Thermal and fluid behavior of nanofluids over a rotating disk: Influence of Darcy–Forchheimer and slip conditions

Understanding nanofluid flow over rotating disks embedded in porous media is crucial for advancing applications in thermal energy systems, microfluidics, and industrial cooling. This comprehensive study investigates nanofluids’ thermal and mass transport characteristics influenced by slip flow, magnetic effects, and the Darcy–Forchheimer porous medium model. The governing equations are transformed using similarity variables and solved using a modified operational matrix method with exceptional accuracy (truncation error 1 0 − 14 ). Numerical simulations reveal that increasing the Hartmann number H a from 0.0 to 1.0 leads to a 52% decrease in radial velocity f ′ ( η ) and a 28% increase in temperature profile θ ( η ) due to the damping effect of Lorentz forces. Similarly, increasing the velocity slip parameter α from 0.15 to 0.9 results in a 38% drop in radial velocity and a 27% rise in fluid temperature. The Brownian motion parameter N b and thermophoresis parameter N t significantly impact concentration profiles, with N t increasing θ ( η ) by 30% and reducing ϕ by 21%. Skin friction coefficients computed using our method match closely with benchmark solutions from Mathematica and literature, confirming model validity. These findings underscore the practical implications of our study. They demonstrate the strong coupling between magnetic, porous, and slip effects in either enhancing or suppressing transport phenomena. This insight offers a valuable guide for optimizing nanofluid-based systems in practical engineering applications, potentially leading to significant advancements in thermal energy systems, microfluidics, and industrial cooling.