*5.4. Evaluation of Second Law Characteristics for Different Nanoparticle Shapes*

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 The thermal entropy generation rate for single-particle and hybrid nanofluids with different nanoparticle shapes is depicted in Figure 9. The thermal entropy generation is due to heat transfer, which depends on the temperature gradient. The thermal entropy generation rates of the hybrid nanofluid are better than that of single-particle nanofluids for OS-, PS2-, PS3- and PS4-shaped nanoparticles due to superior heat transfer properties and temperature gradients. However, in the case of Sp-, PS1-, BL-, PL-, CY- and BR-shaped nanoparticles, the thermal entropy generation rates of hybrid nanofluids are lower than single-particle nanofluids. The thermal entropy generation rates of all nanoparticle shapes except OS-shaped nanoparticles are lower than the water for both single-particle and hybrid nanofluids. The thermal entropy generation rates of single-particle and hybrid nanofluids with PL-shaped nanoparticles are lowest among all nanoparticle shapes. The PL-shaped nanoparticles have a higher velocity, which creates significant mixing and disturbance in the boundary layer. Hence, the temperature gradient decreases, which

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 Al2O3 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.

results in a lower heat transfer and thermal entropy generation. The opposite discussion could be applied for OS-shaped nanoparticles with lower velocity. Bahiraei et al. have also presented that the thermal entropy generation rates are highest and lowest for OS- and PL-shaped nanoparticles, respectively [13,48]. The Al2O<sup>3</sup> and Al2O3/Cu nanofluids with OS-shaped nanoparticles show thermal entropy generation rates as higher by 0.14% and 0.70%, respectively, compared to water; however, the percentage increase is not significantly higher. The thermal entropy generation rates of Al2O<sup>3</sup> and Al2O3/Cu nanofluids with PL-shaped nanoparticles are lower by 6.08% and 6.53%, respectively, compared to water. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 18 of 33

**Figure 8.** Comparison of performance index of single-particle and hybrid nanofluids with different particle shapes. **Figure 8.** Comparison of performance index of single-particle and hybrid nanofluids with different particle shapes.

*5.4. Evaluation of Second Law Characteristics for Different Nanoparticle Shapes*  The thermal entropy generation rate for single-particle and hybrid nanofluids with different nanoparticle shapes is depicted in Figure 9. The thermal entropy generation is due to heat transfer, which depends on the temperature gradient. The thermal entropy generation rates of the hybrid nanofluid are better than that of single-particle nanofluids for OS-, PS2-, PS3- and PS4-shaped nanoparticles due to superior heat transfer properties and temperature gradients. However, in the case of Sp-, PS1-, BL-, PL-, CY- and BRshaped nanoparticles, the thermal entropy generation rates of hybrid nanofluids are lower than single-particle nanofluids. The thermal entropy generation rates of all nanoparticle shapes except OS-shaped nanoparticles are lower than the water for both single-particle and hybrid nanofluids. The thermal entropy generation rates of single-particle and hybrid nanofluids with PL-shaped nanoparticles are lowest among all nanoparticle shapes. The PL-shaped nanoparticles have a higher velocity, which creates significant mixing and disturbance in the boundary layer. Hence, the temperature gradient decreases, which results in a lower heat transfer and thermal entropy generation. The opposite discussion could be applied for OS-shaped nanoparticles with lower velocity. Bahiraei et al. have also presented that the thermal entropy generation rates are highest and lowest for OS- and PL-shaped nanoparticles, respectively [13,48]. The Al2O3 and Al2O3/Cu nanofluids with The comparison of the friction entropy generation rate for single-particle and hybrid nanofluids with different nanoparticle shapes is shown in Figure 10. The friction entropy generation is due to a pressure drop, which depends on the density and viscosity of nanofluids with various nanoparticle shapes. The friction entropy generation rates are lower for hybrid nanofluids compared to single-particle nanofluids for all nanoparticle shapes. Except for single-particle nanofluids with PL- and CY-shaped nanoparticles, the friction entropy generation rates of other combinations are lower than water. The singleparticle and hybrid nanofluids with Sp- and OS-shaped nanoparticles present the lowest and second lowest values of friction entropy generation rates because of the same order of viscosity behavior for both nanoparticle shapes. The single-particle and hybrid nanofluids with PL-shaped nanoparticles show the highest values of friction entropy generation rates due to superior values of viscosity among all nanoparticles. The higher and lower values of friction entropy generation rates correspond to higher and lower velocity gradients of different nanoparticle shapes. Mahian et al. have also shown a trend in similar results, in that the friction entropy generation rate for PL-shaped nanoparticles is superior, followed by CY-, BL- and BR-shaped nanoparticles in the decreasing order [11]. The friction entropy generation rates of Al2O<sup>3</sup> and Al2O3/Cu nanofluids with Sp-shaped nanoparticles are lower by 1.93% and 5.13%, respectively, and those with OS-shaped nanoparticles are lower by 1.91% and 5.11%, respectively, than water. The friction entropy generation rate of the

