*2.1. Design and Manufacture of PCHE*

The printed circuit heat exchanger (PCHE) used in this research consisted of four flat stainless steel plates: two hot plates and two cold plates with lengths, widths, and heights of 0.11 m, 0.145 m, and 0.012 m, respectively, as shown in Figure 1a,b. The rectangular channels had a hydraulic diameter of 0.0021 m and were manufactured using precision machining. The flow area of the plate was divided into three zones. The first sone was the three-channel areas in the plate composed of 13 channels. The second zone was the four pool areas at the side of the channel areas. The channel was designed to guide the fluid flow path turn at 180 degrees to the next channel. The last zone had two baffles with a 0.003-m width on the plate, which guided the flow and separated the channel areas and the aforementioned configuration of the channel. Therefore, the working fluid flowed on the plate in an S-shape. This design was to ensure that each channel was fully filled with working fluid and extended the staying time for the fluid in the flow plate. Moreover, hot and cold fluid plates showed symmetric geometry to increase the area of heat transfer [29].

According to the literature, a high compactness and channel distribution density in the PCHE will improve the overall efficiency [12]. The flow directions of cold and hot fluids and the configuration of the PCHE are shown in Figure 2. During the manufacturing process, the stacked plates, including four runner mirror-symmetrically plates and a top plate with a thickness of 0.004 m, were put in a vacuum (10−3 tor) with a working temperature of 1045 ◦C. The function of the top plate was to protect the PCHE channels from damage during the pressurization process. Next, the plates were subjected to a pressure of 200 bar in the vertical direction to ensure that the distance between the two plates achieved the atomic distance, while cooling down to the surrounding temperature. The fluid flow direction is illustrated in Figure 2c, in which the blue and red arrows represent the cold and hot fluid flows, respectively. After the fluids enter the PCHE, they go into each channel of the plate and then go out. In order to ease the testing of the PCHE, the screw holes at the edge of the plate were designed with a diameter of 0.012 m to facilitate the installation of a 0.375 inch copper joint. Then, heat-resistant silicone hoses were installed on the inlet and outlet of the PCHE.

**Figure 1.** (**a**) The design of the PCHE; (**b**) hot fluid flow plate and cold fluid flow plate in the PCHE.

**Figure 2.** Flow plate geometric of PCHE and flow direction: (**a**) cold and hot fluid flow plate; (**b**) side view and three-dimensional explosion map; and (**c**) schematic diagram of the PCHE.

#### *2.2. Experiment Setup*

The experimental apparatus and setup to measure and calculate the thermal performance of the PCHE is described in Figure 3, which consists of water as the hot and cold working fluids, two flow meters (Shuang Huan, Taiwan, DK800-6) with adjustable valves installed on the hot fluid and cold fluid circulating loop, refrigerated circulating bath (Yih Der, Tainan, Taiwan, BL710-D), pump (HITON, Tainan, Taiwan, HF-8006) and a 40-L water heating system powered by liquified petroleum gas (Ta-Han, Tainan, Taiwan, BDF-23C). The temperatures were measured using eight K-type thermocouples (Chuan Yu, Kaohsiung, Taiwan, K type) connected to an industrial computer, equipped with a thermocouple slot module. Filters were installed at the outlet of the sink and the water heating system to remove impurities in the working fluid and prevent damage to the flow meter. Since the flow layout was set to be in a counterflow, the counterflow pattern was adopted in the flow configuration [30], which resulted in a high effectiveness, where the cold inlet was on the opposite side of the hot inlet. It is also shown in Figure 3 that the flow rate passing through the flowmeters was controlled by a valve; the maximum mass flow rate was 100 L/h. The hot working fluid was driven by a pump and the temperature of the fluid was controlled by a heater. A constant-temperature cold working fluid was supplied by a refrigerated circulating bath to the test rig. The thermocouples were installed at the inlet and outlet of both fluids and inside the tube of the copper joint. They were about 0.001 m away from the entrance of the PCHE. Before performing experiments, the thermocouples were calibrated to an accuracy of ±0.01 ◦C. In addition, the water heating system had thermocouples to accurately monitor and control the temperature. Finally, all piping system and PCHE were insulated with thermal insulation wool to minimize heat loss.

