Irreversibility estimation in electroosmotic MHD shear thinning nanofluid flow through a microchannel with slip-dependent zeta potentials

Shear-thinning nanofluid is extremely useful in medical diagnostics and engineering devices for controlling transport processes. This involves using microchannel flow under pressure-driven and electromagnetic forces. Moreover, a combined model of non-Newtonian fluid provides a versatile framework to accurately simulate or predict fluid behavior in various industrial, scientific, and biomedical applications. In this study, we investigate the heat and mass transfer of a shear-thinning nanofluid as it flows through a vertical microchannel with permeable walls, with electrokinetic effects, slip-dependent zeta potential, and convective boundary conditions. To characterize the shear-thinning behavior, a combined Casson-Williamson non-Newtonian fluid model is utilized. The fluid motion comprises a fusion of pressure-induced and electroosmotic forces, influenced by thermal radiation and slip-dependent zeta potential. Using the MATLAB bvp4c solver, we highlight the effect of electroosmotic flow (EOF) for the nanofluid by solving the non-dimensional differential equations resulting from the governing equations. Graphical representations of important engineering quantities are used to identify the critical influential factors. Our results show that thinner electric double layers (EDLs) amplify the influence of the Casson-Williamson parameters on the temperature profile. Additionally, the impact of the Williamson parameter at $\eta =1.0$ on concentration distribution is enhanced for higher electroosmotic parameters. We observe that heat transfer plays a minimal role in entropy generation in the core region of the channel but increases exponentially near the walls. Conversely, entropy production due to mass transfer is negligible away from the walls. However, the Casson parameter $\beta$ favors entropy production throughout the channel cross-section, while the Williamson parameter $\Gamma$ shows the reverse effect in both halves of the channel. This study has significant implications for the advancement of electro-magneto-mechanical devices and the improvement of efficiency and functionality, particularly in micro-scale thermal management applications.