5.3.3. Pressure Drop

The variation of pressure drop for water, single particle and hybrid nanofluids with various volume fractions and Reynolds number is depicted in Figure 6. The pressure drop increases with increase in the Reynolds number because the turbulence increases as the Reynolds number increases for all working fluids. However, the variation trend of pressure drop with Reynolds number is not linear for all working fluids. The variation trend is exponential as confirmed by many research studies in the open literature. Kristiawan et al.

have presented the exponential (non-linear) variation of pressure drop with Reynolds number and pressure drop increases with Reynolds number for various working fluids flow in a tube [8]. Pressure drop of single particle and hybrid nanofluids are higher than water because the viscosity of single particle and hybrid nanofluids are higher compared to water. In addition, the viscosity of single particle and hybrid nanofluids increases as volume fraction increases due to dispersion of larger volume of nanoparticles into base fluid water. This results into increase of pressure drop with volume fraction for single particle and hybrid nanofluids. Despite of the same viscosity of single particle and hybrid nanofluids at the same volume fraction, the pressure drop for the hybrid nanofluid are lower than the single particle nanofluids for all volume fractions. The pressure drop of 2.0% Al2O<sup>3</sup> nanofluid is highest among all working fluids. The pressure drops of 2.0% Al2O<sup>3</sup> nanofluid and 2.0% Al2O3/Cu nanofluid are higher by 4.5% and 0.34%, respectively compared to water. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 11 of 19 number enhancement for graphene-oxide nanofluid as twice than water for horizontal circular tube under constant heat flux [45].

**Figure 5.** Comparison of Nusselt number of various working fluids with Reynolds number. **Figure 5.** Comparison of Nusselt number of various working fluids with Reynolds number.

#### 5.3.3. Pressure Drop 5.3.4. Friction Factor

compared to water.

The variation of pressure drop for water, single particle and hybrid nanofluids with various volume fractions and Reynolds number is depicted in Figure 6. The pressure drop increases with increase in the Reynolds number because the turbulence increases as the Reynolds number increases for all working fluids. However, the variation trend of pressure drop with Reynolds number is not linear for all working fluids. The variation trend is exponential as confirmed by many research studies in the open literature. Kristiawan et al. have presented the exponential (non-linear) variation of pressure drop with Reynolds number and pressure drop increases with Reynolds number for various working fluids flow in a tube [8]. Pressure drop of single particle and hybrid nanofluids are higher than water because the viscosity of single particle and hybrid nanofluids are higher compared to water. In addition, the viscosity of single particle and hybrid nanofluids increases as volume fraction increases due to dispersion of larger volume of nanoparticles into base fluid water. This results into increase of pressure drop with volume fraction for single particle and hybrid nanofluids. Despite of the same viscosity of single particle and hybrid nanofluids at the same volume fraction, the pressure drop for the hybrid nanofluid are lower than the single particle nanofluids for all volume fractions. The pressure drop of The effect of Reynolds number and volume fraction on friction factor of water, single particle and hybrid nanofluids is shown in Figure 7. The friction factor is affected by the pressure drop and velocity of working fluid. Therefore, the variation trend of friction factor for various working fluids are not same as of pressure drop. The considered Reynolds number range shows the transition from laminar to turbulent regime which results into parabolic variation trend of friction factor with Reynolds number for all working fluids. The friction factor increases up to the Reynolds number of 6000 and decreases beyond this value for all working fluids as can be seen from Figure 7. There is a critical Reynolds number below which the friction factor increases with increase in the Reynolds number due to change of flow from laminar to transition regime and above critical Reynolds number, the friction factor decreases with increase in the Reynolds number because of change of flow from transition to turbulent regime. However, it is important to note that the critical point (Re:6000) for friction factor variation over the Reynolds number is not same as commonly suggested Reynolds number for transition of flow to turbulent (Re:4000). The reason for different critical point of friction factor than commonly suggested is dependency of friction factor on ratio of pressure drop to square of velocity as presented

by Equation (21). Kristiawan et al. have presented the parabolic variation of friction factor with Reynolds number, the friction factor increases up to the critical Reynolds number of 5000 then decreases as the Reynolds number increases beyond the critical value [8]. Kaood et al. have also presented the non-linear trend of the friction factor with Reynolds number, the friction factor decreases as the Reynolds number increases in the turbulent regime [16]. The friction factors of single particle and hybrid nanofluids are higher than water which are increasing with increase in the volume fraction. This is because of higher viscosity of single particle and hybrid nanofluids compared to water which continuously increases with volume fraction. The density of the hybrid nanofluid is higher than the density of single particle nanofluid which results into lower velocity of hybrid nanofluid compared with single particle nanofluid. Therefore, the ratio of pressure drop to square of velocity the hybrid nanofluid shows higher friction factor than single particle nanofluid at the same volume fraction. Despite of lower pressure drop for hybrid nanofluid than single particle nanofluid, the higher density has caused higher friction factor. The friction factors of 0.5% Al2O3, 1.0% Al2O3, 2.0% Al2O3, 0.5% Al2O3/Cu, 1.0% Al2O3/Cu and 2.0% Al2O3/Cu nanofluids are higher by 1.5%, 2.9%, 5.9%, 2.6%, 5.2% and 10.3%, respectively compared to water. The 2.0% Al2O3/Cu nanofluid shows highest value of friction factor among all working fluids. The friction factor of 2.0% Al2O3/Cu nanofluid increases by 1.9% as the Reynolds number increases from 2000 to 12,000. Firoozi et al. have also presented the friction factor variation range from 0.02 to 0.14 for the maximum Reynolds number variation up to 5000 [3]. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 12 of 19

**Figure 6.** Variation of pressure drop for water, single particle and hybrid nanofluids with various volume fractions and Reynolds number. **Figure 6.** Variation of pressure drop for water, single particle and hybrid nanofluids with various volume fractions and Reynolds number.

