**4.1 Effects of fluid properties**

For the effects of fluid properties on heat transfer and fluid flow behaviors, the microchannel heat exchanger T1 was tested; the results were shown more in detail by Dang et al. [26]. The parameters of heat exchangers are listed in Table 2.

## **Flow rate and inlet temperature being constant for the cold side**

For experiments carried out in the study, the inlet temperature and mass flow rate of the cold side were fixed at 26.5 ºC and 0.1773 g/s, respectively. For the hot side, an inlet temperature was fixed at 52 ºC and the mass flow rates were varying from 0.1841 to 0.3239 g/s. The thermal boundary conditions of the top and bottom walls of the heat exchanger were assumed to be constant heat flux. The convective heat transfer coefficient between the wall and the ambient used for this solver was 10 W/(m2K), with the ambient temperature and air velocity of 26 C and 0.2 m/s, respectively. The temperature profile of the microchannel heat exchanger is shown in Fig. 6 for a mass flow rate of 0.2556 g/s at the hot side.

At a constant inlet temperature of 52 ºC at the hot side, for the case with both mass flow rate and temperature constant at the inlet of cold side, a relationship between the outlet temperatures (for both the hot side and cold side) and the mass flow rate of the hot side is shown in Fig. 7a. The outlet temperatures increase as the mass flow rate of the hot side increases. Because that the heat exchanger under study is the one with counter-flow, the outlet temperature of the cold side is higher than that obtained at the hot side [22-24]. A comparison between the numerical and experimental results is also shown in Fig. 7a. Fig 7a shows the outlet temperatures as a function of the mass flow rate of the hot side, and the results obtained from the simulation are in good agreement with those obtained from the experiments. The maximum difference of the outlet temperatures is 0.8 C and the maximum percentage error is 2%.

Fig. 6. The temperature profile of the microchannel heat exchanger.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 263

value, as shown in Eq. (6). When the mass flow rate of the hot side is increased, the heat transfer rate *Q* of the heat exchanger increases also. As a result, heat transfer obtained from the effectiveness increases with a rising the mass flow rate at the hot side. The trends of effectiveness and actual effectiveness are observed to be in the opposite directions, as shown

The results obtained from numerical simulation and from experimental data for the actual effectiveness and for the effectiveness are compared also. Fig. 7c indicates that at various mass flow rates of the hot side, the heat transfer results obtained from the actual effectivenesses are higher than those obtained from the effectivenesses. The maximum difference of the effectivenesses between the two occurs at high mass flow rate of the hot side, with the maximum difference of 0.7 and the maximum percentage error of 8.7 %. This difference may be due to errors in the experiments or mesh generation in the numerical simulations. It is noted that experimental results of effectiveness obtained from this study

Again, at the condition stated above, the heat flux of the microchannel heat exchanger increases from 5.8 to 8.0 W/cm2 with a rising the mass flow rate of the hot side ranging from 0.1841 to 0.3239 g/s, as shown in Fig. 7d. A comparison between the numerical and experimental results for the heat flux at various mass flow rates of the hot side is shown in Fig. 7d. Since the heat flux obtained from the simulation is only slightly higher than that obtained from the experiment, the results obtained from the simulation are judged to be in good agreement with those obtained from the experiments. The maximum difference of heat fluxes is 0.40 W/cm2; it occurs at low mass flow rate of the hot side, and the maximum percentage error is 7.2%. This difference may be due to errors in the experiments or mesh generation in the numerical simulations also. The heat flux obtained from this study is higher than that obtained from [5]; the latter has the heat flux increasing from 0.2 to 1.1 W/cm2 and the mass flow rate increasing from 2.7 to 111.1 g/s. However, due to the variation in presenting data, it is difficult to make a complete comparison between the

To summarize, for this case with the results presented in Figs. 7a-7d, the trends for actual effectiveness and effectiveness indicate that as the mass flow rate of hot side goes up, the former goes down while the latter goes up; this is an important effect observed for the

For this case, the inlet temperature and mass flow rate of the hot side were fixed at 52 ºC and 0.1667 g/s, respectively. For the cold side, an inlet temperature was fixed at 26.5 ºC and the mass flow rates were varying from 0.1859 to 0.3625 g/s. Fig. 8a shows a relationship between the outlet temperatures (for both the hot side and cold side) and the mass flow rates of the cold side at the condition stated above. Contrary to the category of cases of constant mass flow rate and inlet temperature for the cold side, the outlet temperatures decrease as the mass flow rate of the cold side increases. A comparison between the results obtained from numerical simulation and experimental data for the outlet temperatures of both the hot side and the cold side is shown in Fig. 8a. The maximum difference between the two results is 0.4 ºC, occurring at low mass flow rate of cold side, with the maximum

results obtained from the present study and those obtained from [5] and [7].

**Flow rate and inlet temperature being constant for the hot side** 

are higher than those obtained from Kang and Tseng [6].

microchannel heat exchanger used in the study.

percentage error of 1.2%.

in Fig. 7c.

