Non-isothermal study of Yeleswarapu fluid model in the roll coating process using response surface method

Roll coating is a process used to apply a uniform liquid layer to a moving sheet with applications in industries such as plastics, PVC fabrics, and paints. This study theoretically investigates the flow of Yeleswarapu fluid between a heated roll and web during the roll coating process. The governing equations are formulated from fundamental laws, non-dimensionalized, and reduced to ordinary differential equations using the lubrication theory. A regular perturbation method is employed by considering the Weissenberg number as a small parameter to derive expressions for velocity, pressure distribution, pressure gradient, and flow rate. Power input and roll-separating force are computed using the Runge–Kutta method. Furthermore, the response surface method with analysis of variance is applied to optimize the Nusselt number and shear stress, while sensitivity analysis examines the effects of the Weissenberg number (We), Brickman number, and viscosity ratio parameter (β*) on the shear stress and Nusselt number. Results show that a higher Weissenberg number reduces velocity and temperature, while increasing the Brinkman number significantly raises temperature. The Yeleswarapu model predicts up to 6.23% lower pressure in the nip region as We(= 0.12) compared to Newtonian fluid. Moreover, the separation point moves to the right of its Newtonian value, and the exit coating thickness increases with increasing viscoelastic effects.