*2.3. Nanofluid Relations*

The density of nanofluid with various nanoparticle volume fraction is predicted by the Pak et al. [34] as shown in Equation (6). Zhong et al. [35] experimentally measured the density of TiO2-water nanofluid and compared the predictions using the Equation (6) within 0.54%. Therefore, in the current study, the density of various nanofluids with different volume fraction is calculated using Equation (6), where ρ denotes density and φ denotes volume fraction.

$$
\rho\_{nf} = \phi \rho\_n + (1 - \phi)\rho\_f \tag{6}
$$

The viscosity of the nanofluid (µ*n f*) with various nanoparticle volume fraction (φ) using viscosity of fluid (µ*<sup>f</sup>* ) is predicted by various researchers including Batchelor [36], Vand [37], Wang et al. [38], Duangthongsuk et al. [39] and Bobbo et al. [40], as shown in Equations (7)–(11), respectivelyBased on the model prediction accuracy with experimental data [35], in the present study, the model proposed by Want et al. [38] is used for calculating the viscosity of nanofluid.

$$
\mu\_{nf} = \mu\_f \left( 1 + 2.5\phi + 6.5\phi^2 \right) \tag{7}
$$

$$
\mu\_{nf} = \mu\_f \left( 1 + 2.5\phi + 7.349\phi^2 \right) \tag{8}
$$

$$
\mu\_{nf} = \mu\_f \left( 1 + 7.3\phi + 123\phi^2 \right) \tag{9}
$$

$$
\mu\_{nf} = \mu\_f \left( 1.013 + 0.092\phi - 0.015\phi^2 \right) \tag{10}
$$

$$
\mu\_{nf} = \mu\_f \left( 1 + 0.36838\phi + 0.25271\phi^2 \right) \tag{11}
$$

The thermal conductivity and specific heat of nanofluid for various volume fractions are calculated using Equation (12) [41] and Equation (13) [42], respectively. The effect of the nanoparticle volume fraction on the mixture properties is presented in Figure 2.

$$k\_{nf} = k\_f \frac{k\_p + 2k\_f + 2\phi \left(k\_p - k\_f\right)}{k\_p + 2k\_f - 2\phi \left(k\_p - k\_f\right)}\tag{12}$$

$$\left(\rho \mathbb{C}\_p\right)\_{nf} = (1 - \phi) \left(\rho \mathbb{C}\_p\right)\_f + \phi \left(\rho \mathbb{C}\_p\right)\_n \tag{13}$$

*(ρCp)nf=*

൫*1--ϕ*൯*(ρCp)f*

*+ϕ(ρCp)n* (13)

**Figure 2.** Effect of nanoparticle volume fraction on the mixture properties. **Figure 2.** Effect of nanoparticle volume fraction on the mixture properties.
