In this article, the hybrid nanofluid flow across the hot substrate of a heated sink coated with an open-cell metallic foam is explored to increase the rate of heat transfer. Two sorts of nanoparticles are considered to be specific MWCNT and SWCNT taking water as the base liquid. Tiny particles are examined because of their remarkable properties, such as exceptional thermal conductance, which is important in modern nano-technology, cooling systems, material sciences, and electronic parts. The primary goal of this extensive study is to improve heat transportation. The mathematical equations for the considered flow are the Navier–Stokes equations in the form of the Darcy–Brinkman–Forchheirmer model. Using similarity variables, a system of PDEs is converted into a system of dimensionless ODEs. The subsequent ODEs are settled by utilizing the numerical technique bvp4c in MATLAB. The significant results are presented with the guide of figures and tables. From this analysis, it is observed that the Xue model has a larger heat transport rate than the Yamada–Ota and Tiwari–Das models. Furthermore, the Xue model achieves a higher skin friction coefficient and Nusselt number values than the Yamada–Ota and Tiwari–Das models.