Influence of non-linear thermal radiation on 2D unsteady flow of a Williamson fluid with heat source/sink

Abstract

Abstract The present article reports a new mathematical formulation for a time dependent flow of a non-Newtonian Williamson fluid model by taking into account the impacts of infinite shear rate viscosity. By incorporating the constitutive relation of Williamson fluid model the basic conservation equations are obtained for two dimensional boundary layer flow. In addition, the heat transfer characteristics for flow filed over a stretching surface has been explored within the sight of thermal radiation and heat sink or source. The Rosseland approximation is being employed for non-linear thermal radiation impacts in the presence of convective heat transfer mode. The current work aims at revealing the solution of equations describing the flow of Williamson fluid by mean of employing the dimensionless approach. Therefore, the leading nonlinear momentum and energy equations are rendered into a set of simultaneously ordinary differential equations via non-dimensional variables with associated physical boundary conditions. Numerical treatment of these reduced conservation equations has been conducted by utilizing the Runge-Kutta Fehlberg integration scheme. We have examined the influence of various physical variables, like, the unsteadiness parameter, Weissenberg number, viscosity ratio parameter, Biot number, radiation parameter, temperature ratio parameter, Prandtl number and heat source/sink parameter on momentum and thermal boundary layers, which is illustrated by means of graphs and tables. The results suggest that the impact of larger viscosity ratio parameter lead to higher fluid velocity while the converse is true for the temperature field. It is noted that the greater unsteadiness parameter results in a significant enhancement in the friction factor. In addition, an increase in thermal radiation as well as temperature ratio parameters improves the heat transfer performance in fluid flow. The work of previous researchers is correlated with the findings of this paper in some special cases in the absence of Weissenberg number and viscosity ratio parameter for different values of unsteadiness parameter. A reasonably accurate predictions are achieved in this comparison.