Indian Journal of Science and Technology

Abstract

Objectives: This attempt is made to investigate the problem of a study of thin film flow for lift while considering a steady, incompressible, non-isothermal, Phan-Thien Tanner fluid on a vertical belt with slip condition. Method/Comparative analysis: The nonlinear differential equation has been derived from the continuity and momentum equations. Exact solution has been obtained, which gives us velocity-profile of fluid, flow rate, temperature, average velocity of fluid and net upward flow. The special cases such as the linear PTT (LPTT), quadratic PTT (QPTT), cubic PTT (CPTT), exponential PTT (EPTT) and upper convected Maxwell (UCM) models are considered, from the same model of PTT fluid. The behavior the velocity and depth is discussed, in effect of various parameters. The velocity and temperature are compared for those special cases. Findings: The analogy of the EPTT, CPTT, QPTT, LPTT and UCM fluid models for the velocity profile and temperature distribution reveals that the velocity profile of the UCM fluid model increases quickly as compared to the velocity of the EPTT fluid. The temperature distribution for EPTT fluid is higher than the temperature for its special case: UCM fluid model. The velocity of PTT fluid is observed to be increased with incorporation of slip condition on vertical belt. Improvements: None of the previous work has been done using no-slip boundary conditions, however slip conditions are used in piece of work. Also, a thorough discussion on cases is novelty in this work.

Keywords: Exact Solution, Heat Transfer, Lift Problem, Phan-Thien Tanner, Thin Film Flow