Impacts of activation energy and modified Darcy law on the motion of Williamson nanofluid over a stretching riga sheet through Porous medium

Abstract

The present analysis is motivated by the need to elucidate with more accuracy and sophisticaion the motion of Williamson nanofluid with activation energy and modified darcy law through porous medium over a stretching riga sheet. The problem is modulated mathematically by using the momentum,energy and concentration equations. The nonlinear partial differential equations describe the motion is transformed to nonlinear ordinary dfferential equations by using a suitable transformations. The obtained system of equations with boundary conditions inside the boundary layer are solved semi analytically by using homotopy perturbation method. The velocity, temperature and the concentration of the fluid as well skin-frication, Nusselt and Sherwood numbers are obtained as a functions of the physical parameters of the problem. The effects of these parameters on the solutions are discussed numerically and illustrated graphically through some figures. It is found that the parameters play a dramatic role to control the solutions.  For example the velocity increases with increeasing Williamson parameter, permiability parameter and modified Hermann number. On the other hand the fluid temperature increases with increasing both of Brownian parameter and Eckert number. In addition, increasing the activation energy and thermophoresis parameter increases the fluid concentration.