Influence of the Reynolds viscosity model and induced magnetic field on a thin Casson fluid film flow between two rotating disks with cross-diffusion effects

In models of fluid dynamics, the magnetic field is essential for preserving the stability of flow streams and found applications in magnetic resonance imaging, magnetic levitation, and geophysical exploration. Recognizing the significance of this magnetic influence, we aim to investigate the behavior of flow within a three-dimensional squeezed film of Casson fluid situated between two rotating disks, under the influence of an induced magnetic field and the Reynolds viscosity model. The study also meticulously examines the heat and mass transfers, taking into account the effects of thermo-diffusion and diffusion-thermo. The resulting torque on both the upper and lower surfaces is analyzed and presented in a tabulated format. The normalized system of equations is transformed into a set of first-order differential equations, which are then solved using the bvp4c numerical solver in MATLAB. The impacts of various parameters are graphically illustrated in two different scenarios (?=0.0,0.5), i.e., constant and variable viscosity. It is observed that when the variable viscosity parameter is set to zero, the azimuthal velocity profile experiences a more pronounced increase as the rotational parameter rises. Conversely, the azimuthal magnetic profile exhibits a more significant decrease when considering the influence of the variable viscosity parameter. Finally, the results are compared with previous studies in the literature for a limiting case, and error is reduced between 0.000003% and 0.000002%.