Analysis of Roll‐Coating Process for Nonisothermal Flow of Non‐Newtonian Fluid in the Presence of a Fixed Constraining Boundary: A Perturbative and Numerical Study

Roll coating (RC) is a fundamental process in both industrial and decorative applications, including the production of wallpapers, plastic and photographic films, adhesive tapes, magnetic recording media, and packaging materials. In this study, we develop a mathematical model for the flow of Powell–Eyring fluid confined within a narrow gap formed between a moving roll and a fixed substrate. An analytical framework based on the perturbation method is constructed to obtain approximate solutions for the velocity field, temperature distribution, pressure gradient, and pressure profile. A comprehensive comparison between numerical and analytical results is presented, validating the accuracy and reliability of the proposed formulations. Parametric analysis highlights the impact of key material and flow properties on coating thickness, velocity, pressure distribution, temperature variation, separation force, power input, and Nusselt number. The maximum coating thickness attains at , while the minimum value is at . Nusselt number increases with higher Brinkman number, signifying stronger heat transfer effects. A mechanism for controlling the coating thickness, power input, separation force, Nusselt number, and pressure distribution is provided by the material properties involved, offering practical insights for optimizing RC operations across diverse industrial applications.