**4.3 Effects of geometrical configurations**

272 Heat Exchangers – Basics Design Applications

0

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, <sup>0</sup>**

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side, g/s**

Counter Parallel

Num. results of counter-flow Exp. results of counter-flow

**C**

5

10

15

**Performance index, W/kPa**

20

25

0.5

0

4

8

12

**Heat flux, W/cm2**

16

20

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side g/s**

Counter-flow Parallel-flow

Num. results of counter-flow Exp. results of counter-flow

**C**

Fig. 18. Comparison between numerical and experimental results.

a) Effectiveness (NTU method) b) Performance index

Fig. 19. Comparison of the experimental results with a rising mass flow rate of the cold side.

Under another experimental condition, for the experiments done in this study, the inlet temperature and the mass flow rate of the hot side were fixed at 70 ºC and 0.2321 g/s, respectively. For the cold side, the inlet temperature was fixed at 22.5 ºC and the mass flow rates were varying from 0.2043 to 0.401 g/s. The outlet temperatures are a function of the mass flow rate at the cold side, as shown in more detail in [22-25]. Contrary to the case of varying inlet temperature of the hot side, the outlet temperatures decrease as the mass flow rate of the cold side increases. For the counter-flow case, the outlet temperature of the cold side is higher than or equal to that obtained at the hot side. However, for the parallel-flow case, the outlet temperature at the cold side is lower than that obtained at the hot side. As a result, for the microchannel heat exchanger, the heat flux obtained from the counter-flow arrangement is higher than that obtained from the parallel-flow arrangement, as shown in Fig. 19a. The heat flux of 17.81×104 W/m2 (or 17.81 W/cm2) was achieved for water from the

a) Heat flux b) Performance index

0

5

10

15

**Performance index, W/kPa**

20

25

0.52

0.54

**Effectiveness (NTU method)**

0.56

0.58

0.6

In order to study the effects of geometrical configurations on the performance of the heat exchangers, all experimental conditions for the four microchannel heat exchangers were kept the same, more detail in [28,29]. Throughout the section, two cases of testing were discussed: the first one for increasing the inlet temperature of the hot side and the second for increasing the mass flow rate of the cold side. Further details of these cases are as follows:


The flow parameters for these two cases are summarized in Table 5.


Table 5. Flow parameters for the cases under study.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 275

0

**Pressure drop, Pa**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

Hot side-T1 Hot side-T2 Cold side-T1 Cold side-T2

**C**

c) Pressure drop d) Performance index

Fig. 20. Effects of the substrate thickness with a rising inlet temperature of hot side.

T1 T2

**C**

a) Heat flux b) Effectiveness

0.40

0

5

10

15

**Performance index, W/kPa**

20

25

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, 0**

T1 T2

T1 T2

**C**

**C**

0.44

0.48

**Effectiveness**

0.52

0.56

0.60

3

6

9

**Heat flux, W/cm2**

12

15

#### **The effects of substrate thicknesses**

For the effects of substrate thicknesses, the two microchannel heat exchangers (T1 and T2) were tested. These two heat exchangers have the same dimensions of the channel and the manifolds with the same means (that is, the S-type, as shown in Fig. 3a)) for connecting the channels to the manifolds; however, the two heat exchangers under study have different substrate thicknesses. Detailed parameters of the heat exchangers (T1 and T2) are listed in Table 2.

Fig. 20 shows the effects of the substrate thickness with rising inlet temperature of the hot side. The heat flux is a function of the inlet temperature of hot side; the heat flux increases with rising inlet temperature of the hot side, as shown in Fig. 20a. For the substrate thicknesses of 1.2 (Heat Exchanger T1) and 2 mm (Heat Exchanger T2), the heat fluxes of T1 are 1.024 to 1.046 times of those obtained from T2. Besides, it was found that the heat transfer rate obtained from the present study (23 W) is slightly higher than that obtained from García-Hernando et al. [36] (22 W) (At Reynolds number of 400, the present study used the overall channel size with 9.5 mm in width and 32 mm in length (304 mm2 in area), compared with that of 20 mm in width and 16 mm in length (320 mm2 in area) for García-Hernando et al. [36]). It was also found for the present study that the heat transfer rate increases with rising inlet temperature of the hot side. As a result, the effectiveness – defined as the ratio of heat transfer rate to the maximum heat transfer rate, expressed by Eq. (3) – increases with rising inlet temperature of the hot side, as shown in Fig. 20b. Because that the configuration of the heat exchangers and the mass flow rates of water at the hot and cold sides are fixed and the variation of temperature of water at both side is minimal, so the convective heat transfer term is essentially fixed. Further, it is found that the conductive heat transfer term does not affect strongly the overall heat transfer coefficient of the heat exchangers. It is concluded that the results shown in Figs. 20a and 20b indicate that the substrate thickness affects negligibly the parameters associated with the heat transfer process of the heat exchangers with the substrate thicknesses of 1.2 and 2 mm.

