Residual error analysis of Jeffrey hybrid nanofluid flow over a rotating sphere with Cattaneo-Christov heat flux and exothermic chemical reaction: a comparative study of spherical and platelet nanoparticles

Abstract This study aims to investigate the unsteady Jeffrey hybrid nanofluid movement past a rotating sphere, incorporating couple stress effects and Cattaneo-Christov heat flux while examining activation energy’s role in heat and mass transfer dynamics. The study of Jeffrey hybrid nanofluid motion past a rotating sphere is crucial for improving thermal management systems, as it combines non-Newtonian fluid traits with enhanced heat transfer from blended nanoparticles. Practically, this flow model supports the design of more efficient cooling processes in rotating machinery, such as turbine blades or spherical bearings. The transformed governing equations are solved using the bvp4c solver in MATLAB, with rigorous residual error analysis demonstrating stable convergence to O (10 −6 ) within six iterations. A key focus is the comparative analysis of two nanoparticle shapes – spherical and platelet – to evaluate their impact on thermal and hydrodynamic performance. Key results indicate that the velocity profile diminishes with rising Deborah number ( De ) and couple stress parameter, while temperature profiles are suppressed by thermal relaxation but enhanced by radiation and activation energy ( A ). Concentration profile exhibits an inverse relationship with reaction rate. It is found that friction factor rises at a rate of 6.13 % (in both cases) when the value of De falls between 0 and 3. The Nusselt number falls at rates of 1.05 % for spherical shape and 1.17 % for other case when the value of A ranges from 0 to 3. The Sherwood number drops at a rate of 1.6 % for spherical shape and 1.5 % for other case when the value of A ranges from 0 to 3. Entropy generation rises with nanoparticle volume fraction, shifting irreversibility dominance from thermal to viscous effects. The study’s numerical approach ensures high accuracy (residuals ∼10 −6 ), offering insights for optimizing nanofluid applications in microfluidics and thermal systems.