Modeling of an isothermal flow of a magnetohydrodynamic, viscoplastic fluid during forward roll coating process

Abstract

An isothermal and incompressible flow of a magnetohydrodynamici (MHD) viscoplastic fluid has been examined while passing through the area among two co-rotating rolls. Applying lubrication approximation theory (LAT), the basic flow equations of mass and momentum are derived and subsequently non-dimensionalized. Exact solutions of velocity and pressure gradient distributions are evaluated. To evaluate the complex integrals, Trapezoidal rule for numerical integration is used. The significant engineering parameters like, the roll separation force, maximum pressure and the power transferred to the fluid by the rolls, are also numerically computed. The results demonstrate that the velocity field and pressure gradient are significantly affected due to the presence of the viscoplastic parameter. Magnetic field is found to be the controlling parameter for power input, separating force, and distance among attachment and detachment points, being extremely beneficial for the roll coating process. It has been learnt through this study that MHD can be an effective tool in the coating industry to regulate the engineering quantities in which coating thickness is the most important.