A comparative analysis of thermal and pressure distribution in rotating flows of von Karman and Bodewadt using multivariate regression models: A case of machine learning techniques

This work is related to fluid flow over a rotating disk, which has attracted significant interest due to its applications in engineering, aerodynamics, and industrial processes. This research presents a detailed numerical solution of rotating flows of von Karman and Bodewadt. The system of boundary layer approximation consists of the external forces i.e. Hall current, magnetic field, thermal radiation, Darcy-Forchheimer porous model and slip mechanism. The governing equations are boundary value problem which is solved using bvp4c solver, that efficiently handles non-linear differential equations with boundary conditions at two different points. To further analyze the flow characteristics, we employ multivariate linear and polynomial regression models, providing data driven perspective on the dependency of SFC (skin friction coefficient) and LNN (local Nusselt number) on governing parameters. The study reports that, multivariate linear regression and polynomial regression are the machine learning approaches used to estimate the SFC and LNN values for the von Karman and Bodewadt flows, respectively. The MAE (mean absolute error), MSE (mean square error), and$R^2$are used to evaluate the prediction's performance. The highest $R^2$values for the implemented method is obtained as 0.98905073. The results obtained demonstrate the efficacy of machine learning techniques in this field.