**3.1 Basic characteristics of moisture transport through the porous plate**

Figures 4(a) ~ 4(d) show the variations of parameters that represent the basic characteristics of the moisture transport from water to air flowing the channel through theporous plate, such as the mass flux, the heat flux, the temperature, and the relative humidity of the outlet air, with respect to the air volumetric flow. The experimental conditions are a plate thickness of 1 mm, a channel height of 1 mm, a heat conductivity in the plate of 1.7 W/(mK), a pore diameter of 5 μm, and a plate porosity of 30%. From this graph, it is first understood that the mass flux increases with respect to the increase in the air volumetric flow and varies little when the air volumetric flow exceeds approximately 10×10-5 m3/s. This is thought to be because, even though the moisture absorption ability of the air increases with respect to the increase in the amount of air flowing through the channel, when the air volumetric flow exceeds approximately 10×10-5 m3/s, the moisture transport through the porous plate or the heat transport required by the water vaporization were limited by the properties of the porous plate, e.g., the permeability of liquid or the thermal conductivity. In addition, the heat flux was determined from the heat transfer quantity in the heat and mass transport

Plate thickness Δ*x* mm

> 2.0 1.0 2.0

> 3.5

2.0

3.5 1.0 2.0

3.5

0.5

2.0 0.5

2.0

Channel height *h* mm

1.0

0.5

1.5

1.0

0.5

1.5

1.0

1.0 1.0

1.0 1.0

Pore diameter *D* μm

1.0 20%

2.0

5.0

14.0

12% 0.5

2.0

Air volumetric flow: 3.3-24.7×10-5 m3/s, temperature of air at the inlet: 32ºC, relative humidity of air at

Figures 4(a) ~ 4(d) show the variations of parameters that represent the basic characteristics of the moisture transport from water to air flowing the channel through theporous plate, such as the mass flux, the heat flux, the temperature, and the relative humidity of the outlet air, with respect to the air volumetric flow. The experimental conditions are a plate thickness of 1 mm, a channel height of 1 mm, a heat conductivity in the plate of 1.7 W/(mK), a pore diameter of 5 μm, and a plate porosity of 30%. From this graph, it is first understood that the mass flux increases with respect to the increase in the air volumetric flow and varies little when the air volumetric flow exceeds approximately 10×10-5 m3/s. This is thought to be because, even though the moisture absorption ability of the air increases with respect to the increase in the amount of air flowing through the channel, when the air volumetric flow exceeds approximately 10×10-5 m3/s, the moisture transport through the porous plate or the heat transport required by the water vaporization were limited by the properties of the porous plate, e.g., the permeability of liquid or the thermal conductivity. In addition, the heat flux was determined from the heat transfer quantity in the heat and mass transport

Heat conductivity

1.7

20.2

p W/(mK) Porosity<sup>ε</sup>

30%

20%

30%

the inlet: 15%, temperature of constant-temperature water: 69ºC.

Table 1. Specifications of the porous plate and experimental conditions

**3.1 Basic characteristics of moisture transport through the porous plate** 

λ

Fig. 4. Basic characteristics of moisture transport from water to air through a porous plate

process calculated from the airflow and the change in enthalpy of the air between the entrance and exit of the channel. The variation in the heat flux showed the same tendency as that for the above mass flux, because the heat flux is primarily caused by the transport of latent heat accompanying the mass transport in this process.

Moisture Transport Through a Porous Plate with Micro Pores 327

transport to the air from the constant-temperature water through the porous plate, 77% of the heat transport is by the heat conduction in the porous plate, 15% is by the heat conduction in the water including in the porous plate, and 8% is by the transport of the sensible heat accompanying the water transportation through the porous plate. Thus, 85% of the heat transport is used for the evaporation of the water to the air and 7% of the heat transport is used for the temperature increase of the air. That is, the heat transfer between the porous plate and the air is mainly the transport of the latent heat accompanying the

For heating air 3.9 W (7%)

Porous plate

Heat conducted by solid 43.5 W (77%) Heat transfer by water remove 4.4 W (8%)