OS-shaped nanoparticles show thermal entropy generation rates as higher by 0.14% and

significantly higher. The thermal entropy generation rates of Al2O3 and Al2O3/Cu nanofluids with PL-shaped nanoparticles are lower by 6.08% and 6.53%, respectively,

compared to water.

**Figure 9.** Thermal entropy generation rate for single-particle and hybrid nanofluids with different nanoparticle shapes. **Figure 9.** Thermal entropy generation rate for single-particle and hybrid nanofluids with different nanoparticle shapes. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 20 of 33

The comparison of the friction entropy generation rate for single-particle and hybrid

**Figure 10.** Comparison of friction entropy generation rate for single-particle and hybrid nanofluids with different nanoparticle shapes. **Figure 10.** Comparison of friction entropy generation rate for single-particle and hybrid nanofluids with different nanoparticle shapes.

different nanoparticle shapes is depicted in Figure 11. The Bejan number presents the contribution of thermal entropy generation in total entropy generation. The Bejan numbers of hybrid nanofluids are superior to single-particle nanofluids for all nanoparticle shapes. In addition, except the single-particle and hybrid nanofluids with PL- and CY-shaped nanoparticles and single-particle nanofluids with BL-shaped nanoparticles, all other combinations present higher values of Bejan numbers compared to water. The OS-shaped nanoparticles show the highest values of Bejan numbers, followed by Sp, PS1, PS2, PS3, PS4, BR, BL, CY and PL, respectively, in the decreasing order of the Bejan number for single-particle nanofluids. In the case of hybrid nanofluids, the decreasing order of Bejan numbers are OS-, PS2 = PS3-, Sp-, PS4-, PS1-, BR-, BL-, CYand PL-shaped nanoparticles, respectively. The OS-shaped nanoparticles show a higher contribution of the thermal entropy generation rate and a lower contribution of the friction entropy generation rate, which results in the highest value of the Bejan number. The opposite discussion could be applied for PL-shaped nanoparticles for the lowest value of the Bejan number. Al-Rashed et al. and Monfared et al. have also shown the lower Bejan number for PL-shaped nanoparticles [28,29]. The Bejan number is maximum for OSshaped nanoparticles and minimum for PL-shaped nanoparticles, as presented by Bahiraei et al. [48]. Compared to water, the Al2O3 and Al2O3/Cu nanofluids with OSshaped nanoparticles depict the Bejan number as higher by 0.19% and 0.54%, respectively, and those with PL-shaped nanoparticles depict the Bejan number as lower by 0.86% and

0.57%, respectively.