For the present study, the results obtained from the experimental data showed the pressure drop as a function of the inlet temperature of the hot side. For both heat exchangers (T1 and T2), the mass flow rate of the hot side is higher than those of the cold side, so the pressure drop obtained from the hot side is higher than that obtained from the cold side, as shown in Fig. 20c. Fig. 20c illustrates that pressure drop of T2 is not the same as that of T1, due to the fact that the roughness of channels in T2 could be higher than that of channels in T1. However, the maximum difference of pressure drops between T1 and T2 is less than 10 %.

Fig. 20d shows that the performance of the heat exchangers increase with the rising of inlet temperature of the hot side; the performance obtained from T1 is higher than that obtained from T2. The performance index of 21.67 W/kPa was achieved for water from the hot side of Heat Exchanger T1 having the inlet temperature of 70 C and mass flow rate of 0.2308 g/s and water from the cold side having the inlet temperature of 22.5 C and mass flow rate of 0.2135 g/s.

For the effects of substrate thicknesses, the two microchannel heat exchangers (T1 and T2) were tested. These two heat exchangers have the same dimensions of the channel and the manifolds with the same means (that is, the S-type, as shown in Fig. 3a)) for connecting the channels to the manifolds; however, the two heat exchangers under study have different substrate thicknesses. Detailed parameters of the heat exchangers (T1 and T2) are listed in

Fig. 20 shows the effects of the substrate thickness with rising inlet temperature of the hot side. The heat flux is a function of the inlet temperature of hot side; the heat flux increases with rising inlet temperature of the hot side, as shown in Fig. 20a. For the substrate thicknesses of 1.2 (Heat Exchanger T1) and 2 mm (Heat Exchanger T2), the heat fluxes of T1 are 1.024 to 1.046 times of those obtained from T2. Besides, it was found that the heat transfer rate obtained from the present study (23 W) is slightly higher than that obtained from García-Hernando et al. [36] (22 W) (At Reynolds number of 400, the present study used the overall channel size with 9.5 mm in width and 32 mm in length (304 mm2 in area), compared with that of 20 mm in width and 16 mm in length (320 mm2 in area) for García-Hernando et al. [36]). It was also found for the present study that the heat transfer rate increases with rising inlet temperature of the hot side. As a result, the effectiveness – defined as the ratio of heat transfer rate to the maximum heat transfer rate, expressed by Eq. (3) – increases with rising inlet temperature of the hot side, as shown in Fig. 20b. Because that the configuration of the heat exchangers and the mass flow rates of water at the hot and cold sides are fixed and the variation of temperature of water at both side is minimal, so the convective heat transfer term is essentially fixed. Further, it is found that the conductive heat transfer term does not affect strongly the overall heat transfer coefficient of the heat exchangers. It is concluded that the results shown in Figs. 20a and 20b indicate that the substrate thickness affects negligibly the parameters associated with the heat transfer process of the heat exchangers with the substrate thicknesses of 1.2 and 2

For the present study, the results obtained from the experimental data showed the pressure drop as a function of the inlet temperature of the hot side. For both heat exchangers (T1 and T2), the mass flow rate of the hot side is higher than those of the cold side, so the pressure drop obtained from the hot side is higher than that obtained from the cold side, as shown in Fig. 20c. Fig. 20c illustrates that pressure drop of T2 is not the same as that of T1, due to the fact that the roughness of channels in T2 could be higher than that of channels in T1. However, the maximum difference of pressure drops between T1 and

Fig. 20d shows that the performance of the heat exchangers increase with the rising of inlet temperature of the hot side; the performance obtained from T1 is higher than that obtained from T2. The performance index of 21.67 W/kPa was achieved for water from the hot side of Heat Exchanger T1 having the inlet temperature of 70 C and mass flow rate of 0.2308 g/s and water from the cold side having the inlet temperature of 22.5 C and mass flow rate of

**The effects of substrate thicknesses** 

Table 2.

mm.

T2 is less than 10 %.

0.2135 g/s.

Fig. 20. Effects of the substrate thickness with a rising inlet temperature of hot side.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 277

the inlet temperature of the hot side increasing, as shown in Fig. 6a. It is observed that the heat transfer rates obtained from T3 are higher than those obtained from T1, leading to the fact that heat fluxes obtained from T3 are higher than those obtained from T1. The results obtained from the present study are in good agreement with those obtained from [37]. Foli et al. [37] indicated that under the constant mass flow rate condition, the higher the heat flux, the lower the aspect ratio (defined as the ratio of the microchannel height to its width). Under the same condition, the mass flow rates are fixed for two cases T1 and T3 used in this study. The conductive thermal resistance of T1 was found to be lower than that of T3. However, the convective thermal resistance of T1 was found to be higher than that of T3. The heat fluxes obtained from Fig. 22a show that the effect of the convective thermal resistance on the overall thermal resistance (appeared in Eqs. (5) and (6)) of the microchannel heat exchangers is more

