Exploring integrated heat and mass transfer in von-Kármán dynamics involving Reiner-Rivlin fluid with regression models

The rotating disk system is widely used in several important applications, including turbomachinery design, mixing and stirring processes, centrifugal blood pumps development, optimizing electronic component, cooling efficiency, and various others. Moreover, regression models offer comprehensive and reliable prediction for important parameters in flows developed by revolving disks. This article presents similarity solutions for coupled heat and mass transfer with viscous dissipation in an inelastic non-Newtonian fluid flow across a permeable revolving disk. The inclusion of diffusion terms due to Dufour and Soret effects establishes coupling between energy and concentration equations. Temperature and concentrations at disk surface are supposed to vary quadratically along the radial direction. The impacts of MHD, heat source/sink dynamics and Joule heating effects on thermal boundary layer are also scrutinized. MATLAB's bvp5c tool, based on collocation scheme, generates numerical results. Homotopy analysis method, a widely accepted analytical solution procedure, is then applied to produce the series solution. Selection of the optimal auxiliary parameter values featured in the series solution is also included. The impact of Reiner-Rivlin fluid assumption on the torque required by the disk is assessed. Furthermore, linear and quadratic regression models are developed for the skin friction factors, Nusselt number and Sherwood number.