This investigation includes a three-dimensional Darcy–Forchheimer flow model and the heat transfer phenomenon of H2O-CNTs nanofluid for a two-way stretchable surface. Xue’s proposed thermal conductivity model is employed. The numerical analysis scheme is applied to solve the transformed PDEs. The outline of velocities, temperature, surface drag forces and Nusselt number against relevant variables are portrayed. From this study, it has been noted that with an increase in Eckert numbers along both directions, two patterns were obtained for temperature curves, the initial temperature outlines increased and after that they decreased. Moreover, the width of the thermal boundary layer for H2O-MWCNT nanofluid was more compared to H2O-SWCNT nanofluid. To validate the existing code, numerical outcomes were compared to the earlier published data.