In this article, an attempt has been made to study the behavior of non-Newtonian viscoelastic model of a Williamson fluid flow problem containing nanoparticles and is assumed to be flowing over a stretching sheet stretched along its surface in both directions with the same constant surface stretching velocity. The boundary layer governing equations of the conservation of mass, conservation of linear momentum and the energy are first modeled into a set of nonlinear coupled partial differential equations along with the appropriate boundary conditions. A numerical study of impact of nanofluid flow over a stretching sheet is tabulated. The basic equations of Williamson fluid are modeled with the help of Navier-Stokes equations for momentum and heat transfer. With the assistance of appropriate similarity transformations these pair of PEDs is transformed into up-to-date system of coupled nonlinear ODEs. These transformed systems of equations are evaluated numerically with the assistance of shooting method using forth order. The dominant physical properties for system of equations of the model that is wall shear stress, and the coefficient of skin friction are acquired. The behavior of nondimensional velocity and thermal flow profiles are discussed for the important involved dimensionless parameters like the Williamson fluid parameter and the nanoparticles volume fraction through tables and graphs.

In the present article, an attempted have been made to study the behavior of boundary layer viscous fluid flow and heat transfer containing some nanosized solid particles flowing through a permeable porous medium. The problem was first modeled into a coupled system of nonlinear partial differential equations of conservation of mass, momentum and nanoparticle concentration. The system of coupled nonlinear boundary layer partial differential equations governing the flowing fluid momentum and heat transfer characteristics are reduced to a new simplified coupled nonlinear system of ordinary differential equations by means of a suitable similarity transformation. The transformed set of nonlinear coupled ordinary differential equations is than solved numerically by means of the fourth order numerical scheme the Runge-Kutta shooting method. The effects of important involved parameters that control the flow field and heat transfer characteristics, that is the viscosity parameter, the convection parameter, the Porosity parameter, the Prandtl number and the Lewis number have been obtained and discussed. Numerical solutions for velocity and temperature are sketched and graphically analyzed. The graphical results observed are indicating that by increasing the values of the non-dimensional viscosity parameter, the dimension less fluid flow profile increases, while for increasing values of the nanoparticles Brownian motion parameter, the nanoparticle concentration profile increases.