*4.1. Skin Friction Coe*ffi*cients CFx*

Mathematically, it is defined as

$$\mathcal{C}\_{\text{F}\chi} = \frac{2\varphi\_{\text{uv}}}{\rho u\_{\text{\text{\textquotedblleft}op}}^2} \tag{19}$$

The dimensionless form is

$$\mathrm{Re}\_x^{1/2} \mathcal{C}\_{\mathrm{Fx}} = (1+K) \frac{1}{\left(1-\phi\right)^{2.5}} f^{\prime\prime}(0) \tag{20}$$

In which Re1/2 *<sup>x</sup>* designates Reynold number.

#### *4.2. Heat Transfer Rate*

*Nux* is

$$\text{Nu}\_{\text{X}} = \frac{\text{x}Q\_{w}}{k(\text{T}\_{w} - \text{T}\_{\text{ox}})} \tag{21}$$

where the heat flux *Qw* is

$$Q\_w = -\frac{k\_{nf}}{\kappa} \left( \frac{4\sigma\_\varepsilon}{3\kappa\kappa\_R} \mathbf{T}\_\infty \right)\_{\mathcal{O}}^3 + 1 \Big| \mathbf{T}\_y \Big|\_{y=0} \tag{22}$$

$$\mathrm{Re}\_x^{-1/2} \mathrm{Nu}\_x = -\frac{k\_{\mathrm{nf}}}{k\_f} (1 + Rd) \theta'(0) \tag{23}$$
