Research Projects

The study aims to analyze a class of fully coupled, highly nonlinear differential equations resulting from laminar, incompressible non-Newtonian swirling flow problems due to the rotation of circular disks of large radii. The Stokesian fluid will be used as the non-Newtonian fluid model. The study will focus on two fundamental flow problems: rotational symmetric flow over a rotating disk and flow between two infinite rotating disks. The literature survey reveals anomalies in the solutions of these swirling flow problems, such as computational difficulties when disk and fluid rotate in opposite sense, oscillations in velocity components, and the existence of no solution or multiple solutions for a range of flow control parameters. The study also addresses the controversies associated with non-Newtonian fluids, which increase nonlinearity due to the presence of higher order tensors in the constitutive equations. The study will use improved numerical methods and high-end computers to solve the resulting systems of fully coupled and highly nonlinear self-similar equations. Existence and uniqueness analysis using fixed point theorems will be carried out, along with an asymptotic analysis to support the findings. The results will be published in good journals, presented in conferences, and a monograph will be written based on the new findings.