*5.1. Validation*

The experimental conditions applied by Alm et al. [64] for the same geometry and structure of the microplate heat exchanger are reflected in the present work to validate the accuracy of the numerical model. The experimental and numerical results are compared for the hot fluid inlet temperature and mass flow rate of 90 ◦C and 21 kg/h, respectively. The cold fluid mass flow rate ranges from 20 kg/h to 120 kg/h and the cold fluid inlet temperature is fixed at 12.5 ◦C for the comparison. The warm water as the hot fluid and

cold water as the cold fluid are considered for the comparison. The outlet temperatures and pressure drops of hot and cold fluids are compared for the experimental and numerical methods, as presented in Figure 4. The trends for the experimental and numerical results are same for outlet temperatures and pressure drops of hot and cold fluids. The cold fluid outlet temperature decreases with increase in the cold fluid inlet mass flow rate, which results in an increase in the hot fluid outlet temperature. Whereas, the pressure drops for hot and cold fluids have increased with an increase in the cold fluid inlet mass flow rate. Over the variation range of the cold fluid inlet mass flow rate, the maximum deviation between the experimental and numerical results of the hot fluid outlet temperature is 4.64%, that of cold fluid outlet temperature is 4.93%, that of hot fluid pressure drop is 5.64% and that of the cold fluid pressure drop is 6.49%. The numerical results are in closer agreement with the corresponding experimental results, with a maximum deviation within ±10% for both thermal and flow characteristics of the microplate heat exchanger. Therefore, the numerical model is valid and reliable for the detailed thermodynamic investigations on the microplate heat exchanger. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 13 of 33

**Figure 4.** Comparison experimental and numerical results of temperature and pressure drop for hot and cold fluids. **Figure 4.** Comparison experimental and numerical results of temperature and pressure drop for hot and cold fluids.

#### *5.2. Evaluation of Nanofluid Thermophysical Properties for Different Nanoparticle Shapes 5.2. Evaluation of Nanofluid Thermophysical Properties for Different Nanoparticle Shapes*

The density and specific heat are not affected by changes in nanoparticle shape, unlike thermal conductivity and viscosity. Timofeeva et al. [4] have proved that the whole area of a solid-liquid interface greatly affects the thermal conductivity and viscosity of nanofluids. Therefore, the behavior of thermal conductivity and viscosity of singleparticle and hybrid nanofluids with different nanoparticle shapes are depicted in Figure 5a,b, respectively. The behavior comparison is presented for 1.0% volume fraction of the nanoparticle in both single-particle and hybrid nanofluids. The nanoparticles of Al2O3 and Cu are mixed in the proposition of 50–50% in the hybrid nanofluid. The stability and agglomeration of different-shaped nanoparticles significantly affect the thermal conductivity of nanofluids. The thermal conductivity of both single-particle and hybrid nanofluids with all nanoparticle shapes are superior compared to water because of dispersion of high thermal conductivity nanoparticles into the base fluid. For nanoparticle shapes of Sp, OS, PS1, PS2, PS3 and PS3, the thermal conductivity of the hybrid nanofluid The density and specific heat are not affected by changes in nanoparticle shape, unlike thermal conductivity and viscosity. Timofeeva et al. [4] have proved that the whole area of a solid-liquid interface greatly affects the thermal conductivity and viscosity of nanofluids. Therefore, the behavior of thermal conductivity and viscosity of single-particle and hybrid nanofluids with different nanoparticle shapes are depicted in Figure 5a,b, respectively. The behavior comparison is presented for 1.0% volume fraction of the nanoparticle in both single-particle and hybrid nanofluids. The nanoparticles of Al2O<sup>3</sup> and Cu are mixed in the proposition of 50–50% in the hybrid nanofluid. The stability and agglomeration of different-shaped nanoparticles significantly affect the thermal conductivity of nanofluids. The thermal conductivity of both single-particle and hybrid nanofluids with all nanoparticle shapes are superior compared to water because of dispersion of high thermal conductivity nanoparticles into the base fluid. For nanoparticle shapes of Sp, OS, PS1, PS2, PS3 and PS3, the thermal conductivity of the hybrid nanofluid are better than the single-particle

