Bi-viscous Bingham nanofluid radiative flow in a stationary cone-disk system with Hall current: Heat transfer optimization

Research on dynamics and heat transport in the conical gap of cone-disk or cone-plate apparatus has potential applications in medical devices, rheometers, viscosimeters, and conical diffusers. The Bi-viscosity Bingham plastic model has been widely used to describe the rheological properties of polymeric gels, emulsions, and heavy oils used in medical devices. In this theoretical investigation, the heat transport features in the conical region of a stationary cone-disk system (SCDS) using a Bi-viscous Bingham plastic nanofluid model are analyzed. For the first time, external effects such as magnetic fields, Hall currents, and thermal radiation on SCDS were examined. A comparative analysis of non-swirling and swirling flow scenarios is conducted. Lie-group scaling transformations were derived to obtain self-similar nonlinear ordinary differential equations describing the physical phenomenon, which were then solved numerically. We examined flow features along with heat and mass transfer for variations in the physical parameters involved in the model. Heat/mass transport rates at the wall of the SCDS were quantified using the Nusselt and Sherwood numbers, for which nonlinear multivariate regression models were subsequently developed. Optimization of heat and mass transport was carried out using the Response Surface Methodology. Our findings indicate that the Bingham plastic fluid parameter diminishes velocity profiles in the radial and azimuthal directions while improving the rate of heat and mass transport at the disk surface. Hall current and magnetic field parameters enhance both the heat and mass transport. Furthermore, the optimization procedure established that low levels of Brownian motion and thermophoresis parameters, combined with high levels of the Lewis number, maximize heat and mass transport simultaneously at the disk surface.