The effectiveness obtained from T3 is higher than that obtained from T1, as shown in Fig. 22b. However, because that the hydraulic diameter of channel in T3 is smaller than that of channel in T1, this results in the velocity in the channel of T3 to be higher than that of T1, leading to a higher pressure drop in T3 than that in T1, as shown in Fig. 22c. It was found that the pressure drop of T3 is 2 times higher than that of T1, while the effectiveness of T3 is 1.04 times higher than that of T1. As a result, the performance index (defined as the ratio of the heat transfer rate to the pressure drop in the heat exchanger) obtained from T1 is higher

For Case 2, Fig. 23 shows the effects of the cross-sectional area on the behaviors of heat flux and performance index for T1 and T3 with the mass flow rates of the cold side ranging from 0.2135 to 0.401 g/s. It was found that the heat fluxes of T3 are higher than those of T1, as shown in Fig. 23a. For microchannel heat exchanger T3, a heat flux of 18.7 W/cm2 (or overall average heat transfer coefficient of 8,500 W/m2K) was achieved for water from the hot side having a fixed inlet temperature of 70 C and a fixed mass flow rate of 0.2308 g/s and for water from the cold side having a fixed inlet temperature of 22.5 C and a mass flow rate of 0.401 g/s. It was also found that the pressure drop of T3 is higher than that of T1; the curve of the pressure drop is at a higher slope than that of the heat flux; as a result, the

From Figs. 20-23 obtained in this study, it indicates that for the microchannel heat exchangers being investigated, the effect of the hydraulic diameter on the performance index is more pronounced than that of the substrate thickness. In addition, it demonstrates

Again, in Dang [3] and Dang and Teng [25], two cases were investigated: (1) Case 1 for the study of the effects of inlet/out location for the heat exchanger at various inlet temperatures of the hot side and (2) Case 2 for the study of the effects of inlet/out location for the heat exchanger at various mass flow rates of the cold side. The inlet/outlet locations affect significantly the behaviors of heat transfer and fluid flow of the microchannel heat exchangers. The two microchannel heat exchangers T2 and T4 were tested for this case. These two heat exchangers have the same dimensions of the channel and manifold; however, as shown in Fig. 3, the configuration of manifold together with the channel for T2 is the S-type and that for T4 is

that the lower the hydraulic diameter, the higher the heat flux and the pressure drop.

the I-type. Parameters of the heat exchangers are listed in more detail in Table 2.

performance index of T1 is higher than that of T3, as shown in Fig. 23b.

significantly than that of the conductive thermal resistance.

than that obtained from T3, as shown in Fig. 22d.

**The effects of inlet/outlet location** 

Fig. 21. Effects of the substrate thickness with a rising mass flow rate of cold side.

For the case of increasing the mass flow rate of the cold side (Case 2 was developed to study the effects of substrate thickness at various mass flow rates of the cold side), the heat fluxes of the heat exchangers increase with rising mass flow rate of the cold side, as shown in Fig. 21. Fig. 21 shows the effects of the substrate thickness with rising mass flow rate of the cold side. For this case, the heat flux obtained from T1 is also higher than that obtained from T2, as shown in Fig. 21a. When the mass flow rate of the cold side increases, the pressure drop of the cold side also increases; when the mass flow rate of the cold side increases, the average temperature of the hot side decreases, resulting in an increase of the pressure drop of the hot side. Besides, it was observed from the experimental data that the pressure drops increase at a higher slope than those for the effectiveness. It is noted that the performance index decreases with the rising mass flow rate of the cold side, as shown in Fig. 21b; however, the performance index obtained from the T1 is higher than that obtained from T2.

#### **The effects of cross-sectional areas**

For the evaluation of the effects of cross-sectional areas on the fluid and heat transfer of the microchannel heat exchangers, two cases were investigated: (1) Case 1 for the study of the effects of cross-sectional area for the heat exchanger at various inlet temperatures of the hot side and (2) Case 2 for the study of the effects of cross-sectional area for the heat exchanger at various mass flow rates of the cold side. Two microchannel heat exchangers T1 and T3 are tested for the effects of magnitude of cross-sectional area on the behaviors of heat transfer and fluid flow. These two microchannel heat exchangers have the same physical configurations for their substrates, manifolds, and lengths of channels. However, only the cross-sectional areas of microchannels are different. The microchannels of T1 have a rectangular cross-section with width of 500 m and depth of 300 m; the microchannel of T3, width of 500 m and depth of 180 m. These dimensions are listed in Table 2.

