Abstract
The non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient is obtained. While the pressure and flow rate are obtained numerically. The impact of involved parameters on important physical quantities such as temperature, pressure, and pressure gradient are elaborated through graphs and in tabular form. The pressure and pressure gradient decreases for variation of the couple stress parameter and velocity ratio parameter K. While the variation of the slip parameter increases the pressure and pressure gradient inside the flow geometry. Additionally, flow rate decreases for the variation of the slip parameter as fluid starts moving rapidly along the roller surface. The most important physical quantity which is responsible for maintaining the quality of the coating and thickness is flow rate. For variation of both the couple stress parameter and the slip parameter, the flow rate decreases compared to the Newtonian case, consequently the coating thickness decreases for the variation of the discussed parameter.
Highlights
Our calculations are based on geometrical information that indicates that a major dynamic phenomenon occurs in the reverse roll coating near the nip
Using an incompressible non-isothermal couple stress fluid, the reverse roll coating process is examined in this study
The closed form solution is obtained for velocity and pressure gradient
Summary
The roll coating is familiar in engineering and is an industrial procedure in which a shrill (thin) liquid layer is consistently deposited onto a movable surface (substrate). Kanwal et al [24] employed LAT for the solution of governing flow equations by using viscous nanofluid, which consists of copper nanoparticles, with a porous substrate, in this case, a flexible blade coater is used for the analysis They adopted two distinct models that may differ in dynamics viscosities. Ali et al [41] investigated the non-isothermal magnetohydrodynamics (MHD) viscoplastic fluid in reverse roll coating process and simplified the involved equations through LAT They concluded that, for the temperature distributions, Brinkman’s number and ratio of velocities are controlling factors. The theoretical investigation of pseudoplastic polymer was carried out by Ali et al [42] by considering reverse roll coating They used LAT for simplification of flow equations and obtained the required results through perturbation technique. The problem formulation, mathematical modeling, problem simplification, solution to the problem, and results along with the conclusion based on the analysis are presented in following sections
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