*5.8. Effect of Cold Fluid Mass Flow Rate on First and Second Law Characteristics*

The behavior of first and second law characteristics of the hybrid nanofluid with OS-shaped nanoparticles for various volume fractions and cold fluid mass flow rates is presented in Figure 18. The cold fluid mass flow rate is varied at 10 kg/h, 20 kg/h and 30 kg/h. The ratio of heat transfer to pumping power is dominating at a higher volume fraction and lower cold fluid mass flow rate. Therefore, the performance index increases with the increase in volume fraction and decrease in cold fluid mass flow rate. The performance index of the Al2O3/Cu nanofluid with OS-shaped nanoparticles increases by 13.41%, 9.43% and 5.79% for cold fluid mass flow rates of 10 kg/h, 20 kg/h and 30 kg/h, respectively, as the volume fraction increases from 0.5% to 2.0%. The performance index of the Al2O3/Cu nanofluid with OS-shaped nanoparticles decreases by 6.41%, 7.52% and 9.70% as the cold fluid mass flow rate increases from 10 kg/h to 20 kg/h, and that decreases

by 38.71%, 40.13% and 42.82% as the cold fluid mass flow rate increases from 10 kg/h to 30 kg/h for volume fractions of 0.5%, 1.0% and 2.0%, respectively. The thermal entropy generation rate increases with the volume fraction and cold fluid mass flow rate due to an increase in the heat transfer at a higher volume fraction and higher cold fluid mass rate. For the same cold fluid mass flow rate, the ratio of pressure drop to average temperature is less dominant at a higher volume fraction; therefore, the friction entropy generation rate decreases with an increase in volume fraction. The friction entropy generation increases with an increase in the cold fluid mass flow rate for all volume fractions because the ratio of pressure drop to average temperature is highly dominant at higher cold fluid mass flow rates. The ratio of thermal entropy generation rate to total entropy generation rate presents an increasing trend of Bejan numbers with an increase in volume fraction and a decrease in the cold fluid mass flow rate. With the increase in volume fraction from 0.5% to 2.0%, the Bejan number of the Al2O3/Cu nanofluid with OS-shaped nanoparticles increases by 0.94%, 0.73% and 0.69% for cold fluid mass flow rates of 10 kg/h, 20 kg/h and 30 kg/h, respectively. The Bejan number of the Al2O3/Cu nanofluid with OS-shaped nanoparticles decreases by 1.06%, 1.13% and 1.26% as the cold fluid mass flow rate increases from 10 kg/h to 20 kg/h, and that decreases by 6.21%, 6.30% and 6.45% as the cold fluid mass flow rate increases from 10 kg/h to 30 kg/h for volume fractions of 0.5%, 1.0% and 2.0%, respectively. Tiwari et al. have proved that the lower cold fluid mass flow rate shows the better first law characteristics compared to the higher cold fluid mass flow rate [59,61]. The contributions of thermal and friction entropy generation rates for Al2O3/Cu with OS-shaped nanoparticles at various cold fluid mass flow rates are depicted in Figure 19. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 25 of 33

**Figure 15.** Contributions of thermal and friction entropy generation rates for Al2O3/Cu with OSshaped nanoparticles at various hot fluid mass flow rates. **Figure 15.** Contributions of thermal and friction entropy generation rates for Al2O3/Cu with OSshaped nanoparticles at various hot fluid mass flow rates.

shaped nanoparticles for various volume fractions and cold fluid temperatures is depicted in Figure 16. The cold fluid temperature is varied as 10 °C, 20 °C and 30 °C. The cold fluid at the lower temperature absorbs more heat and presents the higher temperature gradient and heat transfer rate. The pressure drop is not significantly affected by change in the cold fluid temperature. Therefore, the performance index increases as the cold fluid temperature decreases. With the increase in volume fraction, the dominance of the increase in heat transfer is superior to the increase in the pressure drop; therefore, the performance index increases with the increase in the volume fraction. The performance index of the Al2O3/Cu nanofluid with OS-shaped nanoparticles decreases by 12.5% and 24.99% when the cold fluid temperature increases from 10 °C to 20 °C and 10 °C to 30 °C, respectively, for all volume fractions. With an increase in the volume fraction from 0.5% to 2.0%, the performance index increases by 9.43% for all cold fluid temperatures. The thermal entropy generation increases with the increase in volume fraction and decrease in the cold fluid temperature because the heat transfer rate increases with the increase in volume fraction and decrease in the cold fluid temperature. The friction entropy generation rate decreases with the increase in volume fraction despite an increase in pressure drop, because the increase in the average temperature with an increase in the volume fraction is dominant compared to an increase in pressure drop. Similar to the hot fluid temperature, the lower cold fluid temperature presents higher values of the friction entropy generation rate, and vice versa. The higher Bejan number is obtained at the lower cold fluid temperature because the dominance of the thermal entropy generation increase is higher than the friction entropy generation increase with a decrease in the cold fluid temperature. The thermal entropy generation increases and the friction entropy generation decreases with an increase in the volume fraction, which results in an increase

