Influence of cross-diffusion on an unsteady inclined magnetised Carreau nanofluid flow over a rough sphere

A fascinating aspect of electromagnetic phenomena is the dynamic interaction between magnetic forces and directional inclinations, emphasized by the captivating notion of an angled magnetic field and the effects of non-Newtonian fluids. The applications of the Carreau fluid in biomedical engineering, polymer processing, petroleum, and chemical engineering enlighten the importance of the present study. This study investigates cross-diffusion dynamics in a Carreau nanofluid around a rough sphere within an inclined magnetic field environment. The partial differential equations (PDEs) that describe the fluid flow system give rise to nondimensional PDEs due to the application of non-similar transformations. Finally, the implicit finite difference approach is employed to numerically solve the Quasilinearized partial differential equations. The numerical results are obtained in MATLAB. Transitioning from Newtonian nanofluid to Carreau nanofluid results in a significant increase and decrease of around 11% and 61% in the energy transfer and friction coefficient values, respectively, for the shear thickening scenario. Larger roughness amplitudes are associated with more pronounced roughness effects, manifesting as more extensive oscillations. The fluid velocity is slowed down to improve the inclination angle α1 and magnetic attribute M.