Dynamics of accelerating and decelerating flow of an electrically conducting Jeffrey fluid between two narrowly flat permeable disks

The radial flow between two flat disks plays a crucial role in engineering and industrial applications due to its relevance in lubrication systems, cooling technologies, and fluid transport mechanisms. This study investigates the laminar radial flow of an incompressible Jeffrey fluid between permeable flat disks under the influence of a magnetic field. The exact solutions for both accelerating and decelerating flows are derived using the Jacobi elliptic function of the first kind. The effects of key physical parameters on velocity profiles are analyzed graphically, while torque variations are presented in tabular form. Additionally, the streamline patterns and 2D velocity graphs exhibit consistent trends across parameter variations, reinforcing the accuracy of the findings. Results indicate that accelerating velocity increases with a stronger magnetic field but decreases for all other parameters. In contrast, decelerating velocity rises with increasing porosity and declines for all remaining factors. Torque analysis reveals that an increase in the Jeffrey fluid parameter enhances torque on both disks, whereas a higher Darcy number increases the torque on the upper disk but reduces it on the lower disk. Streamline analysis is conducted to illustrate flow behavior under varying parameter conditions. The results confirm a parabolic velocity profile, with maximum velocity at the central region and minimum velocity at the disk surfaces.