*3.3. Validation Test for Distilled Water*

The Nuavg and heat transfer coefficients (h) obtained with the data from Equations (7)–(9) are disclosed in Figure 6a–c. The data demonstrated outstanding agreement between the present findings and equations such as <8% with the Petukhov formula. The Gnielinski equation is better at low-range Re than the Petukhov equation at higher Re-values [43]. Figure 6b–d demonstrated the relative errors between the collected and equations data for average heat transfer coefficients and Nuavg.

**Figure 6.** The verification assessment; (**a**) heat transfer coefficients measurement and prediction for 11,205 W/m2, (**b**) the magnitude of the relative error metric, (**c**) The value of the average Nusselt number at 11,205 W/m2, (**d**) the magnitude of the relative error metric, (**e**) Frictional head loss, (**f**) the magnitude of the relative error metric, (**g**) Pressure loss, (**h**) the magnitude of the relative error metric. **Figure 6.** The verification assessment; (**a**) heat transfer coefficients measurement and prediction for 11,205 W/m<sup>2</sup> , (**b**) the magnitude of the relative error metric, (**c**) The value of the average Nusselt number at 11,205 W/m<sup>2</sup> , (**d**) the magnitude of the relative error metric, (**e**) Frictional head loss, (**f**) the magnitude of the relative error metric, (**g**) Pressure loss, (**h**) the magnitude of the relative error metric.

Assessment of the experimental friction factor was calculated based on the measurement of the pressure loss in the entire applied heating pipe. The validation and verifica-

The prepared samples in this study were made without adding surfactant due to their long-term stability [46]. The present study analyzed functionalized and commercial metallic oxide nanofluids to enhance convective heat transfer inside a square heat exchanger. Essentially, turbulent forced convective flow is typically conducted under heat

The convective heat transfer coefficients of the functionalized and metal oxides-based nanofluids are shown in Figure 7a versus multiple nanofluids and Re-numbers. Increased nanofluids convective heat transfer coefficient as the velocity of the working fluid increased. This improvement resulted from solid nanoparticles' Brownian forces, thermal diffusion, and thermophoresis [47]. In the meantime, the increase in heat transfer might also result from the thin thermal boundary layer, which caused the higher velocities that caused thermal conductivity and decreased thermal resistance between the flowing nanofluid and the temperature of the internal wall surface of the heated pipe. Compared to DW, the maximum increase in heat transfer coefficients was as follows: PEG@GNPs = 44.4%, PEG@TGr = 41.2%, Al2O3 = 22.5%, and SiO2 = 24% at 0.1 wt.%. As per experimental data, the increase in heat transfer, as per test data, may be due either to the delay of the thermal boundary layers or due to increased thermal conductivity of the nanofluids.

smooth pipes [44,45]. The validation of the experimental data for pressure loss and friction factor is shown in Figure 6e–g, while that of the data from the equations and the current

*3.4. Convective Heat Transfer of Functionalized Nanofluids* 

study is shown in Figure 6f–h.

transfer demands.

11,205 W/m<sup>2</sup>

metric.

number at 11,205 W/m<sup>2</sup>

Assessment of the experimental friction factor was calculated based on the measurement of the pressure loss in the entire applied heating pipe. The validation and verification procedures have been carried out using the Blasius and Petukhov equations for smooth pipes [44,45]. The validation of the experimental data for pressure loss and friction factor is shown in Figure 6e–g, while that of the data from the equations and the current study is shown in Figure 6f–h. Assessment of the experimental friction factor was calculated based on the measurement of the pressure loss in the entire applied heating pipe. The validation and verification procedures have been carried out using the Blasius and Petukhov equations for smooth pipes [44,45]. The validation of the experimental data for pressure loss and friction factor is shown in Figure 6e–g, while that of the data from the equations and the current study is shown in Figure 6f–h.