At the condition stated above, the heat transfer rates of the hot side and cold side increase with rising mass flow rate of the hot side, as shown in Fig. 7b. The maximum difference of the heat transfer rate between the numerical results and experimental data is 1.08 W and the maximum percentage error is 7.3%. However, it is observed that the heat transfer rate for the hot side increases at a higher slope than that for the cold side as the mass flow rate increases. It is also observed that the actual effectiveness for the microchannel heat exchanger decreases with rising mass flow rate of the hot side, as shown in Fig. 7c. This means that the heat loss increases with rising flow rate of the hot side. Fig. 7c shows a relation of effectivenesses (actual effectiveness and NTU effectiveness) as a function of the mass flow rate of the hot side.

Because that the inlet temperatures of both sides are fixed at constant values and that the heat capacity rate *(mc)min* is fixed, the maximum heat transfer *Qmax* is fixed at a constant

At the condition stated above, the heat transfer rates of the hot side and cold side increase with rising mass flow rate of the hot side, as shown in Fig. 7b. The maximum difference of the heat transfer rate between the numerical results and experimental data is 1.08 W and the maximum percentage error is 7.3%. However, it is observed that the heat transfer rate for the hot side increases at a higher slope than that for the cold side as the mass flow rate increases. It is also observed that the actual effectiveness for the microchannel heat exchanger decreases with rising mass flow rate of the hot side, as shown in Fig. 7c. This means that the heat loss increases with rising flow rate of the hot side. Fig. 7c shows a relation of effectivenesses (actual effectiveness and NTU effectiveness) as a function of the

0.0

2.0

4.0

6.0

**Heat flux, W/cm2**

8.0

10.0

a) Outlet temperature b) Heat transfer rate

c) Effectiveness d) Heat flux

Fig. 7. A comparison between numerical and experimental results at constant inlet

Because that the inlet temperatures of both sides are fixed at constant values and that the heat capacity rate *(mc)min* is fixed, the maximum heat transfer *Qmax* is fixed at a constant

0

0.1600 0.2000 0.2400 0.2800 0.3200 0.3600 **Mass flow rate of hot side, g/s**

0.1600 0.2000 0.2400 0.2800 0.3200 0.3600 **Mass flow rate of hot side, g/s**

Num. results Exp. results

Num. results of hot side Exp. results of hot side Num. results of cold side Exp. results of cold side

4

8

12

**Heat transfer rate,** 

**W**

16

20

mass flow rate of the hot side.

Num. results of hot side Exp. results of hot side Num. results of cold side Exp. results of cold side

0.1600 0.2000 0.2400 0.2800 0.3200 0.3600 **Mass flow rate of hot side, g/s**

0.1600 0.2000 0.2400 0.2800 0.3200 0.3600 **Mass flow rate of hot side, g/s**

temperature and mass flow rate for the cold side.

Num. results of actual eff. Exp. results of actual eff. Num. results of eff. Exp. results of eff.

30

0.00

0.20

0.40

**Effectiveness**

0.60

0.80

1.00

34

38

**Outlet temperature, o**

**C**

42

46

50

value, as shown in Eq. (6). When the mass flow rate of the hot side is increased, the heat transfer rate *Q* of the heat exchanger increases also. As a result, heat transfer obtained from the effectiveness increases with a rising the mass flow rate at the hot side. The trends of effectiveness and actual effectiveness are observed to be in the opposite directions, as shown in Fig. 7c.

The results obtained from numerical simulation and from experimental data for the actual effectiveness and for the effectiveness are compared also. Fig. 7c indicates that at various mass flow rates of the hot side, the heat transfer results obtained from the actual effectivenesses are higher than those obtained from the effectivenesses. The maximum difference of the effectivenesses between the two occurs at high mass flow rate of the hot side, with the maximum difference of 0.7 and the maximum percentage error of 8.7 %. This difference may be due to errors in the experiments or mesh generation in the numerical simulations. It is noted that experimental results of effectiveness obtained from this study are higher than those obtained from Kang and Tseng [6].

Again, at the condition stated above, the heat flux of the microchannel heat exchanger increases from 5.8 to 8.0 W/cm2 with a rising the mass flow rate of the hot side ranging from 0.1841 to 0.3239 g/s, as shown in Fig. 7d. A comparison between the numerical and experimental results for the heat flux at various mass flow rates of the hot side is shown in Fig. 7d. Since the heat flux obtained from the simulation is only slightly higher than that obtained from the experiment, the results obtained from the simulation are judged to be in good agreement with those obtained from the experiments. The maximum difference of heat fluxes is 0.40 W/cm2; it occurs at low mass flow rate of the hot side, and the maximum percentage error is 7.2%. This difference may be due to errors in the experiments or mesh generation in the numerical simulations also. The heat flux obtained from this study is higher than that obtained from [5]; the latter has the heat flux increasing from 0.2 to 1.1 W/cm2 and the mass flow rate increasing from 2.7 to 111.1 g/s. However, due to the variation in presenting data, it is difficult to make a complete comparison between the results obtained from the present study and those obtained from [5] and [7].

To summarize, for this case with the results presented in Figs. 7a-7d, the trends for actual effectiveness and effectiveness indicate that as the mass flow rate of hot side goes up, the former goes down while the latter goes up; this is an important effect observed for the microchannel heat exchanger used in the study.