BL, PL, CY and BR, the thermal conductivity values are the same for single-particle and hybrid nanofluids. Among all nanoparticle shapes, OS presents highest, and PL presents lowest thermal conductivity values in the respective cases of single-particle and hybrid nanofluids. The order of thermal conductivity is obtained based on the enhancement in the aspect ratio due to the fact that a rise in the contact area causes significant heat transfer when nanoparticles collide with each other [65]. Kim et al. have stated that BR-shaped nanoparticles present better thermal conductivity compared to BL-shaped nanoparticles due to rapid agglomeration [1]. The thermal conductivity values of Al2O3 and Al2O3/Cu nanofluids with OS-shaped nanoparticles are higher by 5.48% and 10.61%, respectively, compared to water. The thermal conductivity of Al2O3 and Al2O3/Cu nanofluids with PLshaped nanoparticles is higher by 2.61% compared to water. The viscosity of singleparticle and hybrid nanofluids with different nanoparticle shapes are higher than water because of the dispersion of nanoparticles into the base fluid. However, the viscosity values are same for single-particle and hybrid nanofluids with the same nanoparticle

nanofluid. Whereas, in cases of nanoparticle shapes of BL, PL, CY and BR, the thermal conductivity values are the same for single-particle and hybrid nanofluids. Among all nanoparticle shapes, OS presents highest, and PL presents lowest thermal conductivity values in the respective cases of single-particle and hybrid nanofluids. The order of thermal conductivity is obtained based on the enhancement in the aspect ratio due to the fact that a rise in the contact area causes significant heat transfer when nanoparticles collide with each other [65]. Kim et al. have stated that BR-shaped nanoparticles present better thermal conductivity compared to BL-shaped nanoparticles due to rapid agglomeration [1]. The thermal conductivity values of Al2O<sup>3</sup> and Al2O3/Cu nanofluids with OS-shaped nanoparticles are higher by 5.48% and 10.61%, respectively, compared to water. The thermal conductivity of Al2O<sup>3</sup> and Al2O3/Cu nanofluids with PL-shaped nanoparticles is higher by 2.61% compared to water. The viscosity of single-particle and hybrid nanofluids with different nanoparticle shapes are higher than water because of the dispersion of nanoparticles into the base fluid. However, the viscosity values are same for single-particle and hybrid nanofluids with the same nanoparticle shape. The Al2O<sup>3</sup> and Al2O3/Cu nanofluids with PL-shaped nanoparticles present the highest viscosity among all nanoparticle shapes, which is 43.23% superior to the viscosity of water. The Al2O<sup>3</sup> and Al2O3/Cu nanofluids with Sp- and OS-shaped nanoparticles show the lowest and the second lowest values of viscosity, which are higher by 3.42% and 3.57%, respectively, compared to water. The PL-, CY- and BL-shaped nanoparticles present larger viscosity values compared to other-shaped nanoparticles due to limitation of rotational and Brownian motions. In addition, the PLand CY-shaped nanoparticles stay in contact with one another for longer periods and interact between themselves significantly compared to other-shaped nanoparticles, which results in a higher viscosity in PL- and CY-shaped nanoparticles. Mahian et al. have presented the highest viscosity for PL-shaped nanoparticles, which increases with volume fraction [11]. The density and specific heat of the Al2O<sup>3</sup> nanofluid are 1017.63 kg/m<sup>3</sup> and 4072.28 J/kg·K, respectively, and those of the Al2O3/Cu nanofluid are 1047.04 kg/m<sup>3</sup> and 3965.29 J/kg·K, respectively, for all nanoparticle shapes. From this comparison, it could be concluded that the single-particle and hybrid nanofluids with OS-shaped nanoparticles have excellent thermophysical properties compared to other nanoparticle shapes. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 14 of 33 shape. The Al2O3 and Al2O3/Cu nanofluids with PL-shaped nanoparticles present the highest viscosity among all nanoparticle shapes, which is 43.23% superior to the viscosity of water. The Al2O3 and Al2O3/Cu nanofluids with Sp- and OS-shaped nanoparticles show the lowest and the second lowest values of viscosity, which are higher by 3.42% and 3.57%, respectively, compared to water. The PL-, CY- and BL-shaped nanoparticles present larger viscosity values compared to other-shaped nanoparticles due to limitation of rotational and Brownian motions. In addition, the PL- and CY-shaped nanoparticles stay in contact with one another for longer periods and interact between themselves significantly compared to other-shaped nanoparticles, which results in a higher viscosity in PL- and CY-shaped nanoparticles. Mahian et al. have presented the highest viscosity for PLshaped nanoparticles, which increases with volume fraction [11]. The density and specific heat of the Al2O3 nanofluid are 1017.63 kg/m3 and 4072.28 J/kg∙K, respectively, and those of the Al2O3/Cu nanofluid are 1047.04 kg/m3 and 3965.29 J/kg∙K, respectively, for all nanoparticle shapes. From this comparison, it could be concluded that the single-particle and hybrid nanofluids with OS-shaped nanoparticles have excellent thermophysical properties compared to other nanoparticle shapes.

