LAUSR

Abstract In this article, a two-dimensional numerical simulation is conducted to examine the physical characteristics of a non-Newtonian Williamson fluid flow along with heat transfer in the presence of suspended nanoparticles. Moreover, the transient flow of Williamson nanofluid is formulated by using Buongiorno's model for nanoparticles. Impacts of non-uniform magnetic field and convective heat transfer are further considered for the flow generated by an expanding/contracting cylinder. The reduced system of coupled equations representing continuity, momentum, energy and concentration equations are resolved using an efficient Runge–Kutta scheme with Cash–Karp coefficients. The numerical simulations are performed in MATLAB software and dual solutions were detected for velocity, temperature and concentration profiles for some combination of shrinking and mass transfer parameters. To achieve the better perception of current problem, the flow and heat transfer features are investigated for the various values of physical parameters, like, unsteadiness parameter, viscosity ratio parameter, magnetic parameter, thermophoresis parameter and Brownian motion parameter. The obtained results showed that the skin-friction coefficient increases by increasing the viscosity ratio parameter. In addition, the outcomes confirmed that the temperature profiles increase with increasing convective heat transfer parameter. At last, a good agreement is found between obtained results of this study and already published data.