Delta Perturbation Method for Thin Film Flow of a Third Grade Fluid on a Vertical Moving Belt

Abstract

In this paper, we theoretically investigate the lift problem for thin film flow of a third-grade fluid on a vertical moving belt by using of delta perturbation method (DPM). The continuity and momentum equations model the problem and DPM method is employed to solve equations analytically. The DPM is type of perturbation technique and introduced by Bender and his colleagues in 1980s.
Substitutions ????2 + ????3 = 0and subsequently DPM method leads to Newtonian solution. The closed form expressions for velocity and temperature profiles, average velocity, volume flux and net upward flow are worked out. The relation between various emerging parameters and velocity profile vz, and temperature profile are presented graphically and as well as by using table, from where, we have pointed out that third grade fluid will uplift quickly as the increase of dynamic viscosity and decrease of the  constant parameters, density and uniform thickness, it is also noted for proposed model that temperature distribution rises for the constant parameters, uniform thickness and density of the fluid and small values of thermal conductivity and dynamic viscosity of the fluid.