**Figure 3.** Schematic diagram of the experiment setup.

#### *2.3. Operations and Data Analysis of Experimentations*

Three different hot fluid inlet temperatures, 75 ◦C, 85 ◦C, and 95 ◦C, were used in this study. The inlet temperature of the cold fluid (water) was 20 ◦C. The range of the cold and hot fluids' flow rates were 0.1667–1.667 L/min (i.e., 10–100 L/h), they were adjusted by the valve on the flowmeter. This corresponds to the Reynolds numbers of 50–514. The Reynolds number (Re) was calculated in Equation (1) in light of the method suggested by Cowell [31]. The average convective heat transfer coefficient (*h*) and Nusselt number (Nu) were obtained using Equations (2) and (3) as [9]:

$$\text{Re} = \frac{\rho V D\_h}{\mu} \tag{1}$$

$$h = \frac{\left(\dot{m}c\_p\Delta T\right)\_{hot}}{A\left(T\_s - T\_\infty\right)}\tag{2}$$

$$\text{Nu} = \frac{hD\_h}{k} \tag{3}$$

In Equation (1), *Dh* (0.0021 m) is the hydraulic diameter, *V* is the velocity of the fluid, *μ* is the dynamic viscosity of the fluid, and ρ is the density of the fluid. In Equation (2), the product in the numerator is the heat flux of hot fluid, including *cp* (specific heat), . *m* (flow rate), and Δ*T* (the temperature difference between the inlet and outlet), respectively. In addition, *Ts* and *T*<sup>∞</sup> are the temperature of channel surface and fluid temperature, respectively. In Equation (3), k represents the thermal conductivity.

The effectiveness (ε) of the PCHE [9] is assessed as the ratio of the actual heat transfer rate (*Qactual*) to the theoretical maximum rate of the heat transfer (*Qmax*) and is expressed using the equation below:

$$\varepsilon = \frac{Q\_{\text{actual}}}{Q\_{\text{max}}} = \frac{C\_{\text{hot}} \left(T\_{\text{h,in}} - T\_{\text{h,out}}\right)}{C\_{\text{min}} \left(T\_{\text{h,in}} - T\_{\text{c,in}}\right)} = \frac{\left(\dot{m} \ c\_p\right)\_{\text{hot}} \left(T\_{\text{h,in}} - T\_{\text{h,out}}\right)}{\left(\dot{m} \ c\_p\right)\_{\text{min}} \left(T\_{\text{h,in}} - T\_{\text{c,in}}\right)}\tag{4}$$

In Equation (4), *Tc*,*in*, *Th*,*in*, and *Th*,*out* represent the temperature of the cold inlet, hot inlet, and hot outlet, respectively. *Chot* denotes the product of the mass flow and specific heat of the hot and fluid, and *Cmin* is the smaller one between the cold and hot fluid.

The value of the overall heat transfer coefficient (*U*) can be calculated from the heat transfer area and the logarithmic mean temperature difference (LMTD) between the hot and cold fluid flows and average heat transfer rate ( . *Qaverage*) by Thulukkanam [9]. They are expressed as follows: .

$$
\dot{Q}\_{\text{average}} = \frac{\dot{Q}\_{\text{hot}} + \dot{Q}\_{\text{cold}}}{2} \tag{5}
$$

$$
\dot{U} = \frac{\dot{Q}\_{\text{average}}}{A\_{\text{total}} \, LMTD} \tag{6}
$$

$$LMTD = \frac{\Delta T\_1 - \Delta T\_2}{LnN(\frac{\Delta T\_1}{\Delta T\_2})}\tag{7}$$

where Δ*T*<sup>1</sup> and Δ*T*<sup>2</sup> are the temperature difference of the inlet and outlet between the hot and cold working fluid, respectively, as shown below:

$$
\Delta T\_1 = T\_{hot, inlet} - T\_{cold, outlet} \tag{8}
$$

$$
\Delta T\_2 = T\_{hot, outlet} - T\_{cold, inlet} \tag{9}
$$

The number of transfer units (NTU) value can be calculated by the overall heat transfer coefficient [32], as shown in Equation (10). In the equation, *Atotal* is the total area of heat transfer of the PCHE, *Cmin* is the smaller one between heat capacity of cold and hot fluid, *cp*,*<sup>c</sup>* is the heat capacity of cold fluid. Similar to other literature analysis, the usual heat exchanger effectiveness ε is defined as the relation function between *Cr* and NTU, as shown in Equation (11) and can be simplified to Equation (12) [33]:

$$NTUI = \frac{UA\_{total}}{C\_{min}} = \frac{UA\_{total}}{(mc\_{p,c})\_C} \tag{10}$$

$$\varepsilon = \frac{1 - \varepsilon^{[-NTU(1-C\_r)]}}{1 - C\_r \varepsilon^{[-NTU(1-C\_r)]}} \tag{11}$$

$$\varepsilon = \frac{NTU}{1 + NTU} \tag{12}$$

$$\mathbf{C}\_{I} = \frac{\mathbf{C}\_{\text{min}}}{\mathbf{C}\_{\text{max}}} \tag{13}$$

#### *2.4. Uncertainties Analysis*

The results of the experiment and its measurements were affected by many factors. Uncertainty analysis was used to make sure that the precision of the measurement device was set before the experiments, and to calibrate and ascertain their accuracies. This included electronic load, flowmeters, and thermocouples. The ranges of measuring or operating, resolution, and uncertainty in measurement is tabulated in Table 2, where uncertainty in the measurement of devices is defined as in Equation (14) [34]:

$$\text{Relative uncertainty} = \frac{0.5 \times \text{resolution}}{\text{value of measuring or operating}} \tag{14}$$

**Table 2.** Uncertainty analysis of the equipment used in this study.


Table 2 lists the data for supplying and the deviation analysis of experiments, including temperature, which was controlled between 75 ◦C and 95 ◦C and the flow rate was between 10 L/h and 100 L/h. The analysis results of the uncertainty of the measurement due to the equipment was less than 2.5%.

