Scrutinization of Unsteady Magnetohydrodynamics Williamson Nanofluid Flow and Heat Transfer Past a Permeable Shrinking Sheet

Abstract

This study contributes to the thermal characteristics and flow behaviour of magnetohydrodynamics (MHD) unsteady flow of Williamson nanofluid over a permeable stretching/shrinking sheet in the presence of velocity slip at the boundary. The PDEs with the corresponding constraints are transformed into a set of non-linear ODEs using similarity transformations and are then solved numerically using fourth order Runge-Kutta integration scheme along with shooting technique. The results show that for the flow past a shrinking sheet, dual solutions exist for a certain range of physical parameters. The analysis shows that velocity profile is an increasing function of magnetic parameter M (0.0 ≤ M ≤ 0.3), velocity slip parameter δ (0.0 ≤ δ ≤ 0.25) and suction parameter s (2.0 ≤ s ≤ 2.2) while decreasing function of Williamson parameter β (0.0 ≤ β ≤ 0.8) and unsteadiness parameter A (−3.5 ≤ A ≤ 0.0) for the first solution branch. The temperature profile augments due to the increase of M and δ for the first solution branch. Computational outcomes of the skin friction coefficient, the Nusselt number, the Sherwood number are tabulated with suitable interpretations. The temporal stability analysis reveals that among the two solutions, first solution is stable and physically realizable. Our method of finding dual solutions and analyzing stability analysis is of practical importance to those interested in fluid dynamics as it provides one with a way to determine whether a steady state solution is physically meaningful or not.