**Figure 5.** *Cont.*

**Figure 5.** Behavior of (**a**) thermal conductivity and (**b**) viscosity of single-particle and hybrid nanofluids with different nanoparticle shapes. **Figure 5.** Behavior of (**a**) thermal conductivity and (**b**) viscosity of single-particle and hybrid nanofluids with different nanoparticle shapes.

#### *5.3. Evaluation of First Law Characteristics for Different Nanoparticle Shapes 5.3. Evaluation of First Law Characteristics for Different Nanoparticle Shapes*

The comparison of NTU for single-particle and hybrid nanofluids with different nanoparticle shapes is shown in Figure 6. The NTU of single-particle and hybrid nanofluids are improved for nanoparticle shapes of Sp, OS, PS1, PS2, PS3, PS4, BL and BR compared to water because of improvement in the thermophysical properties of singleparticle and hybrid nanofluids. In the case of PL-shaped nanoparticles, the NTU values are lower for both single-particle and hybrid nanofluids compared to water, due to a higher velocity of PL-shaped nanoparticles. The OS- and PL-shaped nanoparticles present the lowest and highest velocities, respectively, which results correspondingly into the lower and higher values of heat transfer coefficients. The lower velocity of OS-shaped nanoparticles results in a lower heat capacity, which dominates the lower heat transfer coefficients. Hence, as per Equation (43), it results in the highest NTU value. The higher velocity of PL-shaped nanoparticles results in a higher heat capacity and higher heat transfer coefficient; therefore, based on Equation (43), the combined effect of a higher heat transfer coefficient and a higher heat capacity presents a lower NTU for PL-shaped nanoparticles. The higher heat capacity dominates the higher heat transfer coefficient for PL-shaped nanoparticles. In the case of CY-shaped nanoparticles, the hybrid nanofluid shows superior NTU values and single-particle nanofluid shows poorer NTU values than water. In addition, for the same nanoparticle shape, the NTU of the Al2O3/Cu nanofluid is superior to the NTU of the Al2O3 nanofluid due to the addition of high thermal conductivity Cu nanoparticles to the Al2O3 nanofluid, which results in the thermal conductivity improvement of the Al2O3/Cu nanofluid. Bahiraei et al. have shown similar results of OS- and PL-shaped nanoparticles with the highest and lowest NTU, respectively, for single-particle nanofluids [19]. The NTU values of the Al2O3 and Al2O3/Cu nanofluids with OS-shaped nanoparticles are higher by 2.86% and 6.38%, respectively, compared to the NTU of water. The Al2O3 and Al2O3/Cu nanofluids with PL-shaped The comparison of NTU for single-particle and hybrid nanofluids with different nanoparticle shapes is shown in Figure 6. The NTU of single-particle and hybrid nanofluids are improved for nanoparticle shapes of Sp, OS, PS1, PS2, PS3, PS4, BL and BR compared to water because of improvement in the thermophysical properties of single-particle and hybrid nanofluids. In the case of PL-shaped nanoparticles, the NTU values are lower for both single-particle and hybrid nanofluids compared to water, due to a higher velocity of PL-shaped nanoparticles. The OS- and PL-shaped nanoparticles present the lowest and highest velocities, respectively, which results correspondingly into the lower and higher values of heat transfer coefficients. The lower velocity of OS-shaped nanoparticles results in a lower heat capacity, which dominates the lower heat transfer coefficients. Hence, as per Equation (43), it results in the highest NTU value. The higher velocity of PLshaped nanoparticles results in a higher heat capacity and higher heat transfer coefficient; therefore, based on Equation (43), the combined effect of a higher heat transfer coefficient and a higher heat capacity presents a lower NTU for PL-shaped nanoparticles. The higher heat capacity dominates the higher heat transfer coefficient for PL-shaped nanoparticles. In the case of CY-shaped nanoparticles, the hybrid nanofluid shows superior NTU values and single-particle nanofluid shows poorer NTU values than water. In addition, for the same nanoparticle shape, the NTU of the Al2O3/Cu nanofluid is superior to the NTU of the Al2O<sup>3</sup> nanofluid due to the addition of high thermal conductivity Cu nanoparticles to the Al2O<sup>3</sup> nanofluid, which results in the thermal conductivity improvement of the Al2O3/Cu nanofluid. Bahiraei et al. have shown similar results of OS- and PL-shaped nanoparticles with the highest and lowest NTU, respectively, for single-particle nanofluids [19]. The NTU values of the Al2O<sup>3</sup> and Al2O3/Cu nanofluids with OS-shaped nanoparticles are higher by 2.86% and 6.38%, respectively, compared to the NTU of water. The Al2O<sup>3</sup> and Al2O3/Cu nanofluids with PL-shaped nanoparticles present the NTU values as lower by 3.99% and 1.82%, respectively, compared to the NTU of water.

nanoparticles present the NTU values as lower by 3.99% and 1.82%, respectively,

compared to the NTU of water.

**Figure 6.** Comparison of NTU for single-particle and hybrid nanofluids with different nanoparticle shapes. **Figure 6.** Comparison of NTU for single-particle and hybrid nanofluids with different nanoparticle shapes.

