Thermal analysis of Cross fluid blade coating influenced by magnetohydrodynamics and non-linear slip

This study investigates non-isothermal blade coating process involving a Cross fluid model for both magnetohydrodynamic (MHD) effects and nonlinear slip at the blade surface. The governing equations for continuity, momentum, and energy are formulated and simplified using dimensionless variables and the lubrication approximation appropriate for thin film flows. The nonlinear partial differential equations are solved using hybrid numerical scheme combined with the methods of cords to discuss the influence of main parameters, including the slip coefficient (γ), magnetic parameter ( M ), Cross fluid parameters, Brinkman number, Graetz number, and the dimensionless coating thickness ( k ). It is derived from the results that increasing the slip parameter speed up the fluid velocity and reduce surface friction. Slip parameter thickens the coated layer with lower blade load. Magnetic parameter imposes a damping effect that decreases the velocity profile and coating thickness. Increasing the magnetic field M to seven significantly reduces coating thickness, with a 67.6% decrease compared to the Newtonian case. The blade load Π declines 99.3%, highlighting how the magnetic field dampens the pressure buildup beneath the blade. These findings are useful in optimizing blade geometries and flow conditions in advanced polymer coating applications.