On the study of stationary points and uniform thickness of PTT fluid film on a vertically upward moving belt

Abstract

This paper investigates the thin film flow of Phan-Thien Tanner (PTT) fluid on a vertically moving belt. Three different models, namely, the upper convected Maxwell model (UCM), linear version of Phan-Thien Tanner model (LPTT), and exponential version of Phan-Thien Tanner model (EPTT), are taken into consideration. Exact expressions for velocity profiles, flow rates, average velocities, film thicknesses, shear stresses, and normal stresses are obtained. Special consideration is given to the predictions of stationary points in withdrawal of these fluids from the belt. It is observed that the stationary point of the UCM model lies closer to the free surface and the stationary point of the LPTT model lies in the middle of the stationary points of UCM and EPTT models. It is also observed that the stationary points tend to move towards the belt with the increase in Stokes number, Deborah number, and elongational parameter. Graphical results are also presented for various dimensionless flow parameters.