Convective heat transfer during the flow of Williamson nanofluid with thermal radiation and magnetic effects

Recently, several studies have been presented to show that nanofluids are amongst the best tools for the enhancement of heat transfer characteristics. It has been experimentally verified that nanofluids are a new type of enhanced working fluids, engineered with enhanced thermo-physical properties. Therefore, we present a novel study to develop and understand a mathematical model for a non-Newtonian Williamson fluid flow in the presence of nanoparticles. This study aims at describing the thermal characteristics of nanoparticles via Rosseland approximation to illustrate the non-linear radiation effects. Convective heat transfer model alongside Brownian motion are studied for the electrically conducting nanofluids flow. A set of partial differential equations for Williamson nanofluid flow has been derived by basic conservation laws, i.e., momentum, energy and concentration conservations. These equations are initially converted to ordinary differential equations by employing non-dimensional quantities. The numerical simulation of these equations is performed using the Runge-Kutta-Fehlberg scheme. The corresponding important physical parameters have been produced as function of the unsteadiness parameter, Weissenberg number, magnetic parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, Biot number, velocity slip parameter and Lewis number. The examination is done to investigate the impact of the above-said parameters on momentum, thermal and concentration boundary layers. It is concluded from our computations that the nanofluids velocity and temperature accelerate when the Brownian motion parameter rises. Results proved that temperature gradient enhances with increase of solid particle concentration, while it decreases with increasing magnetic field. Finally, a comparison of the obtained numerical solution against previous literature is presented which shows satisfactory agreement.