Fully Developed Flow of Third-Grade Fluid in the Plane Duct with Convection on the Walls

Abstract

In this paper, an appropriate analysis has been performed to study the incompressible fully developed flow of a non-Newtonian third-grade fluid in a plane duct with convection on the walls. The governing equations, continuity, momentum and energy for this problem are reduced to a nonlinear ordinary form. The momentum nonlinear equation and the resulting energy equation with Robin mixed boundary condition are solved with the collocation method. The effects of non-Newtonian parameter on dimensionless velocity profiles, dimensionless temperature profiles and also effect of Biot number on dimensionless temperature profiles have been shown. Finally, the results show that the collocation method was successfully used for solving nonlinear differential equations with Robin mixed condition.