*5.7. Effect of Cold Fluid Temperature on First and Second Law Characteristics* 

depicted in Figure 17.

depicted in Figure 17.

in the Bejan number. The Bejan number of the Al2O3/Cu nanofluid with OS-shaped nanoparticles decreases by 1.16%, 1.12% and 1.07% as the cold fluid temperature increases from 10 °C to 20 °C, and that decreases by 2.66%, 2.59% and 2.45% as the cold fluid temperature increases from 10 °C to 30 °C for volume fractions of 0.5%, 1.0% and 2.0%, respectively. With the increase in volume fraction from 0.5% to 2.0%, the Bejan number of Al2O3/Cu nanofluid with OS-shaped nanoparticles increases by 0.63%, 0.73% and 0.85% for cold fluid temperatures of 10 °C, 20 °C and 30 °C, respectively. Garud et al. have proved that the performance of the heat exchanger is optimum for the lower mass flow rate of cold fluid [66]. The contributions of thermal and friction entropy generation rates for Al2O3/Cu with OS-shaped nanoparticles at various cold fluid temperatures are

in the Bejan number. The Bejan number of the Al2O3/Cu nanofluid with OS-shaped nanoparticles decreases by 1.16%, 1.12% and 1.07% as the cold fluid temperature increases from 10 °C to 20 °C, and that decreases by 2.66%, 2.59% and 2.45% as the cold fluid temperature increases from 10 °C to 30 °C for volume fractions of 0.5%, 1.0% and 2.0%, respectively. With the increase in volume fraction from 0.5% to 2.0%, the Bejan number of Al2O3/Cu nanofluid with OS-shaped nanoparticles increases by 0.63%, 0.73% and 0.85% for cold fluid temperatures of 10 °C, 20 °C and 30 °C, respectively. Garud et al. have proved that the performance of the heat exchanger is optimum for the lower mass flow rate of cold fluid [66]. The contributions of thermal and friction entropy generation rates for Al2O3/Cu with OS-shaped nanoparticles at various cold fluid temperatures are

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 26 of 33

**Figure 16.** Variation in first and second law characteristics of hybrid nanofluid with OS-shaped nanoparticles with various volume fractions and cold fluid temperatures. **Figure 16.** Variation in first and second law characteristics of hybrid nanofluid with OS-shaped nanoparticles with various volume fractions and cold fluid temperatures. **Figure 16.** Variation in first and second law characteristics of hybrid nanofluid with OS-shaped nanoparticles with various volume fractions and cold fluid temperatures.

**Figure 17.** Contributions of thermal and friction entropy generation rates for Al2O3/Cu with OSshaped nanoparticles at various cold fluid temperatures.

The above-mentioned results in Sections 5.3–5.8 are summarized as the comparison of single-particle and hybrid nanofluids with different nanoparticle shapes, based on numerous first and second law characteristics of the microplate heat exchanger. The Al2O3/Cu nanofluid with OS-shaped nanoparticles presents the excellent first and second law characteristics among all combinations of single-particle and hybrid nanofluids with nanoparticle shapes. The first and second law characteristics in terms of performance index and Bejan number are investigated under various conditions of volume fraction, temperature and mass flow rate for the best combination of Al2O3/Cu nanofluid with OS-shaped nanoparticles. The performance index and Bejan number of the Al2O3/Cu

nanofluid with OS-shaped nanoparticles are maximum at a higher hot fluid temperature, lower cold fluid temperature and lower mass flow rates of hot and cold fluids. rate [59,61]. The contributions of thermal and friction entropy generation rates for Al2O3/Cu with OS-shaped nanoparticles at various cold fluid mass flow rates are depicted in Figure 19.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 27 of 33

shaped nanoparticles at various cold fluid temperatures.

