Stagnant points and uniform film analysis of Eyring fluid film flow on a vertically upward moving slippery flat plate

Abstract

In this paper, we analyze how Eyring fluid film behavior on a vertically upward moving slippery flat plate can help predictive models in engineering, notably in coating and lubrication operations. This paper deals with the stagnant points and uniform film analysis of Eyring fluid film flow on a vertically upward moving slippery flat plate. The formulated ordinary differential equation is solved for exact analytic solution. Exact analytic expressions for velocity, flow rate, average velocity, shear stress components, and stagnant points are derived. A highly nonlinear algebraic equation is derived for film thickness. Equation is solved by Newton’s method using Maple code. The thickness of film widens with increasing relaxation time, constant plate velocity, and fluid density, while it decreases with increasing fluid viscosity and constant slip parameter. The analysis delineates that the positions of stagnant points tend to relocate closer the slippery plate as the Stokes number, Deborah number, and constant slip parameter increase. A high Deborah number enhances drainage, causing stagnant points to relocate closer to the slippery plate and the development of a stable elastic layer adjacent to the plate. For stagnant points and fluid film thickness, a comparison between the Eyring fluid and existing studies (EPTT, LPTT, UCM, and Newtonian fluid) is also provided. The validity of this paper with the existing studies is also presented by reducing Eyring fluid model to Newtonian model. The results of this research are significant for a wide range of biofluid applications, including agrochemical uses, paint and surface coating flow behavior, thin films on the cornea and lungs, and chemical and nuclear reactor design.