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The purpose of this paper is to construct mathematical model for squeezed flow of carbon-water nanofluid between parallel disks considering Darcy–Forchheimer porous medium. Thermal conductivity of carbon nanotubes is estimated through the well-known Xue model. Such research work is not carried out in the past even in the absence of Darcy–Forchheimer porous space. Forchheimer equation is preferred here to account for both low and high velocity inertial effects. Researchers also found that dispersion of carbon nanotubes in water elevates the thermal conductivity of resulting nanofluid by 100 per cent.

Homotopy analysis method (HAM) is used for the convergent series solutions of the governing system.

Nusselt number at the lower disk increases when squeezing parameter Sq enlarges. This illustrates that heat transfer rate at the lower wall can be enhanced by increasing the squeezing velocity of the lower disk. The results demonstrate a decreasing trend in temperature profile for increasing volume fraction of carbon nanotubes. Moreover, improvement in heat transfer rate because of existence of carbon nanotubes is also apparent. A significant enhancement in temperature profile is depicted when inertial permeability coefficient is enhanced. Skin friction coefficients at the lower and upper disks are higher for MWCNTs in comparison to the SWCNTs.

To the best of author’s knowledge, no such consideration has been given in the literature yet.