**Figure 17.** Contributions of thermal and friction entropy generation rates for Al2O3/Cu with OS-

The behavior of first and second law characteristics of the hybrid nanofluid with OSshaped nanoparticles for various volume fractions and cold fluid mass flow rates is presented in Figure 18. The cold fluid mass flow rate is varied at 10 kg/h, 20 kg/h and 30 kg/h. The ratio of heat transfer to pumping power is dominating at a higher volume fraction and lower cold fluid mass flow rate. Therefore, the performance index increases with the increase in volume fraction and decrease in cold fluid mass flow rate. The performance index of the Al2O3/Cu nanofluid with OS-shaped nanoparticles increases by 13.41%, 9.43% and 5.79% for cold fluid mass flow rates of 10 kg/h, 20 kg/h and 30 kg/h, respectively, as the volume fraction increases from 0.5% to 2.0%. The performance index of the Al2O3/Cu nanofluid with OS-shaped nanoparticles decreases by 6.41%, 7.52% and 9.70% as the cold fluid mass flow rate increases from 10 kg/h to 20 kg/h, and that decreases by 38.71%, 40.13% and 42.82% as the cold fluid mass flow rate increases from 10 kg/h to 30 kg/h for volume fractions of 0.5%, 1.0% and 2.0%, respectively. The thermal entropy generation rate increases with the volume fraction and cold fluid mass flow rate due to an increase in the heat transfer at a higher volume fraction and higher cold fluid mass rate. For the same cold fluid mass flow rate, the ratio of pressure drop to average temperature is less dominant at a higher volume fraction; therefore, the friction entropy generation rate decreases with an increase in volume fraction. The friction entropy generation increases with an increase in the cold fluid mass flow rate for all volume fractions because the ratio of pressure drop to average temperature is highly dominant at higher cold fluid mass flow rates. The ratio of thermal entropy generation rate to total entropy generation rate presents an increasing trend of Bejan numbers with an increase in volume fraction and a decrease in the cold fluid mass flow rate. With the increase in volume fraction from 0.5% to 2.0%, the Bejan number of the Al2O3/Cu nanofluid with OS-shaped nanoparticles increases by 0.94%, 0.73% and 0.69% for cold fluid mass flow rates of 10 kg/h, 20 kg/h and 30 kg/h, respectively. The Bejan number of the Al2O3/Cu nanofluid with OS-shaped nanoparticles decreases by 1.06%, 1.13% and 1.26% as the cold fluid mass flow rate increases from 10 kg/h to 20 kg/h, and that decreases by 6.21%, 6.30% and 6.45% as the cold fluid mass flow rate increases from 10 kg/h to 30 kg/h for volume fractions of 0.5%, 1.0% and 2.0%, respectively. Tiwari et al. have proved that the lower cold fluid mass flow rate shows the better first law characteristics compared to the higher cold fluid mass flow

*5.8. Effect of Cold Fluid Mass Flow Rate on First and Second Law Characteristics* 

**Figure 18.** Behavior of first and second law characteristics of hybrid nanofluid with OS-shaped nanoparticles for various volume fractions and cold fluid mass flow rates. **Figure 18.** Behavior of first and second law characteristics of hybrid nanofluid with OS-shaped nanoparticles for various volume fractions and cold fluid mass flow rates.

**Figure 19.** Contributions of thermal and friction entropy generation rates for Al2O3/Cu with OSshaped nanoparticles at various cold fluid mass flow rates. **Figure 19.** Contributions of thermal and friction entropy generation rates for Al2O3/Cu with OSshaped nanoparticles at various cold fluid mass flow rates.

#### The above-mentioned results in sections 5.3 to 5.8 are summarized as the comparison **6. Conclusions**

**6. Conclusions** 

present study.

of single-particle and hybrid nanofluids with different nanoparticle shapes, based on numerous first and second law characteristics of the microplate heat exchanger. The Al2O3/Cu nanofluid with OS-shaped nanoparticles presents the excellent first and second law characteristics among all combinations of single-particle and hybrid nanofluids with nanoparticle shapes. The first and second law characteristics in terms of performance index and Bejan number are investigated under various conditions of volume fraction, The first and second law analyses have been conducted on the microplate heat exchanger, comprising of single-particle and hybrid nanofluids with different-shaped nanoparticles. Firstly, the first and second law characteristics are compared for differentshaped nanoparticles, and then the effect of various volume fractions, temperatures and mass flow rates are investigated on the first and second law characteristics of the optimumshaped nanoparticles. The following key findings are highlighted from the present study.

nanofluid with OS-shaped nanoparticles are maximum at a higher hot fluid temperature,

The first and second law analyses have been conducted on the microplate heat exchanger, comprising of single-particle and hybrid nanofluids with different-shaped nanoparticles. Firstly, the first and second law characteristics are compared for differentshaped nanoparticles, and then the effect of various volume fractions, temperatures and mass flow rates are investigated on the first and second law characteristics of the optimum-shaped nanoparticles. The following key findings are highlighted from the

(a) The decreasing order of first law characteristics is evaluated as hybrid nanofluid, single-particle nanofluid and water, respectively, for all nanoparticle shapes. The Al2O3/Cu nanofluid with OS-shaped nanoparticles shows maximum values of NTU,

lower cold fluid temperature and lower mass flow rates of hot and cold fluids.


**Author Contributions:** Conceptualization, K.S.G.; and M.-Y.L.; methodology, K.S.G.; S.-G.H.; and M.-Y.L.; formal analysis, K.S.G.; S.-G.H.; and M.-Y.L.; investigation, K.S.G.; S.-G.H.; T.-K.L.; N.K.; and M.-Y.L.; resources, K.S.G.; and M.-Y.L.; data curation, K.S.G.; and T.-K.L.; validation, K.S.G.; software, K.S.G.; writing—original draft preparation, K.S.G.; and M.-Y.L.; writing—review and editing, K.S.G.; T.-K.L.; N.K.; and M.-Y.L.; visualization, K.S.G.; and M.-Y.L.; supervision, M.-Y.L.; project administration, M.-Y.L.; funding acquisition, M.-Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study will be available on request to the corresponding author.

**Acknowledgments:** This work was supported by the Dong-A University research fund.

**Conflicts of Interest:** The authors declare no conflict of interest.
