Modeling of non-isothermal flow of a magnetohydrodynamic, viscoplastic fluid during calendering

We have modeled an incompressible, non-isothermal flow of a magnetohydrodynamic (MHD) viscoplastic fluid when it passes through the tapered area between two co-rotating rolls. The basic conservation equations like mass, momentum, and energy based on the lubrication approximation theory (LAT) are developed, non-dimensionalized, and solved exactly for the velocity-, pressure gradient-, and temperature-distribution. The value of γ, where the sheet leaves the rolls, is calculated using Simpson's 1/3 formula for numerical integration along with the modify regula-falsi method. Moreover, quantities of engineering interest such as extreme pressure, the roll separation force and the power transferred to the fluid by the rolls are also computed. The results show that the inclusion of the viscoplastic parameter affects the velocity field, pressure gradient-, and temperature-distribution substantially. It is found that the magnetic field provides a mechanism to control power transmission, separation force, and distance between attachment and detachment points, which are very useful for the calendering process.