Contour and regression insights into Casson–Williamson nanofluid flow with suction/injection, hall currents, and ion slip effects

The focus of this article is on the analysis of mass and energy transmission for the viscous dissipative Casson Williamson nanofluid in the presence of ion slip effect and hall current. The ordinary differential equations are formed by similarity transformation from governing equations. Fifth-order Runge–Kutta–Fehlberg scheme is utilized to solve extremely non-linear ordinary differential equations via shooting approach. Physical mechanisms for different parameters are graphically presented and well explained. The main results showed the velocity profile reduced for Casson and Williamson parameter. The quantitative findings for the Sherwood number, Nusselt number, and local skin friction coefficient across a range of parameters are shown which demonstrates that the rising values on suction parameter reduces the surface drag force by 73.99% and growing values of Prandtl number uplifts the energy transmission by 60.07% and elevating values of Lewis number enhances the mass transfer by 47.7%. Moreover, Contour analysis provides a thorough understanding of mass transport mechanisms, fluid behavior, and thermal efficiency. Additionally, computation of linear and quadratic regression analysis was carried out for different values of Brownian motion and thermophoresis parameter with suction and injection. Results indicate the sensitiveness of Nusselt number in thermophoresis parameter is higher than Brownian motion parameter for suction and opposite trend is found for injection. Studies from the literature were compared to the present investigation and the findings were determined to be in good agreement.