For Case 1, Fig. 22 shows the effects of the cross-sectional areas on the behaviors of heat flux, effectiveness, pressure drop, and performance index for T1 and T3 with the inlet temperatures of the hot side ranging from 45 to 70 C. The heat fluxes of the heat exchangers increase with the inlet temperature of the hot side increasing, as shown in Fig. 6a. It is observed that the heat transfer rates obtained from T3 are higher than those obtained from T1, leading to the fact that heat fluxes obtained from T3 are higher than those obtained from T1. The results obtained from the present study are in good agreement with those obtained from [37]. Foli et al. [37] indicated that under the constant mass flow rate condition, the higher the heat flux, the lower the aspect ratio (defined as the ratio of the microchannel height to its width). Under the same condition, the mass flow rates are fixed for two cases T1 and T3 used in this study. The conductive thermal resistance of T1 was found to be lower than that of T3. However, the convective thermal resistance of T1 was found to be higher than that of T3. The heat fluxes obtained from Fig. 22a show that the effect of the convective thermal resistance on the overall thermal resistance (appeared in Eqs. (5) and (6)) of the microchannel heat exchangers is more significantly than that of the conductive thermal resistance.

The effectiveness obtained from T3 is higher than that obtained from T1, as shown in Fig. 22b. However, because that the hydraulic diameter of channel in T3 is smaller than that of channel in T1, this results in the velocity in the channel of T3 to be higher than that of T1, leading to a higher pressure drop in T3 than that in T1, as shown in Fig. 22c. It was found that the pressure drop of T3 is 2 times higher than that of T1, while the effectiveness of T3 is 1.04 times higher than that of T1. As a result, the performance index (defined as the ratio of the heat transfer rate to the pressure drop in the heat exchanger) obtained from T1 is higher than that obtained from T3, as shown in Fig. 22d.

For Case 2, Fig. 23 shows the effects of the cross-sectional area on the behaviors of heat flux and performance index for T1 and T3 with the mass flow rates of the cold side ranging from 0.2135 to 0.401 g/s. It was found that the heat fluxes of T3 are higher than those of T1, as shown in Fig. 23a. For microchannel heat exchanger T3, a heat flux of 18.7 W/cm2 (or overall average heat transfer coefficient of 8,500 W/m2K) was achieved for water from the hot side having a fixed inlet temperature of 70 C and a fixed mass flow rate of 0.2308 g/s and for water from the cold side having a fixed inlet temperature of 22.5 C and a mass flow rate of 0.401 g/s. It was also found that the pressure drop of T3 is higher than that of T1; the curve of the pressure drop is at a higher slope than that of the heat flux; as a result, the performance index of T1 is higher than that of T3, as shown in Fig. 23b.

From Figs. 20-23 obtained in this study, it indicates that for the microchannel heat exchangers being investigated, the effect of the hydraulic diameter on the performance index is more pronounced than that of the substrate thickness. In addition, it demonstrates that the lower the hydraulic diameter, the higher the heat flux and the pressure drop.

#### **The effects of inlet/outlet location**

276 Heat Exchangers – Basics Design Applications

0

 a) Heat flux b) Performance index Fig. 21. Effects of the substrate thickness with a rising mass flow rate of cold side.

For the case of increasing the mass flow rate of the cold side (Case 2 was developed to study the effects of substrate thickness at various mass flow rates of the cold side), the heat fluxes of the heat exchangers increase with rising mass flow rate of the cold side, as shown in Fig. 21. Fig. 21 shows the effects of the substrate thickness with rising mass flow rate of the cold side. For this case, the heat flux obtained from T1 is also higher than that obtained from T2, as shown in Fig. 21a. When the mass flow rate of the cold side increases, the pressure drop of the cold side also increases; when the mass flow rate of the cold side increases, the average temperature of the hot side decreases, resulting in an increase of the pressure drop of the hot side. Besides, it was observed from the experimental data that the pressure drops increase at a higher slope than those for the effectiveness. It is noted that the performance index decreases with the rising mass flow rate of the cold side, as shown in Fig. 21b; however, the performance index obtained from

For the evaluation of the effects of cross-sectional areas on the fluid and heat transfer of the microchannel heat exchangers, two cases were investigated: (1) Case 1 for the study of the effects of cross-sectional area for the heat exchanger at various inlet temperatures of the hot side and (2) Case 2 for the study of the effects of cross-sectional area for the heat exchanger at various mass flow rates of the cold side. Two microchannel heat exchangers T1 and T3 are tested for the effects of magnitude of cross-sectional area on the behaviors of heat transfer and fluid flow. These two microchannel heat exchangers have the same physical configurations for their substrates, manifolds, and lengths of channels. However, only the cross-sectional areas of microchannels are different. The microchannels of T1 have a rectangular cross-section with width of 500 m and depth of 300 m; the microchannel of

For Case 1, Fig. 22 shows the effects of the cross-sectional areas on the behaviors of heat flux, effectiveness, pressure drop, and performance index for T1 and T3 with the inlet temperatures of the hot side ranging from 45 to 70 C. The heat fluxes of the heat exchangers increase with

T3, width of 500 m and depth of 180 m. These dimensions are listed in Table 2.

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side, g/s**

T1 T2

5

10

15

**Performance index, W/kPa**

20

25

0

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side, g/s**

the T1 is higher than that obtained from T2.

