This paper presents Darcy–Forchheimer three-dimensional (3D) flow of water-based carbon nanotubes (CNTs) with heterogeneous–homogeneous reactions. A bi-directional linear extendable surface has been employed to create the flow. Flow in porous space is represented by Darcy–Forchheimer expression. Heat transfer mechanism is explored through convective heating. Equal diffusion coefficients are considered for both autocatalyst and reactants. Results for single-wall carbon nanotube (SWCNT) and multiwall carbon nanotube (MWCNT) have been presented and compared. The diminishment of partial differential framework into nonlinear ordinary differential framework is made through suitable transformations. Optimal homotopy scheme is used for arrangements development of governing flow problem. Optimal homotopic solution expressions for velocities and temperature are studied through plots by considering various estimations of physical variables. The skin friction coefficients and local Nusselt number are analyzed through plots. Our findings depict that the skin friction coefficients and local Nusselt number are enhanced for larger values of the nanoparticles volume fraction.