This article describes the development of a mathematical model of the reverse roll coating of a thin film for an incompressible non-isothermal magnetohydrodynamics (MHD) viscoplastic fluid as it passes through a small gap between two rolls rotating reversely. The equations of motion required for the fluid added to the web are constructed and simplified using the lubrication approximation theory (LAT). Analytical results are obtained for the velocity profile, pressure gradient, and temperature distribution. The pressure distributions and flow rate are calculated numerically using the trapezoidal rule and regular false position method, respectively. Some of these results are presented graphically, while others are shown in a tabular form. From the present analysis, it has been observed that the magnitude of pressure distributions increases by increasing the value of the involved parameters. It is worth mentioning that the velocities ratio and Brickman’s number are controlling parameters for the temperature distributions. The results indicate the strong effectiveness of the viscoplastic parameter and velocities ratio for the velocity and pressure distributions. It is also concluded that the coating of Casson material has been remarkably affected by the magnetohydrodynamics effects.
This article presents a mathematical model and theoretical analysis of coating of a thin film of non-Newtonian polymers as they travel through a small space between two reverse-rotating rolls. The dimensionless forms of the governing equations are simplified with the help of the lubrication approximation theory (LAT). By using the perturbation technique, the analytical solutions for velocity, flow rate and pressure gradient were obtained. From an engineering point of view, some significant results such as thickness of the coated web, pressure distribution, separation points, separation force and power input were computed numerically. The effect of velocities ratio k and Weissenberg number We on these physical quantities is presented graphically; others are shown in tabular form. It is noted that the involved material parameters provide a mechanism to control the flow rate, pressure distribution, the thickness of coating, separation force and power input. Moreover, the separation point is shifted toward the nip region by increasing velocities ratio k.
Electrostatic powder coating in fluidized beds is a technique that has been known for more than 30 years. The present paper attempts to model the changes in the electric fields produced by the progression of the powder coating layer on the surface of a metallic wire substrate immersed in a fluidized bed of charged powder. The intersections of wire geometries often present coating difficulties due to Faraday cage effects. The current modeling will show that as powder deposits on the substrate on areas where the electric field is strongest, the electric field is enhanced in the original weaker areas thus promoting powder deposition towards the intersections. Also, the effects of varying the size of the fluidized bed are investigated and show that as the bed size increases, while the substrate size remains constant, the electric fields in the bed increase significantly; however, the electric field enhancement at the intersections of the substrate decreases. Varying the charge density of the deposited paint layer on the metallic substrate shows that a minimum charge density of deposited powder is required for the electric field enhancement phenomena to occur. The current modeling employs commercially available Finite Element software.
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