#### **3. Results and Discussion**

#### *3.1. Effectiveness*

Figure 4 illustrates the effectiveness of the PCHE for three different inlet temperatures of the hot fluid flow versus the cold-to-hot fluid flow rate ratio. The effectiveness (ε) can be observed to easily decrease with an increase in flow rate ratio. The effectiveness of the heat exchanger drops by at least 50% when the ratio of flow rate increases from 0.1 to 1, showing the pronounced influence of the ratio of the flow rate on the effectiveness of the PCHE. On the other hand, the differences between the three curves are not significant, revealing that the effect of increasing the inlet temperatures is not as obvious as the flow rate ratio.

**Figure 4.** The effectiveness of the PCHE on different hot inlet temperatures.

In Figure 4, the highest effectiveness of 0.979 was achieved at a flow rate ratio of 0.1 (i.e., the minimum ratio of flow rate), whereas the lowest effectiveness of 0.428 is exhibited at a flow rate ratio of 1, rendering a 53% difference in the effectiveness between the two ratios under the same hot inlet temperature. On account of the higher effective value at a ratio of 0.1, this ratio is suitable for the operation of PCHEs. On the contrary, a flow rate ratio of 1 will lead to poor performance of the PCHE. Overall, the effectiveness of the PCHE under the hot inlet temperature of 95 ◦C is better than the other two temperatures at a low flow rate ratio. In summary, operating the heat exchanger with high inlet temperature and low flow rate ratio is conducive to intensifying the effectiveness and thereby the heat exchange. Attala et al.'s [35] experimental results on the plate heat exchanger had a similar behavior at a low Reynolds number.

#### *3.2. Temperature Distribution*

The temperature distribution of the hot and cold fluid inlet and outlet at three different hot inlet fluid temperatures (75, 85, and 95 ◦C), along with a fixed cold inlet temperature (20 ◦C) for different flow rate ratios, are shown in Figure 5. Altering the flow rate ratio causes variations in the temperature of the distribution. At low flow ratios, such as 0.1, 0.125, and 0.167, the temperature slopes of the hot fluid flow are relatively insignificant, whereas the temperature slopes of the cold fluid flow are steeper. This is ascribed to more heat being contained in the hot fluid and relatively less heat being transferred to the cold fluid, stemming from a lower cold fluid flow rate. As a consequence, the temperature variation of the hot fluid flow is small, whereas it is pronounced in the cold fluid flow. On the contrary, at higher flow rate ratios, such as 0.333, 0.667, and 1, the variation in the temperature of the hot fluid flow tends to become obvious, whereas the rising tendency in the temperature of the cold fluid flow becomes less obvious [36]. For the cases of a flow rate ratio of <0.667, it is noteworthy that, after heat exchange, the outlet temperature of

the cold fluid flow is always higher than that of the hot fluid flow, whereas an opposite result is observed at flow rate ratio =0.667 and 1. For the two factors of the hot fluid inlet temperature and the flow rate ratio investigated in this study, Figure 5 indicates that the flow rate ratio is more influential on the temperature profile when compared with the hot fluid inlet temperature. Figley et al. [32] explored the correlation between flow rate ratio and hot fluid inlet temperature, which had a similar temperature changing trend, and established the thermal-hydraulic performance in their PCHE numerical model.

#### *3.3. Temperature Difference and Effectiveness*

Figure 6a examines the temperature difference of the cold and hot fluids' between the inlet and outlet. The temperature difference of the hot fluid between the outlet and inlet decreases with the rising flow rate ratio, but it shows an opposite trend for the cold fluid. Physically, the higher the temperature difference, the better the heat transfer. At low flow rate ratios, the temperature difference of the cold fluid flow is higher which is contributed by a high flow rate of the cold fluid. Thus, the temperature of the cold fluid flow can be easily raised. Meanwhile, the temperature difference in the hot fluid flow is small, which is ascribed to the high flow rate of the hot fluid. It is not surprising that an increase in the hot fluid's inlet temperature increases the temperature differences of the hot and cold fluids. A past study [37] provided several cross-flow configurations and explained the correlation between the effectiveness and the temperature difference which is in line with the obtained results in the present study.