**The effects of cross-sectional areas** 

T1 T2

4

8

12

**Heat flux, W/cm2**

16

20

Again, in Dang [3] and Dang and Teng [25], two cases were investigated: (1) Case 1 for the study of the effects of inlet/out location for the heat exchanger at various inlet temperatures of the hot side and (2) Case 2 for the study of the effects of inlet/out location for the heat exchanger at various mass flow rates of the cold side. The inlet/outlet locations affect significantly the behaviors of heat transfer and fluid flow of the microchannel heat exchangers. The two microchannel heat exchangers T2 and T4 were tested for this case. These two heat exchangers have the same dimensions of the channel and manifold; however, as shown in Fig. 3, the configuration of manifold together with the channel for T2 is the S-type and that for T4 is the I-type. Parameters of the heat exchangers are listed in more detail in Table 2.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 279

0

a) Heat flux b) Performance index

Fig. 23. Effects of the cross-sectional area with a rising mass flow rate of cold side.

For Case 1, Fig. 24 shows the effects of the inlet/outlet location on the behaviors of heat flux, effectiveness, pressure drop, and performance index for heat exchangers T2 and T4 with the inlet temperatures of the hot side ranging from 45 to 70 C. In these two heat exchangers, the effects of maldistribution by the manifolds are important for heat transfer and pressure drop. The distance of flow path for the fluid moving from the entrance to the exit for the Stype microchannel heat exchanger is longer than that for the I-type, leading to the fact that the heat flux of T2 is higher than that of T4, as shown in Fig. 24a; as a result, the effectiveness of T2 is also higher than that of T4, as shown in Fig. 24b. However, it is also due to the fact that the distance the fluid moves from the entrance to the exit for the S-type is longer than that obtained with the I-type, so the pressure drop obtained from T2 is higher than that obtained from T4 for the same mass flow rate through the two heat exchangers being investigated, as shown in Fig. 24c. Fig. 24d shows the performance index of the heat exchangers as a function of the inlet temperature of the hot side. The performance index

For Case 2, Fig. 25 shows the effects of the cross-sectional area on the behaviors of heat flux and performance index for the heat exchangers T2 and T4 with the mass flow rates of the cold side ranging from 0.2135 to 0.401 g/s. It was found that the heat fluxes obtained from T2 are higher than those from T4, as shown in Fig. 25a. However, when the mass flow rates of the cold side increase, the pressure drops increase also, leading to the fact that the pressure drop of T4 is lower than that of T2. it was also found that the performance index of

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side, g/s**

T1 T3

5

10

15

**Performance index, W/kPa**

20

25

0

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side, g/s**

obtained from T4 is higher than that obtained from T2.

T4 is higher than T2, as shown in Fig. 25b.

T1 T3

4

8

12

**Heat flux, W/cm2**

16

20

Fig. 22. Effects of the cross-sectional area with a rising inlet temperature of hot side.

0.40

0

5

10

15

**Performance index, W/kPa**

20

25

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, 0**

T1 T3

**C**

T1 T3

**C**

0.44

0.48

**Effectiveness**

0.52

0.56

0.60

0

0

400

Hot side-T1 Hot side-T3 Cold side-T1 Cold side-T3

800

1200

**Pressure drop, Pa**

1600

2000

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

**C**

c) Pressure drop d) Performance index

Fig. 22. Effects of the cross-sectional area with a rising inlet temperature of hot side.

T1 T3

**C**

a) Heat flux b) Effectiveness

4

8

**Heat flux, W/cm2**

12

16

Fig. 23. Effects of the cross-sectional area with a rising mass flow rate of cold side.

For Case 1, Fig. 24 shows the effects of the inlet/outlet location on the behaviors of heat flux, effectiveness, pressure drop, and performance index for heat exchangers T2 and T4 with the inlet temperatures of the hot side ranging from 45 to 70 C. In these two heat exchangers, the effects of maldistribution by the manifolds are important for heat transfer and pressure drop. The distance of flow path for the fluid moving from the entrance to the exit for the Stype microchannel heat exchanger is longer than that for the I-type, leading to the fact that the heat flux of T2 is higher than that of T4, as shown in Fig. 24a; as a result, the effectiveness of T2 is also higher than that of T4, as shown in Fig. 24b. However, it is also due to the fact that the distance the fluid moves from the entrance to the exit for the S-type is longer than that obtained with the I-type, so the pressure drop obtained from T2 is higher than that obtained from T4 for the same mass flow rate through the two heat exchangers being investigated, as shown in Fig. 24c. Fig. 24d shows the performance index of the heat exchangers as a function of the inlet temperature of the hot side. The performance index obtained from T4 is higher than that obtained from T2.

