The present article gives an analysis of the impact of Darcy–Forchheimer flow and partial slip along with heat transfer in single-wall carbon nanotube/multi-wall carbon nanotube (SWCNT/MWCNT)-water nanofluid flow over a stretching/shrinking rotating disk. The study considers the heat transfer in nanofluids, using both static and dynamic models, namely the Xue and Buongiorno models, respectively. The effects of thermal radiation and viscous dissipation are considered. Nonlinear transformed coupled equations are solved computationally using a spectral quasilinearisation method. The numerical results show the impact of several physical parameters on radial and tangential velocity, temperature and nanoparticle concentration fields. The slip parameter accounts for a significant enhancement in the radial velocity and a decline in the tangential/azimuthal velocity. The presence of a porous medium has the effect of reducing the amplitude of velocity and momentum layer thickness for both SWCNTs-water and MWCNTs-water nanofluids. The present study indicates that the tangential velocity of SWCNT/MWCNT-water nanofluids diminishes due to the increment in slip parameter, while the radial velocity exhibits the reverse trends. The results also show that the involvement of a porous matrix gives rise to reduced velocity of SWCNT/MWCNT-water nanofluids. It is also observed that MWCNTs make a greater contribution in augmenting the heat transfer rate compared to SWCNT nanoparticles.