Dynamical and statistical analysis of tiny particles magnetization in radiative and convective Marangoni–Casson fluid with heat loss and Ohmic heating

Nanofluids with Marangoni–Casson convective-driven behaviour have attracted substantial scientific attention owing to thermal conduction capabilities and extensive usefulness in industrial heat exchangers, microfluidics, biomedical engineering, and others. Motivated by the engineering systems’ predictive modelling and efficient thermal regulation needs, this study examines the dynamical and statistical analysis of tiny particles magnetization in radiative and convective Marangoni–Casson fluid with heat loss and Ohmic heating. A coupled mathematical model is developed using boundary-layer approximations and similarity variables. The resulting nonlinear derivative models are solved via a shooting technique jointly with a fourth-order Runge–Kutta scheme. A statistical technique is used to determine the sensitivity of parameters and engineering quantities’ predictive relationships. The results depict that buoyancy forces pointedly augment fluid velocity, while the magnetic field, Casson fluid term, and medium resistance porosity damp momentum transport. Thermal distribution is amplified by porosity and Casson terms due to Ohmic heating mechanisms, and the species transport reduces with Brownian motion and Schmidt number. The Statistical analyses show high predictive capabilities with regression models of approximately 85.11%, 96.04%, and 73.84% of the engineering quantities variability. The findings offer guidance for the design and optimization of thermal biomedical therapies, solar collectors, and coating technologies.