**3. Thermophysical Properties of Nanofluids**

The properties of base fluid, water and considered nanoparticles, Al2O<sup>3</sup> and Cu are depicted in Table 1 [36,37]. The considered Al2O<sup>3</sup> and Cu nanoparticles are of spherical shape with 100 nm size. The thermophysical properties of single particle nanofluid and hybrid nanofluid are calculated using equations presented in Subsections (a) and (b) based on the depicted properties of basefluid and nanoparticles in Table 1. The widely used models in the open literature are employed to evaluate the thermophysical properties of single particle and hybrid nanofluids. All thermophysical properties are calculated by assuming the constant temperature hence, the temperature effect is neglected [5].

**Table 1.** Properties of base fluid and nanoparticles.


(a) Single particle nanofluid properties [38,39]; Volume fraction of nanoparticles in nanofluid

$$\mathcal{O} = \frac{V\_{np}}{V\_{bf} + V\_{np}} \tag{7}$$

Density of nanofluid

$$
\rho\_{nf} = (1 - \mathcal{Q})\rho\_{bf} + \mathcal{Q}\rho\_{np} \tag{8}
$$

Specific heat of nanofluid

$$\mathbb{C}\_{p,nf} = \frac{(1 - \mathcal{O})\rho\_{bf}\mathbb{C}\_{p,bf} + \mathcal{O}\rho\_{np}\mathbb{C}\_{p,np}}{\rho\_{nf}} \tag{9}$$

Thermal conductivity of nanofluid

$$\frac{k\_{nf}}{k\_{bf}} = \frac{\left(k\_{np} + 2k\_{bf}\right) - 2\mathcal{O}\left(k\_{bf} - k\_{np}\right)}{\left(k\_{np} + 2k\_{bf}\right) + \mathcal{O}\left(k\_{bf} - k\_{np}\right)}\tag{10}$$

Viscosity of nanofluid

$$
\mu\_{nf} = \mu\_{bf} \frac{1}{\left(1 - \mathcal{O}\right)^{2.5}} \tag{11}
$$

Here, Ø is volume fraction of nanoparticles in nanofluid, *Vb f* (L) is volume of basefluid, *<sup>V</sup>np* (L) is volume of nanoparticles = *<sup>m</sup>np ρnp* , *mnp* (kg) is mass of nanoparticles, *ρnp* (kg/m<sup>3</sup> ) is density of nanoparticles, *ρn f* (kg/m<sup>3</sup> ) is density of nanofluid, *ρb f* (kg/m<sup>3</sup> ) is density of base fluid, *Cp*,*n f* (J/kg·K) is specific heat of nanofluid, *Cp*,*b f* (J/kg·K) is specific heat of basefluid, *Cp*,*np* (J/kg·K) is specific heat of nanoparticles, *kn f* (W/m·K) is thermal conductivity of nanofluid, *kb f* (W/m·K) is thermal conductivity of basefluid, *knp* (W/m·K) is thermal conductivity of nanoparticle, *µn f* (Pa·s) is viscosity of nanofluid and *µb f* (Pa·s) is viscosity of basefluid.

(b) Hybrid nanofluid properties [40];

Volume fraction of nanoparticles in nanofluid

$$\mathcal{O}\_{\text{hnf}} = \mathcal{O}\_{\text{np1}} + \mathcal{O}\_{\text{np2}} \tag{12}$$

Density of hybrid nanofluid

$$
\rho\_{\ln f} = \mathcal{O}\_{np1}\rho\_{np1} + \mathcal{O}\_{np2}\rho\_{np2} + \left(1 - \mathcal{O}\_{\ln f}\right)\rho\_{bf} \tag{13}
$$

Specific heat of hybrid nanofluid

$$\mathbb{C}\_{p, \ln f} = \frac{\mathcal{O}\_{np1} \rho\_{np1} \mathbb{C}\_{p, np1} + \mathcal{O}\_{np2} \rho\_{np2} \mathbb{C}\_{p, np2} + \left(1 - \mathcal{O}\_{\ln f}\right) \rho\_{bf} \mathbb{C}\_{p, bf}}{\rho\_{\ln f}} \tag{14}$$

Thermal conductivity of hybrid nanofluid

$$k\_{\rm hnf} = \frac{\frac{\mathcal{O}\_{\rm np1}k\_{\rm np1} + \mathcal{O}\_{\rm np2}k\_{\rm np2}}{\mathcal{O}\_{\rm Inf}} + 2k\_{bf} + 2\left(\mathcal{O}\_{\rm np1}k\_{\rm np1} + \mathcal{O}\_{\rm np2}k\_{\rm np2}\right) - 2\mathcal{O}\_{\rm hnf}k\_{bf}}{\frac{\mathcal{O}\_{\rm np1}k\_{\rm np1} + \mathcal{O}\_{\rm np2}k\_{\rm np2}}{\mathcal{O}\_{\rm hnf}} + 2k\_{bf} - 2\left(\mathcal{O}\_{\rm np1}k\_{\rm np1} + \mathcal{O}\_{\rm np2}k\_{\rm np2}\right) + \mathcal{O}\_{\rm hnf}k\_{bf}}} \tag{15}$$

Viscosity of hybrid nanofluid

$$
\mu\_{\text{hnf}} = \mu\_{bf} \frac{1}{(1 - \mathcal{O}\_{np1} - \mathcal{O}\_{np2})^{2.5}} \tag{16}
$$

Here, Ø*hn f* is volume fraction of hybrid nanofluid, Ø*np*<sup>1</sup> is volume fraction of nanoparticle1, Ø*np*<sup>2</sup> is volume fraction of nanoparticle2, *ρhn f* (kg/m<sup>3</sup> ) is density of hybrid nanofluid, *ρnp*<sup>1</sup> (kg/m<sup>3</sup> ) is density of nanoparticle1, *ρnp*<sup>2</sup> (kg/m<sup>3</sup> ) is density of nanoparticle2, *Cp*,*hn f* (J/kg·K) is specific heat of hybrid nanofluid, *Cp*,*np*<sup>1</sup> (J/kg·K) is specific heat of nanoparticle1, *Cp*,*np*<sup>2</sup> (J/kg·K) is specific heat of nanoparticle2, *khn f* (W/m·K) is thermal conductivity of hybrid nanofluid, *knp*<sup>1</sup> (W/m·K) is thermal conductivity of nanoparticle1, *knp*<sup>2</sup> (W/m·K) is thermal conductivity of nanoparticle2 and *µhn f* (Pa·s) is viscosity of hybrid nanofluid.

The volume fractions of 0.5%, 1.0% and 1.5% as well as density, specific heat, thermal conductivity and viscosity of water, Al2O<sup>3</sup> and Cu nanoparticles as shown in Table 1 are imported in Equations (7)–(16) to calculate the density, specific heat, thermal conductivity and viscosity of single particle Al2O<sup>3</sup> and hybrid Al2O3/Cu nanofluids. The calculated properties of Al2O<sup>3</sup> and Al2O3/Cu nanofluids are elaborated in Section 5.2.
