surface temperature gradient over a rotating disk

Abstract

Marangoni driving problem is very important in many practical science engineering, such as semiconductor industry, crystal growth, aerospace, material synthesis. Consider these applications, this work we investigate Marangoni boundary-layer Copper/Water nanofluid driven by the surface temperature gradient over a rotating disk in the presence of magnetic field. Buongiorno model of nanofluids, which contains two important terms, thermophoresis and Brownian motion, are taken into account. Rotating disk model is established, also a suitable Kármán transformation and the multi-shooting technique are applied. Graphical discussion include free stream concentration, rotating speed, magnetic field, Marangoni driving, thermophoresis, Brownian diffusion, Prandtl number, and Schmidt number. The results show that rotating speed inertia and Marangoni driving force tend to reduce temperature/concentration and thickness of thermal/mass boundary layer, while free stream concentration and magnetic field raise up. Meanwhile, Prandtl number tends to reduce temperature, while thermophoresis and Brownian diffusion raise up, and Schmidt number has little influence on temperature, and Schmidt number and Brownian diffusion tend to reduce concentration, while thermophoresis raises up, and Prandtl number has an important influence on concentration. For most selected values of physical parameters, as the nanofluid far away from the disk, the local temperature decreases directly, and the local concentration firstly increases to a peak and then decreases to zero.