*3.5. The Number of Transferred Unit Value (NTU)*

The value of the number of transferred unit (NTU) signifies the rate of net heat exchange between two fluids in the PCHE. The profiles of NTU and effectiveness are plotted in Figure 9 to show the relationship between NTU, effectiveness, and flow rate ratio. Both the NTU and effectiveness values decrease with rising flow rate ratios, revealing that the trend of NTU follows the trend of effectiveness. A past simulation study [40] explored the relationship between NTU and effectiveness, and observed that the heat exchanger effectiveness ε and NTU have the same trend in counterflow. When the ratio of flow rate decreases from 1 to 0.1, the NTU value is increased by 70.3% at a low flow rate. These explain that a longer residence time in the PCHE is beneficial to heat transfer. When the Cr value is 1, the values of the effectiveness and NTU with the hot inlet temperature of 95 ◦C are 0.428 and 0.83, respectively. The calculated effectiveness using Equation (12), in terms of NTU, is 0.453, which is close to the calculated effectiveness using Equation (3), which is 0.428. Sheldon et al. [41] compared the most common estimated efficiency methods for heat exchangers—effectiveness and NTU methods—and mentioned that the two methods were equivalent.

**Figure 9.** The profiles of NTU value versus the flow rate ratio.

#### *3.6. Comparison to Other Research*

This study provides the effectiveness of PCHEs using water as a working fluid at low Reynolds numbers. The experimental results showed that the obtained effectiveness values in this study were between the values of past reported studies, as shown in Figure 10. In past studies, heat exchangers with compact microchannel were constructed and water was used as a working fluid in counterflow at low Reynolds numbers. Hasan et al. [42] studied the influence of channel geometry on the performance of microchannel heat using simulations, where the effectiveness values of the circular and square channels were higher and lower, respectively. The hydraulic diameter was about 24 times smaller than our PCHE. In general, the attained effectiveness in this study is better than that of the Hasan et al. design [42]. On the other hand, the effectiveness of this study is lower than the results of Seyf et al. [43] and Mohammadian et al. [44]. Seyf et al. [43] studied microchannel heat exchangers using simulations. The hydraulic diameter in the study of Seyf et al. [43] was smaller than our PCHE by a factor of around 23 times. This is the reason why their results are better. In the study of Mohammadian et al. [44], they numerically studied nanofluid (Al2O3-water) in a counterflow heat exchanger, which had a better heat transfer

performance. The nanofluid could easily increase the cold outlet temperature and make the temperature difference increase, so their results are better than those of the present study.

**Figure 10.** Comparison with the studies from the literature.

#### **4. Conclusions**

In the present study, a printed circuit heat exchanger (PCHE) is successfully fabricated using precision manufacturing and diffusion bonding. The printed circuit heat exchanger with an S-shaped meandering design for a flow path was tested at laminar flow (50 < Re < 300). The experimental results showed that the printed circuit heat exchanger provides high effectiveness and thermal performance at low flow rate ratios. The highest effectiveness of the PCHE is about 0.979 for an inlet flow temperature of 95 ◦C. The highest heat transfer coefficient obtained from the experiment is about 347.8 for Re = 300. The waste heat at a hot spring can be effectively harvested through the S-type meandering design of the flow path on the heat exchanger plate. This design will provide a larger heat transfer area and maximize the heat exchange between the fluids. A combination of the multiple flow rate ratios shows the best operating conditions. Regardless of the inlet temperature, the effectiveness of the PCHE is always higher. When the flow rate ratio is 1, the NTU value and effectiveness are about 0.83 and 0.428, respectively. In future work, the printed circuit heat exchanger will be tested under turbulent flow conditions to further characterize its thermal performance.

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

**Funding:** This research was supported in part by Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at National Cheng Kung University(NCKU). The authors also acknowledge the financial support of the Ministry of Science and Technology, Taiwan, R.O.C., under the contracts The authors acknowledge the financial support of the Ministry of Science and Technology, Taiwan, R.O.C., under the contract MOST 109-2622-E-006-006-CC1.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This research was supported in part by Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at National Cheng Kung University(NCKU). The authors also acknowledge the financial support of the Ministry of Science and Technology, Taiwan, R.O.C., under the contracts. The authors acknowledge the financial support of the Ministry of Science and Technology, Taiwan, R.O.C., under the contract MOST 109-2622-E-006- 006-CC1.

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

#### **Nomenclature**


#### **References**