For Case 2, Fig. 25 shows the effects of the cross-sectional area on the behaviors of heat flux and performance index for the heat exchangers T2 and T4 with the mass flow rates of the cold side ranging from 0.2135 to 0.401 g/s. It was found that the heat fluxes obtained from T2 are higher than those from T4, as shown in Fig. 25a. However, when the mass flow rates of the cold side increase, the pressure drops increase also, leading to the fact that the pressure drop of T4 is lower than that of T2. it was also found that the performance index of T4 is higher than T2, as shown in Fig. 25b.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 281

0

 a) Heat flux b) Performance index Fig. 25. Effects of the inlet/outlet location with a rising mass flow rate of cold side.

In summary, Figs. 20-25 indicate that the highest heat flux achievable for all cases studied is the microchannel heat exchanger T3. However, the performance index of T3 is lowest among all cases being investigated. It is observed that the heat flux and pressure drop obtained from the S-type manifold together with the channels are higher than that from the I-type. However, the performances indexes of both types of heat exchangers are essentially the same. For all cases studied, the microchannel heat exchanger T1 yields the highest performance index, with T4 being the second best. From the experimental data shown in Figs. 20-25, the overall average heat transfer coefficients of the heat exchangers with a value of 8,500 W/(m2K) which was evaluated in this study are in good agreement with the overall heat transfer coefficient obtained in Kandlikar et al. [34] for microchannels with the same hydraulic diameter; however, the overall average heat transfer coefficient obtained from the present study is higher than that (~5,100 W/(m2K)) obtained in García-Hernando et al. [36]

An experimental study of the effects of gravity on the fluid in microchannel heat exchangers was carried out in the study to find out how does the gravity affect the behaviors of heat transfer and pressure drop for the microchannel heat exchangers? For the experimental system, the inlet temperature and the mass flow rate of the hot side were fixed at 70 ºC and 0.2308 g/s, respectively; at the cold side, the inlet temperature was fixed at 22.5 ºC and the mass flow rates were varying from 0.2135 to 0.401 g/s. In this study, influence of gravity was determined by two cases: one with horizontal channels, the other with vertical channels. For vertical channels, the hot water is flowing upward which is against the gravitational field, while the cold water is flowing downward which is in the same direction as the gravitational field [26,27]. Two microchannel heat exchangers T1 and T3 were tested: these two microchannel heat exchangers have the same physical configurations for their substrates, manifolds, and lengths of channels; only the cross-sectional areas of microchannels are different. The microchannels of T1 have a rectangular cross-section with width of 500 m and depth of 300 m; the microchannel of T3, width of 500 m and depth of 180 m. Parameters of the heat exchangers (T1 and T3) are listed in more detail in Table 2.

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side, g/s**

T4 T2

5

10

15

**Performance index, W/kPa**

20

25

0

due to the difference in design.

**4.4 Effects of gravity** 

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **Mass flow rate of cold side, g/s**

T4 T2

4

8

12

**Heat flux, W/cm2**

16

20

Fig. 24. Effects of the inlet/outlet location with a rising inlet temperature of hot side.

Fig. 25. Effects of the inlet/outlet location with a rising mass flow rate of cold side.

In summary, Figs. 20-25 indicate that the highest heat flux achievable for all cases studied is the microchannel heat exchanger T3. However, the performance index of T3 is lowest among all cases being investigated. It is observed that the heat flux and pressure drop obtained from the S-type manifold together with the channels are higher than that from the I-type. However, the performances indexes of both types of heat exchangers are essentially the same. For all cases studied, the microchannel heat exchanger T1 yields the highest performance index, with T4 being the second best. From the experimental data shown in Figs. 20-25, the overall average heat transfer coefficients of the heat exchangers with a value of 8,500 W/(m2K) which was evaluated in this study are in good agreement with the overall heat transfer coefficient obtained in Kandlikar et al. [34] for microchannels with the same hydraulic diameter; however, the overall average heat transfer coefficient obtained from the present study is higher than that (~5,100 W/(m2K)) obtained in García-Hernando et al. [36] due to the difference in design.

#### **4.4 Effects of gravity**

280 Heat Exchangers – Basics Design Applications

0.40

0

c) Pressure dropd) Performance index

5

10

15

**Performance index, W/kPa**

20

25

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, 0**

T4 T2

**C**

T4 T2

**C**

0.44

0.48

**Effectiveness**

0.52

0.56

0.60

0

**Pressure drop, Pa**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, o**

40 45 50 55 60 65 70 75 **Inlet temperature of hot side, 0**

Hot side-T4 Hot side-T2 Cold side-T4 Cold side-T2

**C**

Fig. 24. Effects of the inlet/outlet location with a rising inlet temperature of hot side.

