Flow and Heat Transfer of Powell–Eyring Fluid due to an Exponential Stretching Sheet with Heat Flux and Variable Thermal Conductivity

Abstract

Abstract An analysis was carried out to describe the problem of flow and heat transfer of Powell–Eyring fluid in boundary layers on an exponentially stretching continuous permeable surface with an exponential temperature distribution in the presence of heat flux and variable thermal conductivity. The governing partial differential equations describing the problem were transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the shooting method over the entire range of physical parameters. The effects of various parameters like the thermal conductivity parameter, suction parameter, dimensionless Powell–Eyring parameters and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. In this work, special attention was given to investigate the effect of the thermal conductivity parameter on the velocity and temperature fields above the sheet in the presence of heat flux. The numerical results were also validated with results from a previously published work on various special cases of the problem, and good agreements were seen.