Non-Newtonian fluid flows over deformable rotating disk: Exact flow/heat solutions

This study presents exact solutions for flow and heat transfer in non-Newtonian fluids driven by a rotating and deforming disk under a transverse external magnetic field. These three-dimensional solutions are of exponential form, fully satisfying the asymptotic decay conditions of the boundary layer equations in the far field. The existence of such solutions depends on the material properties and driving mechanisms, with their boundaries determined analytically. Numerical simulations confirm successfully such exact non-Newtonian solutions belonging to the deformable rotating disk family. We further demonstrate that under specific circumstances, the solutions collapse to two-dimensional counterparts dominated by either pure radial dilation or pure rigid-body rotation. These simplified solutions offer a valuable tool for testing the validity of numerical schemes commonly used to simulate similar physical phenomena in future studies of the rotating disk problem.