Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology

Abstract

In the current investigation, we propose the analytical and numerical solutions of the Navier–Stokes equation for the reverse roll coating process (RRCP) using a bath of the Sisko fluid model (SFM). A suitable transformation is applied to the partial differential equation-based mathematical model of SFM-RRCP, resulting in a set of nonlinear ordinary differential equations. The perturbation method has been employed to find the analytical solutions for velocity, flow rate, pressure gradient, pressure, and temperature distribution. The Newton–Raphson method has been used to find coating thickness. Furthermore, numerical integration has been applied to compute some mechanical quantities of interest, including power input and roll separation force. Sensitivity analysis is another approach implemented using response surface methods to examine the impacts of velocity ratio and non-Newtonian parameters on coating thickness, power input, and roll separating forces. The residual graphs and contour diagrams are also shown. It has been observed that as the value of non-Newtonian fluid parameters increases, the velocity profile decreases. However, the coating thickness on the web is a decreasing function. Further, it has been observed that separation points moved toward the nip region when the value of the velocity ratio was raised. Moreover, the sensitivity of roll separating forces and power input to input parameters is negative.