The effectiveness of single-particle and hybrid nanofluids with different nanoparticle shapes are compared in Figure 7. For the same nanoparticle shapes, the effectiveness of the Al2O3/Cu nanofluid are better than the Al2O3 nanofluid because of an increase in the thermal conductivity of the hybrid nanofluid by the dispersion of high thermal conductivity nanoparticles. The behavior of effectiveness is same as of the NTU for singleparticle and hybrid nanofluids with all nanoparticle shapes. For the single-particle nanofluids, OS-shaped nanoparticles present the highest effectiveness, followed by Sp, PS1 = PS2, PS3, PS4, BR, BL, CY and PL in decreasing order of effectiveness, in which the effectiveness of CY- and PL-shaped nanoparticles are lower than water. In the case of the hybrid nanofluid, the decreasing order of effectiveness is OS, PS4, PS3, PS2, PS1, Sp, BR, BL, CY and PL, respectively, in which the effectiveness value of PL-shaped nanoparticles is lower than water. Shahsavar et al. have also presented a lower effectiveness for alumina nanofluids with PL-shaped nanoparticles [26]. The velocity of different-shaped nanoparticles is in the inverse relation with the temperature gradient. Therefore, the lower velocity of OS-shaped nanoparticles raises the temperature variation of nanofluids, which results in higher effectiveness. The effectiveness values of Al2O3 and Al2O3/Cu nanofluids with OS-shaped nanoparticles are higher by 2.75% and 6.10%, respectively, and those with PL-shaped nanoparticles are lower by 3.65% and 1.54%, respectively, compared to the The effectiveness of single-particle and hybrid nanofluids with different nanoparticle shapes are compared in Figure 7. For the same nanoparticle shapes, the effectiveness of the Al2O3/Cu nanofluid are better than the Al2O<sup>3</sup> nanofluid because of an increase in the thermal conductivity of the hybrid nanofluid by the dispersion of high thermal conductivity nanoparticles. The behavior of effectiveness is same as of the NTU for single-particle and hybrid nanofluids with all nanoparticle shapes. For the single-particle nanofluids, OSshaped nanoparticles present the highest effectiveness, followed by Sp, PS1 = PS2, PS3, PS4, BR, BL, CY and PL in decreasing order of effectiveness, in which the effectiveness of CY- and PL-shaped nanoparticles are lower than water. In the case of the hybrid nanofluid, the decreasing order of effectiveness is OS, PS4, PS3, PS2, PS1, Sp, BR, BL, CY and PL, respectively, in which the effectiveness value of PL-shaped nanoparticles is lower than water. Shahsavar et al. have also presented a lower effectiveness for alumina nanofluids with PL-shaped nanoparticles [26]. The velocity of different-shaped nanoparticles is in the inverse relation with the temperature gradient. Therefore, the lower velocity of OSshaped nanoparticles raises the temperature variation of nanofluids, which results in higher effectiveness. The effectiveness values of Al2O<sup>3</sup> and Al2O3/Cu nanofluids with OS-shaped nanoparticles are higher by 2.75% and 6.10%, respectively, and those with PL-shaped nanoparticles are lower by 3.65% and 1.54%, respectively, compared to the effectiveness of water.

