1.2.6. The Effective Thermal Conductivity Model

In the literature, there are several theoretical models available to calculate the thermal conductivities of carbon nanotubes (e.g., Maxwell's, Jeffery's, Davis's, Hamilton's, and crosser models), but only Xue's model [44] employs principal models, which are effective for spherical and elliptical shape particles. Xue's model was established from the Maxwell model of turning elliptical carbon nanotubes through a big axial ratio and paying the effect of the space sharing on CNTs. Here, for the thermal conductivity of nanofluid *kn f* , Xue's model [44] has been utilized.

$$\frac{k\_{nf}}{k\_f} = \frac{1 - \varrho + 2\varrho\left(\frac{k\_{CNT}}{k\_{CNT} - k\_f}\right)\ln\left(\frac{k\_{CNT} + k\_f}{2\ k\_f}\right)}{1 - \varrho + 2\varrho\left(\frac{k\_f}{k\_{CNT} - k\_f}\right)\ln\left(\frac{k\_{CNT} + k\_f}{2\ k\_f}\right)}.\tag{6}$$

*k <sup>f</sup>* , *kCNT* signify the thermal conductivity of the base fluid and CNTs, respectively.
