This paper presents a mathematical model for the thin film roll coating process of an incompressible Williamson material, passing through a closed passage between a rotating roll and a web. In light of lubrication approximation theory, the flow equations are nondimensionalized. The regular perturbation approach is used to provide solutions for the velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface. Important engineering quantities such as coating thickness, maximum pressure, separation point, roll/sheet separating force, and roll-transmitted power to the fluid are also obtained. The effects of several factors are graphically projected. The study shows that the material factors that are involved determine the operating variables. Coating thickness and separation point are controlled by Weissenberg’s number, therefore acting as a controlling parameter for the rate of flow, thickness in coating, power contribution, pressure, roll separating force, and separation point. In comparison to the existing results in the literature, the current results are broader and zero-order results are more accurate.
Perturbation Approach in the Dynamic Buckling of a Model Structure with a Cubic-quintic Nonlinearity Subjected to an Explicitly Time Dependent Slowly Varying Load