*2.3. Hybrid Nanofluid Modelling*

The density ρ*hn f* , viscosity μ*hn f* , thermal expansion coefficient β*hn f* , thermal conductivity *khn f* of the hybrid nanofluid, and heat capacity *cp hn f* are given according to [18,19], as:

$$
\rho\_{\rm Inf} = \left(1 - q \rho\_{\rm np2}\right) \left\{ (1 - q \rho\_{\rm np1}) \rho\_f + q \rho\_{\rm np1} \rho\_{\rm np1} \right\} + q \rho\_{\rm np2} \rho\_{\rm np2} \tag{17}
$$

$$
\mu\_{\rm Inf} = \mu\_{bf} \left( 1 - \varphi\_{\rm np1} \right)^{-2.5} \left( 1 - \varphi\_{\rm np2} \right)^{-2.5},
\tag{18}
$$

$$\left(\rho c\_{p}\right)\_{\text{luf}} = \left(1 - \rho \eta \, \mathrm{p}\right) \big(1 - \rho \, \mathrm{p}\big) \big(\rho c\_{p}\big)\_{f} + \left.\rho \, \mathrm{p}\big(\rho c\_{p}\big)\_{\text{np}1}\right| + \left.\rho \eta \, \mathrm{p}\big(\rho c\_{p}\big)\_{\text{np}2} \tag{19}$$

$$(\rho\beta)\_{\text{lnf}} = \left(1 - q\rho\_{\text{np2}}\right) \left(1 - q\rho\_{\text{np1}}\right) (\rho\beta)\_f + q\rho\_{\text{np1}} (\rho\beta)\_{\text{np1}} + q\rho\_{\text{np2}} (\rho\beta)\_{\text{np2}} \tag{20}$$

$$\frac{k\_{\rm hnf}}{k\_{bf}} = \frac{k\_{\rm np2} + (n-1)k\_{bf} - (n-1)\varphi\_{\rm np2}(k\_{bf} - k\_{\rm np2})}{k\_{\rm np2} + (n-1)k\_{bf} + \varphi\_{\rm np2}(k\_{bf} - k\_{\rm np2})},\tag{21}$$

$$\frac{k\_{nf}}{k\_{bf}} = \frac{(n-1)k\_{bf} + k\_{np1} - (n-1)\,\varphi\_{np1} \Big(k\_{bf} - k\_{np1}\Big)}{(n-1)k\_{bf} + k\_{np1} + \varphi\_{np1} \Big(k\_{bf} - k\_{np1}\Big)}\,\tag{22}$$

The subscripts *np*<sup>1</sup> and *np*<sup>2</sup> represent the nanoparticles of Al2O3 and Cu, whereas *b f* and *hn f* represent the base fluid and hybrid nanofluid. The symbol ϕ is the fraction of whole volume, which is the combination of two different types of nanoparticles, Alumina–Copper dispersed in the transferor fluid in order to develop the hybrid nanofluid, which is: ϕ = ϕ*np*<sup>1</sup> + ϕ*np*2.
