Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena

The current study theoretically and computationally analyses the viscoelastic Sisko fluids during the non-isothermal rollover web phenomenon. The mathematical modeling produces a system of partial differential equations, which we further simplify into ordinary differential equations through appropriate transformations. We have formulated the problem based on the lubrication approximation theory. The solution has been obtained with the perturbation method, and the outcomes are found in mathematical, tabular, and graphical forms that highlight the influence of pertinent parameters on velocity profiles, pressure gradients, flow rates per unit width, Nusselt number, pressure profile, temperature distributions, and other significant engineering quantities. Further, A comparative analysis between analytic and numerical solutions, utilizing the middefer method in the Maple environment, demonstrates reasonable agreement. Also, we observe that the fluid parameter significantly influences both velocity and temperature profiles. Moreover, the determination of a separation point 2.5000, accompanied by the observation of a maximum coating thickness of 0.6960. The enhancement in fluid heat transfer rate is approximately 5% compared to non-Newtonian fluid parameter values, with potential for further improvement by increasing the non-Newtonian parameter values. This comprehensive investigation offers valuable insights for practical implementation and future scholarly endeavors, with zero-order findings showcasing enhanced precision.