**Figure 6.** The verification assessment; (**a**) heat transfer coefficients measurement and prediction for

the magnitude of the relative error metric, (**g**) Pressure loss, (**h**) the magnitude of the relative error

, (**b**) the magnitude of the relative error metric, (**c**) The value of the average Nusselt

, (**d**) the magnitude of the relative error metric, (**e**) Frictional head loss, (**f**)

#### *3.4. Convective Heat Transfer of Functionalized Nanofluids 3.4. Convective Heat Transfer of Functionalized Nanofluids*

*Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 13 of 21

The prepared samples in this study were made without adding surfactant due to their long-term stability [46]. The present study analyzed functionalized and commercial metallic oxide nanofluids to enhance convective heat transfer inside a square heat exchanger. Essentially, turbulent forced convective flow is typically conducted under heat transfer demands. The prepared samples in this study were made without adding surfactant due to their long-term stability [46]. The present study analyzed functionalized and commercial metallic oxide nanofluids to enhance convective heat transfer inside a square heat exchanger. Essentially, turbulent forced convective flow is typically conducted under heat transfer demands.

The convective heat transfer coefficients of the functionalized and metal oxides-based nanofluids are shown in Figure 7a versus multiple nanofluids and Re-numbers. Increased nanofluids convective heat transfer coefficient as the velocity of the working fluid increased. This improvement resulted from solid nanoparticles' Brownian forces, thermal diffusion, and thermophoresis [47]. In the meantime, the increase in heat transfer might also result from the thin thermal boundary layer, which caused the higher velocities that caused thermal conductivity and decreased thermal resistance between the flowing nanofluid and the temperature of the internal wall surface of the heated pipe. Compared to DW, the maximum increase in heat transfer coefficients was as follows: PEG@GNPs = 44.4%, PEG@TGr = 41.2%, Al2O<sup>3</sup> = 22.5%, and SiO<sup>2</sup> = 24% at 0.1 wt.%. As per experimental data, the increase in heat transfer, as per test data, may be due either to the delay of the thermal boundary layers or due to increased thermal conductivity of the nanofluids. The convective heat transfer coefficients of the functionalized and metal oxides-based nanofluids are shown in Figure 7a versus multiple nanofluids and Re-numbers. Increased nanofluids convective heat transfer coefficient as the velocity of the working fluid increased. This improvement resulted from solid nanoparticles' Brownian forces, thermal diffusion, and thermophoresis [47]. In the meantime, the increase in heat transfer might also result from the thin thermal boundary layer, which caused the higher velocities that caused thermal conductivity and decreased thermal resistance between the flowing nanofluid and the temperature of the internal wall surface of the heated pipe. Compared to DW, the maximum increase in heat transfer coefficients was as follows: PEG@GNPs = 44.4%, PEG@TGr = 41.2%, Al2O<sup>3</sup> = 22.5%, and SiO<sup>2</sup> = 24% at 0.1 wt.%. As per experimental data, the increase in heat transfer, as per test data, may be due either to the delay of the thermal boundary layers or due to increased thermal conductivity of the nanofluids.

Figure 7b introduced Nuavg at 11,205 W/m<sup>2</sup> and the Re-number function. The Nuavg revealed an increase for each tested nanofluid. Observable higher Nuavg of nanofluids reflected the decline in the circulation temperature after the working fluid had risen thermal conductivity; this subsequently reduced the temperature gradient between the wall of the Figure 7b introduced Nuavg at 11,205 W/m<sup>2</sup> and the Re-number function. The Nuavg revealed an increase for each tested nanofluid. Observable higher Nuavg of nanofluids reflected the decline in the circulation temperature after the working fluid had risen thermal conductivity; this subsequently reduced the temperature gradient between the wall of the tube and bulk fluid contained in the test-section. The maximum rise in Nuavg was noted as follows: PEG@GNPs = 54%, PEG@TGr = 43%, SiO<sup>2</sup> = 28%, and Al2O<sup>3</sup> = 26% associated with DW.
