Numerical investigation of Reiner–Rivlin fluid flow and heat transfer over a shrinking rotating disk

Spinning disks are widely used in engineering field due to their capacity for energy storage, efficient heat transmission, and mechanical function. The prime objective of this study is to elucidate the behavior of swirling flow around a radially shrinking rotating disk using a unique Reiner–Rivlin fluid. Through similarity analysis, the partial differential equations governing the flow are transformed into a set of ordinary differential equations. The numerical solutions for these equations is obtained using the bvp4c function in Matlab. The computed outcomes are in good agreement with existing literature on Von-Kármán flow, especially when considering non-Newtonian fluids. The study presents results such as local skin friction, local Nusselt number, velocity, and temperature profiles through graphs and tables. Notably, for the case of a shrinking rotating disk, two distinct solutions are identified. A stability analysis is performed to assess their physical relevance, concluding that the first solution is stable and physically plausible. In contrast, the second solution is unstable.