Fig. 6. Distribution of heat flux in the process of moisture transport through a porous plate As described above, in the process of moisture transport through the porous plate, there are several factors controlling the phenomenon, e.g., the water flow resistance *R*fp and heat transfer resistance *R*tp inside the plate, and the mass transfer resistance *R*ms and heat transfer resistance *R*ts on the surface of the porous plate. Considering the influence of each factor involved and based on the one-dimensional system, the resistances of the mass transfer and heat transfer in the porous plate are defined and their influence on the performance of the moisture transport is discussed. Here, *R*fp depends on the material structure, such as the size and distribution of the pore, and the surface properties of the plate, such as the wettability. Thus, based on the Darcy law, the maximum flux of the liquid water through the porous plate, in which the surface tension, as the driving force, can be determined as follows:

max

*m*

*<sup>f</sup>* 4 cos 1

/ (, ) *R xK D fp* = Δ ε

σ θ

*D Rfp*

μ

= ⋅ (1)

(2)

water transportation.

Heat conducted by liquid 8.5 W (15%)

For water vaporization 48.1 W (85%)

Furthermore, Fig. 4(d) shows that for the case in which the air volumetric flow is less than approximately 10×10-5 m3/s, the relative humidity of the air in the channel exit is approximately 100%. This also explains the tendency of the mass flux variation shown in Fig. 4(a)*.*That is, for the case of the small air volumetric flow, since the moisture absorption capacity of the air is comparatively small, the heat and moisture applied to the air through the porous plate is sufficient.

Figure 5 shows the distribution of temperature in the air flowing through the channel and porous plate. This graph indicates that the temperature of the air and the porous plate increase as the exit of the channel is approached. In the case of a water temperature of 69°C, in the flow direction, the liquid-side porous plate temperature changed from 62°C to 64.4°C due to the water evaporation to the air side. Since the temperature difference between the liquid side and air side of the porous plate decreases in the direction of the air flow, the heat flux, and the moisture transport accompanying it become small as the channel exit is approached. In addition, the temperature difference is found to be greater than that between the air and the porous plate. In particular, this tendency is clearly observed in the vicinity of the channel inlet. Compared to the thickness of 1 mm and thermal conductivity of approximately 1.7 W/(mK) for the porous plate, the heat transfer coefficient of the singlephase air flow in the channel is only a few tens of W/(m2K). This means that the heat transport by the heat conduction passing through the porous plate is far greater than that by the heat transfer of sensible heat on the porous plate surface. This can explain why the heat transport is approximately equal to the latent heat transport accompanying the moisture transport in this moisture transport process, as mentioned above, and indicates that the heat flux and mass flux are bigger in the vicinity of the channel inlet.

Distance from air inlet *x* mm

Fig. 5. Distributions of temperature in an air channel and a porous plate with flow direction

Figure 6 shows the distribution of the heat flux to the air from the constant-temperature water for the experimental conditions shown in Figure 5. This graph shows that, in the heat

Furthermore, Fig. 4(d) shows that for the case in which the air volumetric flow is less than approximately 10×10-5 m3/s, the relative humidity of the air in the channel exit is approximately 100%. This also explains the tendency of the mass flux variation shown in Fig. 4(a)*.*That is, for the case of the small air volumetric flow, since the moisture absorption capacity of the air is comparatively small, the heat and moisture applied to the air through

Figure 5 shows the distribution of temperature in the air flowing through the channel and porous plate. This graph indicates that the temperature of the air and the porous plate increase as the exit of the channel is approached. In the case of a water temperature of 69°C, in the flow direction, the liquid-side porous plate temperature changed from 62°C to 64.4°C due to the water evaporation to the air side. Since the temperature difference between the liquid side and air side of the porous plate decreases in the direction of the air flow, the heat flux, and the moisture transport accompanying it become small as the channel exit is approached. In addition, the temperature difference is found to be greater than that between the air and the porous plate. In particular, this tendency is clearly observed in the vicinity of the channel inlet. Compared to the thickness of 1 mm and thermal conductivity of approximately 1.7 W/(mK) for the porous plate, the heat transfer coefficient of the singlephase air flow in the channel is only a few tens of W/(m2K). This means that the heat transport by the heat conduction passing through the porous plate is far greater than that by the heat transfer of sensible heat on the porous plate surface. This can explain why the heat transport is approximately equal to the latent heat transport accompanying the moisture transport in this moisture transport process, as mentioned above, and indicates that the heat

0 50 100

Fig. 5. Distributions of temperature in an air channel and a porous plate with flow direction Figure 6 shows the distribution of the heat flux to the air from the constant-temperature water for the experimental conditions shown in Figure 5. This graph shows that, in the heat

thermal conductivity 1.7 W/(mK) pore diameter 5 μm plate thickness 1mm channel height 1mm

air volumetric flow 2 ×10 m /s

Distance from air inlet *x* mm

air temperature

 air-side plate temperature water-side plate temperature


flux and mass flux are bigger in the vicinity of the channel inlet.