To further investigate the heat transfer performance, the temperature difference between the cold and hot fluid temperature versus flow rate ratio is shown in Figure 6b. Meanwhile, the profiles of the effectiveness from Equation (12) are also shown in Figure 6b. As a whole, both the D value and effectiveness (*ε*) decrease monotonically with the increase of the flow rate ratio. Physically, the effectiveness is a ratio between the actual heat transfer rate and the maximum (ideal) heat transfer rate. Accordingly, when the effectiveness is larger, the performance of heat transfer is also better. The maximum value of the effectiveness in Figure 6b is 0.979, occurring at a hot fluid flow inlet of 95 ◦C and the flow rate ratio of 0.1. In contrast, the minimum value of the effectiveness is 0.428 occurring at a hot fluid flow inlet of 75 ◦C and a flow rate ratio of 1. This indicates that the low flow rate ratio with low cold fluid flow rate and high hot fluid flow rate is a better combination for optimum thermal performance for the PCHE. Overall, the distributions of D and *ε* showed high correlation.

**Figure 5.** Temperature distributions of hot and cold fluid flow after heat exchange at flow rate ratios of (**a**) 0.1, (**b**) 0.125, (**c**) 0.167, (**d**) 0.333, (**e**) 0.667, and (**f**) 1.

**Figure 6.** The temperature difference plot for different flow rate ratios and effectiveness (**a**) the temperature difference between inlet and outlet of hot (solid line) and cold (dash line) fluid. (**b**) the temperature difference (solid line) between hot and cold fluid and effectiveness (dash line).

#### *3.4. Characteristics of Heat Transfer Performance*

Figure 7 shows the convective heat transfer coefficient of the PCHE under various Reynolds numbers of the cold fluid flows. A higher Reynolds number is conducive to convective heat transfer. A similar behavior was also observed in a previously reported study [38]. This is why there is an increment of convective heat transfer coefficient with a rising Reynolds number. For the hot fluid flow inlet temperature of 95 ◦C, the heat transfer coefficient value is increased from Re = 50 to Re = 300, rendering an increment of 67.8%, and other conditions of hot inlet temperatures are increasing by at least 64%. At low Re values, such as 50 and 100, the sensitivity of the heat transfer coefficient to the hot fluid flow inlet temperature Re is low and the variation is small. However, at Re = 300, the convective heat transfer coefficient at the hot fluid flow inlet temperature at 95 ◦C is about 5% higher than that of the convective heat transfer coefficient at the hot fluid flow inlet temperature at 75 ◦C. The relationship between the effectiveness and the Reynolds number is shown in Figure 7. Unlike the convective heat transfer coefficient, as the Reynolds number increases, the effectiveness shows a downward trend. The convective heat transfer coefficient shows a positive correlation with the Reynolds number of the cold fluid flow where the amount of heat transfer increases. However, the fluid velocity is relatively high and the residence time of the cold fluid in the channel is shorter and reduces the effectiveness of the heat exchanger. The flow plates of PCHE are designed as an S-shape (Figures 1 and 2), which can prolong the residence time of the working fluid. It is obvious that the influence of the residence time prevails over the flow rate. Thus, the effectiveness declines with an increasing Reynolds number. Yan et al. [39] studied the effectiveness values of the different flow rate configurations in which they also observed a similar decreasing trend of the heat exchanger effectiveness with the increasing of the flow rate.

Figure 8 further explores the relationship between the Nusselt number (Nu) and the Reynolds number in the channel. The Nusselt number is proportional to the convective heat transfer coefficient which is a function of the flow rate or Reynolds number. As a consequence, the Nusselt number goes up when the Reynolds number increases, and the entire trend of the Nusselt number curves resembles that of the convective heat transfer coefficient. Yang et al. [38] studied the flow and performance of heat transfer in mini channels configured with hexagonal fins at laminar flow, and obtained a similar heat transfer performance. For the hot fluid flow inlet temperature of 95 ◦C, the Nusselt number increases by 68% when the Reynolds number increases from 50 to 300. Similar to the convective heat transfer coefficient, the Nusselt number is fairly insensitive to the variation of the hot fluid flow inlet temperature at Re = 50 and 100, while its variation at Re = 300 is also insignificant. This reflects that both the Nusselt number and the convective heat transfer coefficient are mainly governed by the Reynolds number, whereas the hot fluid flow inlet temperature is not affecting the Nusselt number and the convective heat transfer coefficient. To develop the correlation for Nusselt number and Reynold number, the basic logarithm form was used, as follows:

$$\text{Nu} = 0.03428 \text{Re}^{0.6135} \tag{15}$$

**Figure 7.** Convective heat transfer coefficient and effectiveness versus Reynolds number for different hot inlet temperatures.

**Figure 8.** Nusselt number with different inlet temperatures for different Reynolds numbers.
