Flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders in the presence of magnetic field

In this paper, the flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders has been investigated in the presence of magnetic field. For this purpose, the constitutive equation of such a fluid flow was simplified, and the existence of the solution to the governing equation was established using Schauder's fixed point theorem. Using the finite difference method, the numerical solution of the non-dimensionalized form of the established governing equation was obtained. The effect of sundry parameters such as the rotating speed of the cylinders, the physical properties of fluid, and magnetic field intensity on the fluid velocity field was studied as well.