Intervention of the Koo-Kleinstreuer and Li Model in Nanofluid Flow over Magnetic Dipole Centered Curved Sheet and Optimizing Entropy using Response Surface Methodology

Nanofluids are recognized as smart fluids, offering significant advantages for enhancing heat and mass transfer. Their utility spans various domains, including electronics, biomedicine, and industrial processes. Against this backdrop, our present study focuses on examining response surface method and carrying out sensitivity analysis for Al2O3 nano-fluid flow over a stretching curved geometry. The response surface mechanism is envisioned for Eckert number, Prandtl number, as well as radiation parameter. This study introduces a novel perspective by investigating the interplay of heat and mass transfer in nano-liquids, incorporating radiative heat flux and the influence of a magnetic dipole. The Koo-Kleinstreuer and Li model analyses Brownian motion effect on viscosity and effective thermal conductivity. The modelled problem is solved using the Runge-Kutta-Fehlberg 4th–5th method. The results show that as ferrohydrodynamic interaction intensifies, it leads to an augmentation in velocity near the boundary, followed by a subsequent rise; however, the temperature profile experiences a decrease. As the thermal radiation parameter escalates, so does the temperature profile. Conversely, the concentration profile diminishes with heightened chemical reaction and Schmidt number. Entropy rises in correlation with an enhancement in the temperature ratio parameter, yet the Bejan number declines. The Pareto chart highlights 2 as the critical point for the Eckert number, Prandtl number, and radiation parameter. Specifically, the Prandtl number demonstrates a negative sensitivity across all levels of radiation parameter. Conversely, both the Eckert number and radiation parameter exhibit positive sensitivity at all levels of radiation parameter.