Unsteady boundary layer flow of Williamson nanofluids over a heated permeable stretching sheet embedded in porous medium in the presence of viscous dissipation

The main objective of this paper is to focus on a numerical study of unsteady boundary layer flow of Williamson Nanofluids over a heated permeable stretching sheet embedded in porous medium in the presence of viscous dissipation. A mathematical modeled which resembles the physical flow problem has been developed. By using an appropriate transformation, we converted the system of dimensional nonlinear partial differential equations into system of coupled dimensionless ordinary differential equations. Numerical solutions of these equations are obtained by Runge-Kutta fourth order with shooting method.  The velocity, temperature and concentration distributions are discussed numerically and presented through graphs. The numerical values of reduced skin-friction coefficient, Nusselt number and Sherwood number at the plate are derived and discussed numerically for various values of physical parameters which are presented through tables. The present results have been compared with existing one for some limiting case and found excellent validation. It is analyzed that the reduced skin friction coefficient enhances with increasing values of an unsteady parameter, magnetic parameter and porosity parameter. In addition, we observe that decrement in velocity profile of the fluid flow is observed for increasing values of the non-Newtonian Williamson parameter and a rise in Eckert number leads to the enhancement of the temperature of the fluid in the thermal boundary layer.