#### 5.3.4. Friction Factor 5.3.5. Performance Evaluation Criteria

The effect of Reynolds number and volume fraction on friction factor of water, single particle and hybrid nanofluids is shown in Figure 7. The friction factor is affected by the pressure drop and velocity of working fluid. Therefore, the variation trend of friction factor for various working fluids are not same as of pressure drop. The considered Reynolds number range shows the transition from laminar to turbulent regime which results into parabolic variation trend of friction factor with Reynolds number for all working fluids. The friction factor increases up to the Reynolds number of 6000 and decreases beyond this value for all working fluids as can be seen from Figure 7. There is a critical Reynolds num-The performance evaluation criteria present the combined effect of thermal and flow characteristics because it is calculated based on the Nusselt numbers and friction factors of water and single particle and hybrid nanofluids. The comparison of performance evaluation criteria (PEC) for single particle and hybrid nanofluids with various volume fractions and Reynolds number is depicted in Figure 8. The effect of Reynolds number on the performance evaluation criteria of single particle and hybrid nanofluids is very small. This is because both Nusselt number and friction factor are affected significantly due to variation in Reynolds number. Hence, the overall effect of Reynolds number on

change of flow from laminar to transition regime and above critical Reynolds number, the friction factor decreases with increase in the Reynolds number because of change of flow from transition to turbulent regime. However, it is important to note that the critical point (Re:6000) for friction factor variation over the Reynolds number is not same as commonly suggested Reynolds number for transition of flow to turbulent (Re:4000). The reason for different critical point of friction factor than commonly suggested is dependency of friction factor on ratio of pressure drop to square of velocity as presented by Equation (21). Kristiawan et al. have presented the parabolic variation of friction factor with Reynolds number, the friction factor increases up to the critical Reynolds number of 5000 then decreases as the Reynolds number increases beyond the critical value [8]. Kaood et al. have also presented the non-linear trend of the friction factor with Reynolds number, the friction factor decreases as the Reynolds number increases in the turbulent regime [16]. The friction factors of single particle and hybrid nanofluids are higher than water which are increasing with increase in the volume fraction. This is because of higher viscosity of single particle and hybrid nanofluids compared to water which continuously increases with volume fraction. The density of the hybrid nanofluid is higher than the density of single particle nanofluid which results into lower velocity of hybrid nanofluid compared with single particle nanofluid. Therefore, the ratio of pressure drop to square of velocity the performance evaluation criteria is nullified. The Nusselt number and friction factor have improved with increase in volume fraction of single particle and hybrid nanofluids as a result of improvement in the thermophysical properties. Therefore, the performance evaluation criteria enhance for both single particle and hybrid nanofluids as volume fraction increases. Azmi et al. have proved that the variation in the performance evaluation criteria is very small and non-linear with Reynolds number. In addition, the performance evaluation criteria increase with increase in volume fraction of nanoparticles [24]. The performance evaluation criteria for hybrid nanofluid are superior compared to single particle nanofluid for the same volume fraction because the increase in the Nusselt number is highly dominant compared to the increase in the friction factor for hybrid nanofluid. The 0.5% Al2O<sup>3</sup> nanofluid presents the lowest value of performance evaluation criteria and 2.0% Al2O3/Cu nanofluid presents the highest value of performance evaluation criteria among all nanofluids. Compared to the performance evaluation criteria of 0.5% Al2O<sup>3</sup> nanofluid, the performance evaluation criteria of 1.0% Al2O3, 2.0% Al2O3, 0.5% Al2O3/Cu, 1.0% Al2O3/Cu and 2.0% Al2O3/Cu nanofluids are higher by 1.9%, 5.9%, 0.7%, 3.3% and 8.9%, respectively. Overall, 2.0% Al2O3/Cu nanofluid with composition of 50/50% has presented the superior heat transfer characteristics among all working fluids. The 2.0% Al2O<sup>3</sup> nanofluid in single particle case and 2.0% Al2O3/Cu nanofluids in hybrid case present the superior performances in the respective groups. Therefore, the simulated contours of temperature and velocity for water, 2.0% Al2O<sup>3</sup> single particle nanofluid and 2.0% Al2O3/Cu hybrid nanofluid with composition of 50/50% are depicted in Figure 9. The most important section to observe the behavior of simulated results is the outlet of tube. Therefore, the temperature and velocity contours are presented for the working fluid domain at the tube outlet cross section considering the Reynolds numbers of 2000 and 12,000. As can be seen from Figure 9, the distribution of temperature and velocity contours at the outlet section of tube are symmetrical for water and nanofluids. The heat transfer characteristics of 2.0% Al2O3/Cu nanofluid is further investigated with additional two compositions of 75/25% and 25/75% and compared with composition of 50/50% as well as water and 2.0% Al2O<sup>3</sup> nanofluid.