#### **Flow rate and inlet temperature being constant for the hot side**

For this case, the inlet temperature and mass flow rate of the hot side were fixed at 52 ºC and 0.1667 g/s, respectively. For the cold side, an inlet temperature was fixed at 26.5 ºC and the mass flow rates were varying from 0.1859 to 0.3625 g/s. Fig. 8a shows a relationship between the outlet temperatures (for both the hot side and cold side) and the mass flow rates of the cold side at the condition stated above. Contrary to the category of cases of constant mass flow rate and inlet temperature for the cold side, the outlet temperatures decrease as the mass flow rate of the cold side increases. A comparison between the results obtained from numerical simulation and experimental data for the outlet temperatures of both the hot side and the cold side is shown in Fig. 8a. The maximum difference between the two results is 0.4 ºC, occurring at low mass flow rate of cold side, with the maximum percentage error of 1.2%.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 265

At the condition stated above, the overall heat transfer coefficient k of the heat exchanger increases from 0.625 to 0.815 W/(cm2K) with the mass flow rate of cold side rising from 0.1859 to 0.3625 g/s, as shown in Fig. 8c. At a hydraulic diameter of 375 m, Kandlikar et al. [44] gave k = 0.85 W/(cm2K), compared to k = 0.815 W/(cm2K) obtained in this study. Thus, the two results are in good agreement. For this case, the change in the log mean temperature difference is small: it reduces from 10.7 to 10.0 C with the mass flow rate of cold side rising from 0.1859 to 0.3625 g/s. The heat flux increases from 6.2 to 8.2 W/cm2 with the mass flow rate of cold side rising from 0.1859 to 0.3625 g/s, as shown in Fig. 8d. Thus, the heat flux affected by the log mean temperature difference is less than that by the overall heat transfer coefficient (7.0% versus 30.4% on a percentage basis). Comparisons between the results obtained from numerical simulation and experimental data for the outlet temperature, the effectiveness, the overall heat transfer coefficient, and the heat flux at various mass flow rates of the cold side are shown in Figs. 8a-8d, respectively, with the maximum percentage

The boundary conditions of the two outlets of the hot side and the cold side are at the atmospheric pressure. Fig. 9 shows the velocity field along channels of the microchannel heat exchanger. The streamlines of water pass from the microchannels to the manifold. At the edge between channels and manifold, the streamlines appear to be curved in shape. The velocity field at the outlet of the manifold is parabolic which is consistent with that

predicted by the laminar flow theory for fluid in a channel.

Fig. 9. The velocity field along channels of the microchannel heat exchanger.

Fig. 10 shows the pressure distribution in channels of the hot side at the mass flow rate of 0.2321 g/s and the inlet temperature of 45 ºC. The pressure decreases gradually from the first channel to the last one, with the first channel being the nearest one to the entrance of

error being less than 7.2%.

the inlet of the manifold [25, 26].

**Fluid behaviors** 

It is observed that with a rising the mass flow rate of the cold side, the outlet temperatures decrease, as shown in Fig. 8a; however, for the same flow rate condition, both the heat transfer rates of the hot side and cold side increase. As the mass flow rate of the cold side increases, the heat transfer rate for the cold side increases at a slightly higher rate than that for the hot side. It is also observed that the actual effectiveness for the microchannel heat exchanger increases with a rising the mass flow rate of the cold side, as shown in Fig. 8b. The results obtained from the effectiveness (NTU method) are lower than those obtained from the actual effectiveness, as shown in Fig. 8.b. Hence, a conclusion can be drawn for the heat exchanger under study: at constant inlet temperature and mass flow rate of the hot side, it is more effective to use the heat exchanger with high mass flow rate of cold side. However, leakage of liquid out of the microchannel heat exchanger can occur when the mass flow rate of the cold side increases above 0.854 g/s, as a result of the excessive pressure exerted on the system under study.

Fig. 8. Comparison between numerical and experimental results at constant inlet temperature and mass flow rate for the hot side.

At the condition stated above, the overall heat transfer coefficient k of the heat exchanger increases from 0.625 to 0.815 W/(cm2K) with the mass flow rate of cold side rising from 0.1859 to 0.3625 g/s, as shown in Fig. 8c. At a hydraulic diameter of 375 m, Kandlikar et al. [44] gave k = 0.85 W/(cm2K), compared to k = 0.815 W/(cm2K) obtained in this study. Thus, the two results are in good agreement. For this case, the change in the log mean temperature difference is small: it reduces from 10.7 to 10.0 C with the mass flow rate of cold side rising from 0.1859 to 0.3625 g/s. The heat flux increases from 6.2 to 8.2 W/cm2 with the mass flow rate of cold side rising from 0.1859 to 0.3625 g/s, as shown in Fig. 8d. Thus, the heat flux affected by the log mean temperature difference is less than that by the overall heat transfer coefficient (7.0% versus 30.4% on a percentage basis). Comparisons between the results obtained from numerical simulation and experimental data for the outlet temperature, the effectiveness, the overall heat transfer coefficient, and the heat flux at various mass flow
