Non-isothermal study of the Yeleswarapu fluid in calendering processes with smooth uniformly moving rolls using a hybrid numerical method

This work explore a heat transfer analysis of the Yeleswarapu fluid model and introduced non-linear slip at the surface of the upper moving roll. The mathematical equations for two dimensional incompressible flows in the calendering process are developed with the help of basic mass, momentum and energy conservation laws. Dimensionless variables are utilized to normalize the obtained equations. These equations are further simplified by the use of lubrication approximation theory. The resulting coupled equations are solved numerically using a hybrid scheme combining the finite difference and shooting methods. The influences of the key parameters on physical quantities are. Results reveal that increasing Weissenberg number (We) enhance pressure and temperature due to elastic and viscous effects, while higher slip reduces pressure buildup and peak temperature. Similarly, larger Brinkman numbers intensify internal heating, whereas higher Graetz number ( Gz ) improve axial heat conduction, reducing thermal accumulation.