*3.6. Performance Index and Performance Evaluation Criterion*

*3.6. Performance Index and Performance Evaluation Criterion* Figures 9 and 10 show changes in the performance characteristics of PI and PEC for different types of nanofluid vs. Re-numbers. The average PI, generally with PEC of the analyzed nanofluid, was noted to be >1 [34], indicating the effectiveness of the well-prepared nano-coolants for heated pipe flows. In addition, the carbon-based nanofluids presented higher augmentation of the metallic oxides due to a better rise in heat transport than the increased pressure loss. The PI of carbon and metallic oxides-based nanofluids improved with the Re-number; the maximum thermal efficiency of the nanofluids increased as follows: PEG@GNPs = 2.14, PEG@TGr = 2.05, Al2O<sup>3</sup> =1.23, and SiO<sup>2</sup> = 1.19 at Re Figures 9 and 10 show changes in the performance characteristics of PI and PEC for different types of nanofluid vs. Re-numbers. The average PI, generally with PEC of the analyzed nanofluid, was noted to be >1 [34], indicating the effectiveness of the wellprepared nano-coolants for heated pipe flows. In addition, the carbon-based nanofluids presented higher augmentation of the metallic oxides due to a better rise in heat transport than the increased pressure loss. The PI of carbon and metallic oxides-based nanofluids improved with the Re-number; the maximum thermal efficiency of the nanofluids increased as follows: PEG@GNPs = 2.14, PEG@TGr = 2.05, Al2O<sup>3</sup> = 1.23, and SiO<sup>2</sup> = 1.19 at Re = 11,907, 0.1 wt.%, and 11,205 W/m<sup>2</sup> . This phenomenon was caused by the increased viscosity and thermal conductivity of nanofluids. The dynamic viscosity of a nanofluid can be increased to reduce the thickness of the boundary layer, resulting in an increase in heat transfer, while enhancing thermal conductivity enhances the thermal performance factor [18]. These results also confirm that the positive effects of heat transfer compensate for the negative impacts of pressure loss for carbon and metal-oxide nanofluids within a wide range of inlet temperatures, mass concentrations, and constant flow rates, stating that prepared nanofluids have excellent convective heat transfer capabilities.

A = 0.804 B = 8 × 10−<sup>5</sup> R<sup>2</sup> = 0.9917

pared nanofluids have excellent convective heat transfer capabilities.

. This phenomenon was caused by the increased vis-

A = 0.9799 B = 2 × 10−<sup>5</sup> R<sup>2</sup> = 0.9956

cosity and thermal conductivity of nanofluids. The dynamic viscosity of a nanofluid can be increased to reduce the thickness of the boundary layer, resulting in an increase in heat transfer, while enhancing thermal conductivity enhances the thermal performance factor [18]. These results also confirm that the positive effects of heat transfer compensate for the negative impacts of pressure loss for carbon and metal-oxide nanofluids within a wide range of inlet temperatures, mass concentrations, and constant flow rates, stating that pre-

= 11,907, 0.1 wt.%, and 11,205 W/m<sup>2</sup>

**Figure 9.** PI against different nanofluids and Reynolds number. **Figure 9.** PI against different nanofluids and Reynolds number.

**Figure 10.** PEC of different nanofluids against Reynolds number. **Figure 10.** PEC of different nanofluids against Reynolds number.

Additionally, the findings of the PEC have shown a slight reduction in Re numbers. The maximum performance assessment of the nanofluids was as follows: PEG@GNPs = 1.52, PEG@TGr =1.41, Al2O3 = 1.24, and SiO2 = 1.26. Additionally, the findings of the PEC have shown a slight reduction in Re numbers. The maximum performance assessment of the nanofluids was as follows: PEG@GNPs = 1.52, PEG@TGr = 1.41, Al2O<sup>3</sup> = 1.24, and SiO<sup>2</sup> = 1.26.

#### *3.7. Pumping Power of Different Nanofluids 3.7. Pumping Power of Different Nanofluids*

less than 1.

When choosing a heat exchanger, several criteria are the heat transfer rate, pumping power, cost, size and weight, type, and material. Friction effects in nanofluids cause pres‐ sure loss, and pressure loss calculations influence pumping power needs. Increased pumping power will result in more extraordinary capital expenses because larger pumps are more expensive and have higher operational costs due to the higher pumping power required. Pumping power measures a system's financial ability to increase industrial and electrical energy. During the design of heat exchangers, it is essential to ensure low pump‐ ing power but effective heat transfer to ensure energy conservation. Figure 11 presents the When choosing a heat exchanger, several criteria are the heat transfer rate, pumping power, cost, size and weight, type, and material. Friction effects in nanofluids cause pressure loss, and pressure loss calculations influence pumping power needs. Increased pumping power will result in more extraordinary capital expenses because larger pumps are more expensive and have higher operational costs due to the higher pumping power required. Pumping power measures a system's financial ability to increase industrial and electrical energy. During the design of heat exchangers, it is essential to ensure low pumping

pumping power for prepared nano‐coolants at various Re with the working fluids. As the pumping power is dependent on the dynamic viscosity and density of both base fluid and

power but effective heat transfer to ensure energy conservation. Figure 11 presents the pumping power for prepared nano-coolants at various Re with the working fluids. As the pumping power is dependent on the dynamic viscosity and density of both base fluid and the nanofluids (Equation (13)), the relative pumping power for all the tested samples is less than 1. *Nanomaterials* **2022**, *12*, x FOR PEER REVIEW 17 of 21

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