T4 T2

**C**

a) Heat flux b) Effectiveness

3

6

9

**Heat flux, W/cm2**

12

15

An experimental study of the effects of gravity on the fluid in microchannel heat exchangers was carried out in the study to find out how does the gravity affect the behaviors of heat transfer and pressure drop for the microchannel heat exchangers? For the experimental system, the inlet temperature and the mass flow rate of the hot side were fixed at 70 ºC and 0.2308 g/s, respectively; at the cold side, the inlet temperature was fixed at 22.5 ºC and the mass flow rates were varying from 0.2135 to 0.401 g/s. In this study, influence of gravity was determined by two cases: one with horizontal channels, the other with vertical channels. For vertical channels, the hot water is flowing upward which is against the gravitational field, while the cold water is flowing downward which is in the same direction as the gravitational field [26,27]. Two microchannel heat exchangers T1 and T3 were tested: these two microchannel heat exchangers have the same physical configurations for their substrates, manifolds, and lengths of channels; only the cross-sectional areas of microchannels are different. The microchannels of T1 have a rectangular cross-section with width of 500 m and depth of 300 m; the microchannel of T3, width of 500 m and depth of 180 m. Parameters of the heat exchangers (T1 and T3) are listed in more detail in Table 2.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 283

The outlet temperatures of hot side obtained from T1 is higher than those obtained from T3; however, the outlet temperatures of cold side obtained from T1 is lower than those obtained from T3. As a result, the heat transfer rate obtained from T3 is higher than that obtained from T1, as shown in Fig. 28. The results obtained from the present study are in good agreement with those obtained from [37]. Foli et al. [37] indicated that under the constant mass flow rate condition, the higher the heat flux, the lower the aspect ratio (defined as the

> 0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **M ass flow rate of cold side , g/s**

It is shown from Fig. 28 that at specified mass flow rate of the cold side the difference between the heat transfer rate obtained from a horizontal channel (either T1 or T3) and that from the vertical one (the corresponding T1 or T3) is negligibly small. The heat transfer rate of the heat exchangers is a function of the mass flow rate of cold side: it increases from 24.8 to 29.92 W with the mass flow rate of cold side rising from 0.2043 to 0.401 g/s (for the heat exchanger T3). Because that the hydraulic diameter of channel in T3 is smaller than that of channel in T1, this results in the velocity in the channel of T3 to be higher than that of T1, leading to a higher total pressure drop in T3 than that in T1, as shown in Fig. 29. Besides, the figure shows that the total pressure drop is a function of Reynolds number of cold side; the total

Experimental results for effects of gravity on the behavior of pressure drop for the microchannel heat exchanger are also shown in Fig. 29. It is observed that the change of pressure drop between the two cases (horizontal channels and vertical channels) is negligibly small; the maximum change in pressure is 7.2% for a pressure drop from 1060 to

T 1-horizontal T 1-vertical T 3-horizontal T 3-vertical

ratio of the microchannel height to its width).

20

pressure drop increases as rising the Re number of cold side.

Fig. 28. Comparison of heat transfer rates.

2044 Pa.

22

24

**Heat transfer rate, W**

26

28

30

Fig. 26. Comparison of outlet temperatures of hot side.

Fig. 26 shows a comparison of at specified mass flow rate of the cold side the difference between outlet temperature of hot side obtained from a horizontal channel (either T1 or T3) and that from the vertical one (the corresponding T1 or T3) is negligibly small. A comparison of the outlet temperatures of cold side of two microchannel heat exchangers is shown in Fig. 27. The outlet temperatures (for both the hot and the cold sides) are functions of the mass flow rate of cold side; the outlet temperatures decrease as the mass flow rate of the cold side increases.

Fig. 27. Comparison of outlet temperatures of cold side.

The outlet temperatures of hot side obtained from T1 is higher than those obtained from T3; however, the outlet temperatures of cold side obtained from T1 is lower than those obtained from T3. As a result, the heat transfer rate obtained from T3 is higher than that obtained from T1, as shown in Fig. 28. The results obtained from the present study are in good agreement with those obtained from [37]. Foli et al. [37] indicated that under the constant mass flow rate condition, the higher the heat flux, the lower the aspect ratio (defined as the ratio of the microchannel height to its width).

Fig. 28. Comparison of heat transfer rates.

282 Heat Exchangers – Basics Design Applications

T 1-horizontal T 1-vertical T 3-horizontal T 3-vertical

0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **M ass flow rate of cold side , g/s**

Fig. 26 shows a comparison of at specified mass flow rate of the cold side the difference between outlet temperature of hot side obtained from a horizontal channel (either T1 or T3) and that from the vertical one (the corresponding T1 or T3) is negligibly small. A comparison of the outlet temperatures of cold side of two microchannel heat exchangers is shown in Fig. 27. The outlet temperatures (for both the hot and the cold sides) are functions of the mass flow rate of cold side; the outlet temperatures decrease as the mass flow rate of

> 0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 **M ass flow rate of cold side , g/s**

T 1-horizontal T 1-vertical T 3-horizontal T 3-verticcal

36

38

Fig. 27. Comparison of outlet temperatures of cold side.

40

**Outlet tem**

**perature of cold side,**

42

44

46

48

 **0**

**C**

50

Fig. 26. Comparison of outlet temperatures of hot side.

38

**Outlet tem**

the cold side increases.

