Unsteady MHD Casson ternary hybrid nanofluid flow over a rotating inclined disk in a non-Darcy porous medium: a comparative study of Xue and Yamada–Ota models

Purpose This study aims to analyze the unsteady magnetohydrodynamic (MHD) flow of a non-Newtonian Casson ternary hybrid nanofluid (THNF) over a rotating, and inclined disk embedded in a non-Darcy porous medium. Particular attention is given to the comparative performance of the Xue and Yamada–Ota models in predicting the thermal and transport behaviors. Design/methodology/approach Similarity transformations are used to reduce the governing coupled partial differential equations into a nonlinear system of ordinary differential equations. The system is solved numerically via the BVP4C algorithm in MATLAB. To ensure accuracy, the obtained results are validated against established benchmark solutions, confirming excellent consistency. Findings The analysis of Casson THNF reveal superior thermal transport properties compared to conventional fluids. This enhancement is particularly pronounced under strong magnetic fields, high porosity and inclined disk configurations. Furthermore, the analysis reveals that thermal radiation markedly enhances the fluid temperature and heat transfer characteristics. It is also found that the Xue model shows slightly more substantial heat transfer augmentation then the Yamada–Ota model. Overall, these results demonstrate that THNF provide significant improvements in energy transport compare to hybrid and mono nanoparticles. Originality/value Previous studies have not examined the comparative influence of the Xue and Yamada Ota models on unsteady THNF fluid flow under specific condition. To address this gape, this study investigates this flow over a rotating inclined desk within a porous medium, incorporating thermal radiation, MHD and Joule heating effects.