A mathematical analysis for magnetohydrodynamics and slip effects is presented for blade coating onto a moving sheet of viscous fluid. An applied magnetic field is imposed normal to the flow and slip is considered at the web surface. The shooting method is applied to obtain the numerical solution of governing differential equations. Both numerical and exact solutions are utilized to describe the velocity profile, volumetric flow rate, pressure gradient, pressure and maximum pressure. How slip parameter and the Hartmann number influences properties is discussed through the graphical results. It is calculated that the presence of slip and applied magnetic field controls the sheet velocity in the blade coating process.
In this article, coating process for a third-grade fluid using a simple fixed blade on a moving substrate is discussed. The analysis is carried out for both exponential (flexible blade) and plane (stiff blade) coaters. Coupled partial differential equations are simplified by applying the lubrication approximation theory and assuming that the coating layer thickness is much less than the blade length. The obtained system is normalized using suitable scales. A numerical solution of the governing boundary value problem is developed for various third-grade parameters. In addition, a perturbation solution is also obtained for small third-grade parameters. Interesting quantities such as pressure, pressure gradient, velocity, and load are computed and shown graphically and in tables. How the involved parameters influence the results is examined. The load on the blade is the most important physical quantity in the present work as it controls the coating thickness and quality. We found that the blade load increases as the third-grade material parameter
β increases.
AbstractA mathematical study of an Oldroyd 4-constant fluid for a blade coating process is studied in this paper. The results for plane as well as exponential coaters are analyzed. Suitable dimensionless variables are used to convert the model governing equations into dimensionless form. Lubrication approximation theory is applied to simplify the dimensionless form of governing partial differential equations. The well-known numerical technique known as the shooting method is used to solve the non-linear boundary value problem. Influence of the involved rheological parameters on the blade coating process is analyzed. From an engineering point of view, load on the blade and pressure are important outcomes of the present study as they ensure the thickness and quality of coating and enhance the life of the substrate. The effects of material parameters on load, thickness, velocity, pressure and pressure gradient are discussed. Obtained results for velocity, pressure gradient and pressure distribution are shown graphically, whereas load and thickness are expressed in a tabulated form.
In this paper, a nonisothermal analysis for the process of blade coating of an incompressible couple stress fluid is presented using both plane and exponential coaters. The governing system is simplified using lubrication approximation theory (LAT). The interesting quantities from engineering point of view like normalized pressure, maximum pressure, pressure gradient, velocity, and effects of involved parameters on temperature distribution, which influence the coating process are evaluated. It is observed that pressure is at maximum near the edge of the blade whereas fluid velocity and temperature are at maximum near the substrate. An increasing couple stress parameter increases the load and decreases the coating thickness. It is worth mentioning that load and pressure are the most significant outcomes of the present exertion as these two physical quantities ensure thickness and the quality of coating.
A new mathematical model for a flexible blade coater is proposed and analysed for slip and magnetohydrodynamic (MHD) effects in blade coating process. The slip is considered at the blade surface and magnetic field is imposed normal to the flow. To obtain the velocity profile, pressure, pressure gradient, volumetric flow rate and maximum pressure both exact and numerical solutions are utilized. In order to obtain the numerical solution shooting technique is applied. The interesting physical quantities like load and deflection are calculated and presented in graphical and tabulated form. The influence of the Hartman number the slip parameter and normalized coating thickness parameter on the flow and deflection are discussed graphically. In the presence of magnetic field and slip the fluid velocity and hence blade deflection can be controlled.
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