Unveiling the role of MHD forces in Oldroyd 8-constant fluid during Forward roll-coating: Comparing numerical and analytical computations

In this article, the rheological effects of an Oldroyd 8-constant fluid model in the presence and absence of magnetic force (MHD) are investigated while traveling between the two rolls rotates in the same direction. The governing equations of the fluid flow have been simplified using the lubrication approximation theory (LAT). Analytical solutions in the presence and absence of MHD are presented using (i) Adomian's decomposition method (ADM), (ii) Homotopy analysis method (HAM), and numerical simulations are performed by (iii) the finite difference method. We present the results of our findings through various graphs and validate the numerical and analytical methods through detailed tables of error comparisons. It has been found that non-Newtonian and magnetic parameters have a significant impact on the velocity profiles, pressure gradient, pressure distribution, separation points, and coating thickness. The material parameters α1 (dilatant parameter) and α2 (pseudoplastic parameter) notably affect the velocity profile of the fluid flow between two rolls. Increasing α1 causes shear thickening and decreases the velocity profile, while increasing α2 results in shear thinning and increases the velocity profile due to diminished internal resistance. A relationship exists between the MHD parameter m and the flow velocity. The greater the MHD force, the higher the resistance in fluid flow, resulting in lower velocity. A reasonable agreement has been found between Newtonian fluid and Oldroyd 8-constant fluid, assuming all the non-Newtonian parameters to be zero. The results provided a comprehensive methodology for regulating the coating thickness by adjusting the modified Capillary's number in the industry.