A multi-technique optimization for boosting energy transmission in time-dependent MHD Casson nanofluid flow under convective boundary conditions

This study optimizes energy transmission in magnetohydrodynamic (MHD) Casson nanofluid flow between parallel disks under convective boundary conditions. A semi-analytical approach using Akbari–Ganji's Method (AGM) solves the complex governing equations, while statistical techniques, including Taguchi’s method, Response Surface Methodology (RSM) and Analysis of Variance (ANOVA), are applied to identify key parameters influencing energy transmission. The study examines the effects of structural and physical parameters, such as suction/injection conditions, magnetic field strength and nano-transport properties, on velocity, temperature and concentration profiles. Results show that geometric-flow parameters and nano-transport properties significantly impact momentum and heat/mass transfer. The results show that the geometric-flow parameter, namely the suction parameter (S), induces region-dependent nonlinear variations in the velocity field, with more pronounced effects under injection conditions due to the additional mass inflow that enhances local acceleration and flow recovery compared to suction. Statistical analysis confirms high predictive reliability, with R² values of 0.9993 for skin friction and 0.9996 for Nusselt number. The study identifies optimized parameter combinations for controlling energy transmission, offering a pathway for enhancing heat and mass transfer without structural redesign. This research provides a strategy for improving energy efficiency through tailored parameter tuning. The findings of this research can be applied to enhance heat and mass transfer in various industrial and biomedical systems, such as energy generation, refrigeration and medical treatments. By optimizing the key parameters in MHD Casson nanofluid flow, this study provides a practical approach for improving the efficiency of thermal management processes without the need for structural redesign.