The behavior of the Bejan number for single-particle and hybrid nanofluids with different nanoparticle shapes is depicted in Figure 11. The Bejan number presents the contribution of thermal entropy generation in total entropy generation. The Bejan numbers of hybrid nanofluids are superior to single-particle nanofluids for all nanoparticle shapes. In addition, except the single-particle and hybrid nanofluids with PL- and CY-shaped nanoparticles and single-particle nanofluids with BL-shaped nanoparticles, all other combinations present higher values of Bejan numbers compared to water. The OS-shaped nanoparticles show the highest values of Bejan numbers, followed by Sp, PS1, PS2, PS3, PS4, BR, BL, CY and PL, respectively, in the decreasing order of the Bejan number for single-particle nanofluids. In the case of hybrid nanofluids, the decreasing order of Bejan numbers are OS-, PS2 = PS3-, Sp-, PS4-, PS1-, BR-, BL-, CY- and PL-shaped nanoparticles, respectively. The OS-shaped nanoparticles show a higher contribution of the thermal entropy generation rate and a lower contribution of the friction entropy generation rate, which results in the highest value of the Bejan number. The opposite discussion could be applied for PL-shaped nanoparticles for the lowest value of the Bejan number. Al-Rashed et al. and Monfared et al. have also shown the lower Bejan number for PL-shaped nanoparticles [28,29]. The Bejan number is maximum for OS-shaped nanoparticles and minimum for PL-shaped nanoparticles, as presented by Bahiraei et al. [48]. Compared to water, the Al2O<sup>3</sup> and Al2O3/Cu nanofluids with OS-shaped nanoparticles depict the Bejan number as higher by 0.19% and 0.54%, respectively, and those with PL-shaped nanoparticles depict the Bejan number as lower by 0.86% and 0.57%, respectively. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 21 of 33

**Figure 11.** The behavior of Bejan number for single-particle and hybrid nanofluids with different nanoparticle shapes. **Figure 11.** The behavior of Bejan number for single-particle and hybrid nanofluids with different nanoparticle shapes.

The combination of hybrid nanofluid with OS shaped nanoparticles show the excellent first law and second law characteristics compared to other combinations as well as water. Therefore, the first law characteristic namely, performance index and the second law characteristic namely, Bejan number of hybrid nanofluid (Al2O3/Cu) with OS shaped nanoparticles are further investigated for different temperatures and mass flow rates of hot and cold fluids. In addition, the influence of volume fraction is also integrated while investigating the effect of temperature and mass flow rate on different characteristics. The The combination of hybrid nanofluid with OS shaped nanoparticles show the excellent first law and second law characteristics compared to other combinations as well as water. Therefore, the first law characteristic namely, performance index and the second law characteristic namely, Bejan number of hybrid nanofluid (Al2O3/Cu) with OS shaped nanoparticles are further investigated for different temperatures and mass flow rates of hot and cold fluids. In addition, the influence of volume fraction is also integrated while investigating the effect of temperature and mass flow rate on different characteristics. The

whereas, the Bejan number presents the combined effect of thermal and friction entropy generations hence, these two parameters are considered as the first and second law

The behavior of first and second law characteristics of the Al2O3/Cu nanofluid with OS-shaped nanoparticles for various volume fractions and hot fluid temperatures is presented in Figure 12. The hot fluid temperature varies at 90 °C, 80 °C, and 70 °C and the volume fraction varies at 0.5%, 1.0% and 2.0%. The performance index increases with an increase in the volume fraction as well as hot fluid temperature. The heat transfer and pressure drop both increase with an increase in volume fraction, but the increase in the heat transfer dominates compared to the increase in the pressure drop, hence, as a result, the performance index increases as the volume fraction increases for all hot fluid temperatures. The hot fluid at the higher temperature could transfer more heat compared to hot fluid at a lower temperature. The pressure drop remains almost the same for various hot fluid temperatures, whereas the heat transfer increases with a rise in the temperature, which shows an enhancement in the performance index with an increase in the hot fluid temperature for all volume fractions. The performance index of Al2O3/Cu with OS-shaped nanoparticles increases by 20% and 40% as the hot fluid temperature increases from 70 °C to 80 °C and 70 °C to 90 °C, respectively, for each volume fraction. With the increase in

characteristics under the influence of various boundary parameters.

*5.5. Effect of Hot Fluid Temperature on First and Second Law Characteristics* 

performance index presents the combined effect of heat transfer and pressure drop whereas, the Bejan number presents the combined effect of thermal and friction entropy generations hence, these two parameters are considered as the first and second law characteristics under the influence of various boundary parameters.
