Nonlinear radiative CNTs nanofluid flow over an inclined rotating disk: engineering insights into PST–PHF thermal regulation

This research examines the unsteady, axisymmetric flow and thermal transfer of water-based single-wall and multi-wall carbon-nanotube (SWCNT/MWCNT) nanofluids over a permeable, inclined spinning disk, including factors such as velocity slip, suction, Hall current, buoyancy, and nonlinear thermal radiation. Prescribed surface temperature (PST) and prescribed heat flux (PHF) are treated independently. The boundary-layer equations are simplified using similarity variables into a linked nonlinear boundary-value problem. The effective CNT thermal conductivity is estimated via the aspect-ratio-sensitive Yamada–Ota model. The equations are solved using the MATLAB bvp4c program with residual-controlled fourth-order collocation for 0≤η≤4 and a relative tolerance of 10⁻⁵. The reported findings and benchmark wall slopes are within 0.071% of each other. Within the stated ranges, an increase in the CNT volume percentage from 0.01 to 0.04 improves the dimensionless Nusselt number by 115.1% for PST and 148.6% for PHF, while an increase in the radiation parameter from 0.1 to 1.0 decreases it by 82.2% for PST and 0.9% for PHF. Elevating the slip parameter from 0.1 to 1.0 results in a reduction of the radial skin-friction coefficient by around 70.8%. The findings indicate that the imposed temperature state greatly influences the perceived sensitivity to radiation and CNT loading. These results provide a comparative framework for optimal rotating-disk cooling, spin coating, centrifugal processing, and rotating heat-exchanger surfaces functioning under temperature-regulated or flux-regulated heating.