Analytical solutions for heat transfer flows of a third grade fluid in case of posttreatment of wire coating

The steady flow of a third grade fluid which belongs to non-Newtonian fluid mechanics deserves more attention than it has been to date, because in the nonlinear systems, the literature is scarce. In this paper, we develop a formulation suitable for solution in the case of posttreatment of wire coating containing thermal effects of third grade fluids. The optimal homotopy asymptotic method (OHAM) and regular perturbation method are used to investigate the flow of the titled problem. Expressions for velocity and temperature distributions are given. It is noted that the solutions are strongly dependent on the Brinkman number, the ratio of velocityU and non-Newtonian parameterb. Finally, a physical interpretation of the results is given with the help of several graphs.