Applications of lubrication approximation theory in the analysis of the roll‐coating using a tangent hyperbolic fluid model

Abstract

Abstract In this study, the process of roll‐over‐web coating for a tangent hyperbolic fluid is theoretically examined. Fundamental laws of fluid mechanics are used to set up the flow equations and then simplified through lubrication approximation theory (LAT). The governing differential equations are solved with the help of the perturbation method in conjunction with the Runge–Kutta method. The outcomes of the study are presented through the graphs and tables. Study shows that enhancing the Weissenberg number upsurges the velocity and pressure while decreasing the pressure gradient. It is also noted that force shows an increasing trend while power is decreasing for bigger values . Results further depict that for a bigger value of the power law index , pressure gradient, pressure, force, and power decrease, and the coating thickness increases. It is worth mentioning here that for the shear thinning case, the tangent hyperbolic model predicts less pressure in the nip region when compared to the Newtonian model.