Unsupervised machine learning solutions for electroosmotically driven Casson hybrid nanofluid flow using sigmoid and Fibonacci neural networks: a biomedical approach.

This work investigates the electroosmotic peristaltic transport of a Casson (blood)-based hybrid nanofluid $\left(F{e}_2{O}_3-\mathrm{Cu}\right)$ via an asymmetric channel embedded inside a porous medium. The model takes into consideration electric and magnetic field effects, Ohmic heating, as well as velocity and thermal slip conditions. The governing equations are simplified and solved by employing unsupervised sigmoid-based neural networks (SNNs), Fibonacci-based neural networks (FNNs), and their hybrid model (FSNNs) under the assumptions of low Reynolds number and long wavelength. Furthermore, a comparative analysis is conducted among SNNs, FNNs, and FSNNs to evaluate their performance. The results reveal that the FSNNs demonstrate superior accuracy and stability compared to the other models. The results show that the temperature rises with larger values of the Grashof number, Brinkman number, and heat source/sink parameter, while lowers with higher values of Casson parameter, porosity factor, and velocity slip parameter. The pressure gradient grows with increasing $\mathrm{Gr}$, $\varrho$, and $U_{\mathrm{hs}},$ but decreases as Hartmann number increases. This study sheds light on the design of efficient microfluidic, biomedical, and thermal management systems, emphasizing the role of electromagnetic modulation and hybrid nanofluids in improving performance and control.