40

42

**perature of hot side, 0**

**C**

44

46

It is shown from Fig. 28 that at specified mass flow rate of the cold side the difference between the heat transfer rate obtained from a horizontal channel (either T1 or T3) and that from the vertical one (the corresponding T1 or T3) is negligibly small. The heat transfer rate of the heat exchangers is a function of the mass flow rate of cold side: it increases from 24.8 to 29.92 W with the mass flow rate of cold side rising from 0.2043 to 0.401 g/s (for the heat exchanger T3).

Because that the hydraulic diameter of channel in T3 is smaller than that of channel in T1, this results in the velocity in the channel of T3 to be higher than that of T1, leading to a higher total pressure drop in T3 than that in T1, as shown in Fig. 29. Besides, the figure shows that the total pressure drop is a function of Reynolds number of cold side; the total pressure drop increases as rising the Re number of cold side.

Experimental results for effects of gravity on the behavior of pressure drop for the microchannel heat exchanger are also shown in Fig. 29. It is observed that the change of pressure drop between the two cases (horizontal channels and vertical channels) is negligibly small; the maximum change in pressure is 7.2% for a pressure drop from 1060 to 2044 Pa.

Single-Phase Heat Transfer and Fluid Flow Phenomena of Microchannel Heat Exchangers 285

In summary, it is concluded that for both heat transfer and pressure drop behaviors, the impact of gravity on the fluid flowing through the microchannel heat exchange can be

In this study, for the cases with both inlet temperature and mass flow rate constant at the cold side of the device, the trends for the results obtained from the actual effectiveness method and those obtained from the effectiveness (-NTU) method are in the opposite directions as the mass flow rate of the hot side increases. However, for the cases with constant inlet temperature and mass flow rate at the hot side of the device, the trends for the results obtained from both methods for evaluating effectiveness are in the same directions. With all cases done in the study, the performance index obtained from the counterflow is always higher than that obtained from the parallel-flow. As a result, the microchannel heat exchanger

In the study, it indicates that the substrate thickness affects negligibly the parameters associated with the heat transfer process of the heat exchangers with the substrate thicknesses of 1.2 and 2 mm. The effect of the hydraulic diameter (cross-sectional area) on the performance index is more pronounced than that of the substrate thickness. In addition, it demonstrates that the lower the hydraulic diameter, the higher the heat flux and the pressure drop. Regarding the effects of inlet/outlet locations, for two types (I-type and Stype) of the microchannel heat exchangers, the heat flux and pressure drop obtained from the S-type are higher than those from the I-type, even though the performance indexes of

The impact of gravity on the fluid flowing through the microchannel heat exchanger was found to be small, with the maximum difference between the results of horizontal and vertical channels being less than 8%. In addition, in this study, good agreements were achieved between the

In the study, good agreements were achieved for the behaviors of heat transfer and fluid flow between the results obtained from numerical simulations and those obtained from experimental data for fluid flowing in the counter-flow microchannel heat exchanger used,

This chapter summarized the work performed and the results obtained both in the fluid flow and heat transfer done by TFAG over the last several years. The authors would like to express their deep appreciation for the financial supports obtained from National Science Council, the Republic of China in Taiwan (Grant Nos. NSC93-2212-E-033-012, NSC94-2212- E-033-017, NSC95-2212-E-033-066, NSC96-2212-E-033-039, NSC97-2212-E-033-050, NSC99- 2212-E-033-025, and NSC 100-2221-E-033-065) and Chung Yuan Christian University (Grant

results obtained from the present study and the results obtained from the literatures.

with the maximum percentage difference between the two results of less than 9%.

with counter-flow should be selected to use for every case (except few special cases).

ignored as indicated in [3,26,27,33,34].

both heat exchangers are essentially the same.

No. CYCU-98-CR-ME).

Ac cross-sectional area, m2 Dh hydraulic diameter, m

f friction factor

**6. Nomenclature** 

**5. Conclusion** 

Fig. 29. Comparison of total pressure drops.

Fig. 30. Comparison of performance indices.

It was found that the pressure drop of T3 is 2 times higher than that of T1, while the heat transfer rate of T3 is 1.06 times higher than that of T1. As a result, the performance index (defined as the ratio of the heat transfer rate to the pressure drop in the heat exchanger) obtained from T1 is higher than that obtained from T3, as shown in Fig. 30. For heat exchanger T1, a performance index of 21.68 W/kPa was achieved for water from the hot side having an inlet temperature of 70 C and a mass flow rate of 0.2308 g/s and for water from the cold side having an inlet temperature of 22.5 C and mass flow rate of 0.2135 g/s. It is also observed that the change of performance between the two cases (horizontal channels and vertical channels) is negligibly small; the maximum change in performance is 5.5%, out of a performance index from 13.69 to 21.68 W/kPa.

In summary, it is concluded that for both heat transfer and pressure drop behaviors, the impact of gravity on the fluid flowing through the microchannel heat exchange can be ignored as indicated in [3,26,27,33,34].
