Heat and mass transport phenomena of nanoparticles on time-dependent flow of Williamson fluid towards heated surface

An enhancement in the thermal conductivity of conventional base fluids has been a topic of great concern in recent years. An effective way to improve the heat transfer rate of conventional base fluids is the suspension of solid nanoparticles. In this framework, a theoretical study is performed to analyse the heat and mass transfer performance in the time-dependent flow of non-Newtonian Williamson nanofluid towards a stretching surface. There exist several studies focusing on the flow of Williamson fluid by assuming zero infinite shear rate viscosity. Nonetheless, there is a lack of knowledge regarding mathematical formulation for two-dimensional flow of the Williamson fluid by taking into account the impacts of infinite shear rate viscosity. In the current review, the Buongiorno model for nanofluids associated with Brownian motion and thermophoretic diffusion is employed to describe the heat transfer performance of nanofluids. The thermal system is composed of flow velocity, temperature, and nanoparticles concentration fields, respectively. The governing dimensionless equations are solved numerically by Runge-Kutta Fehlberg integration method. The numerical results are compared with published results and are found to have an excellent agreement. Effects of numerous dimensionless parameters on velocity, temperature, and nanoparticle concentration field together with the skin friction coefficient and rates of heat and mass transfer are presented with the assistance of graphical and tabular illustrations. With this analysis, we reached that the thermal boundary layer thickness as well as the nanofluids temperature has higher values with increase in thermophoresis and Brownian motion. It is further observed that the rate of heat transfer is significantly raised with an increment in Prandtl number and unsteadiness parameter.