effectiveness of water. The performance index presents the combined effect of heat transfer and pressure drop characteristics. The comparison of the performance index of single-particle and hybrid nanofluids with different particle shapes is presented in Figure 8. The particle shape with the superior combination of thermal conductivity and viscosity shows the higher value of the performance index. Therefore, single-particle and hybrid nanofluids with OS-shaped nanoparticles show the highest values of the performance index among all nanoparticle shapes and water. The performance index values of single-particle and hybrid nanofluids with PL-shaped nanoparticles are lowest among all nanoparticle shapes, as well as water, due to poor thermal conductivity and viscosity. Despite the lower heat transfer rate in OS-shaped nanoparticles, the lowest pressure drop results in the highest performance index. Whereas, the higher pressure drop for PL-shaped nanoparticles results

in the lowest performance index. Vo et al. have also illustrated that the pressure drop of PL-shaped nanoparticles is superior to other nanoparticle shapes, which increases as the volume fraction increases [20]. The OS- and PL-shaped nanoparticles show the maximum and minimum performance indexes for the alumina nanofluid, as proven by Bahiraei et al. and Arani et al. [19,53]. The single-particle and hybrid nanofluids with CY-shaped nanoparticles and the single-particle nanofluids with BL-shaped nanoparticles show a lower performance index than water despite better thermal conductivity because of higher viscosity and density. Apart from these combinations, other nanoparticle shapes present better performance index than water, in which hybrid nanofluids show a superior performance index than the single-particle nanofluid. The Al2O<sup>3</sup> and Al2O3/Cu nanofluids with OS-shaped nanoparticles present the performance index as higher by 2.24% and 6.58%, respectively, and those with PL-shaped nanoparticles present the performance index as lower by 8.78% and 5.80%, respectively, than water. The single-particle and hybrid nanofluids with other nanoparticle shapes show the performance index values in a range between the highest and lowest values. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 17 of 33

**Figure 7.** Effectiveness of single-particle and hybrid nanofluids with different nanoparticle shapes. **Figure 7.** Effectiveness of single-particle and hybrid nanofluids with different nanoparticle shapes.
