Non-isothermal flow dynamics during reverse roll coating phenomena of non-Newtonian polymer

Roll coating plays a major role in industrial coating, including wallpapers, plastic and photographic films, sticky tapes, magnetic recordings, wrapping magazines and books, and so on. The current study proposes a mathematical model for a non-isothermal, incompressible Sutterby fluid flowing through a narrow gap between two heated, counterrotating rollers. Lubrication approximation theory is used to simplify nondimensional expressions. The perturbation technique provides exact results for velocity profile, temperature, flow rate, and pressure gradient, whereas the numerical technique (Simpson rule) is used to compute the pressure profile and flow rate, respectively. The effects of the involved parameters on various physical characteristics like pressure, flow rate, temperature, pressure gradient, force, and power input are depicted in graphs and tabular form. A mechanism for controlling the coating thickness, power input, flow rate, separation force, and pressure distribution is provided by the material properties involved. With variations to a Sutterby fluid parameter $\beta$ and the velocity ratio K, both the pressure gradient and pressure decrease. It is significant to note that the temperature distribution is controlled by the velocities ratio and Brinkman number. Moreover, the separation point is shifted towards the nip area and the coating thickness on the web reduces with increasing velocities ratio K.