Regression modeling of Bödewadt slip flow dynamics involving Reiner-Rivlin nanofluid based on a modified Buongiorno approach

Abstract Regression models are useful in analyzing rotational flows as they enable accurate predictions of wall shear and heat transfer coefficient. In addition, Bödewadt flow is of paramount importance in fluid dynamics of rotating systems such as turbomachinery and geophysical flows. Moreover, nanofluid’s enhanced heat transfer properties can improve cooling efficiency in applications involving turbines and electronic systems. This study delves into the Bödewadt boundary layer flow of a Reiner-Rivlin fluid containing nanoparticles over a stationary porous disk under slip conditions. The two-phase Buongiorno model is employed, incorporating temperature-dependent diffusion coefficients for enhanced accuracy. To facilitate numerical simulations, the transport equations are converted into an ordinary differential system comprising four unknowns. In the present work, a highly reliable Keller-Box methodology is adopted which agrees very well with the MATLAB built-in program ‘bvp4c’. The computed 2-D and 3-D streamlines vividly capture the Bödewadt flow scenario with Reiner-Rivlin nanofluid. The principle aim to investigate the impact of non-Newtonian behaviour and slip on the flow pattern, while also examining the behavior of temperature/concentration field for nanoparticle working fluids. As thermophoretic diffusion increases, the thermal boundary layer thickens considerably, leading to a notable decrease in the cooling rate of the disk. In contrast, Brownian diffusion has only a minimal impact on the heat transport. In addition, wall suction effect is observed to significantly boost the disk’s cooling rate, though at the expanse of increasing skin friction coefficients. This study introduces linear and quadratic regression models designed to precisely predict both the surface drag and disk cooling rate, which are crucial factors in engineering processes.