30

40

50

Temperatues

*T*

℃

60

70

the porous plate is sufficient.

transport to the air from the constant-temperature water through the porous plate, 77% of the heat transport is by the heat conduction in the porous plate, 15% is by the heat conduction in the water including in the porous plate, and 8% is by the transport of the sensible heat accompanying the water transportation through the porous plate. Thus, 85% of the heat transport is used for the evaporation of the water to the air and 7% of the heat transport is used for the temperature increase of the air. That is, the heat transfer between the porous plate and the air is mainly the transport of the latent heat accompanying the water transportation.

For water vaporization 48.1 W (85%)

Heat conducted by liquid 8.5 W (15%)

Fig. 6. Distribution of heat flux in the process of moisture transport through a porous plate

As described above, in the process of moisture transport through the porous plate, there are several factors controlling the phenomenon, e.g., the water flow resistance *R*fp and heat transfer resistance *R*tp inside the plate, and the mass transfer resistance *R*ms and heat transfer resistance *R*ts on the surface of the porous plate. Considering the influence of each factor involved and based on the one-dimensional system, the resistances of the mass transfer and heat transfer in the porous plate are defined and their influence on the performance of the moisture transport is discussed. Here, *R*fp depends on the material structure, such as the size and distribution of the pore, and the surface properties of the plate, such as the wettability. Thus, based on the Darcy law, the maximum flux of the liquid water through the porous plate, in which the surface tension, as the driving force, can be determined as follows:

$$\left[\mathcal{M}\right]\_{\text{max}}^f = \frac{4\sigma\cos\theta}{D} \cdot \frac{1}{\mu\mathcal{R}\_{\text{fr}}}\tag{1}$$

$$R\_{fp} = \Delta \text{x } / \, K(\varepsilon, D) \tag{2}$$

Moisture Transport Through a Porous Plate with Micro Pores 329

thermal conductivity W/(mK)

(a)

(b)

(c)

3-5

10 20 30

Air volumetric flow *V* 10 m /s

Fig. 7. Effect of thermal conductivity of a porous plate on moisture transport (plate thickness:

Figure 8 shows the variations in mass flux, temperature and relative humidity of the outlet air with respect to the air volumetric flow for porous plates having different thermal conductivities and thickness of 1 mm. In the case of the low-thermal-conductivity plate, the mass flux increases with respect to the increase of the air volumetric flow when the air volumetric flow is less than 1.0×10-4m3/s, and the relative humidity in the outlet air is approximately 100%. However, the mass flux changes slightly when the air volumetric flow exceeds 1.0×10-4m3/s. The reason is as mentioned above. Moreover, as shown in Figure 8(a), for the case of the high-thermal-conductivity porous plate with a thickness of 1 mm, there is no range in which the mass flux changes slightly with the air volumetric flow. Furthermore, the temperature in the outlet air is less than the temperature of the constant-temperature water, and the difference exceeds 7 K. At the same time, the relative humidity in the outlet air is approximately 100% with the air volumetric flow. Therefore, it is thought that, in this

 plate thickness 2mm channel height 1mm porosity 20% pore diameter 2μm

 1.7 20.2

0

80

40

1

0.5

Outlet air relative humidity *RH*

2 mm)

0

50

60

70

2

Mass flux

Outlet air temperature

*T*

℃

*m* 10 kg/(m s)


 2

4

6

8

10

$$K(\varepsilon, D) = \mathcal{C}(\varepsilon)D^2 \tag{3}$$

where σ is the surface tension of the water, *D* is the characteristic pore diameter of the porous plate, *K*(ε,*D*) is the permeability of the plate, Δ*x* is the thickness of the plate, and *C*(ε) is a coefficient depending on the porosity of the plate. In addition, as mentioned above, most of the heat from the constant-temperature water to the air through the porous plate is used for the water evaporation at the air-side of the plate. Therefore, the maximum evaporation of the liquid water at the air side can be determined by the heat transfer resistance of the porous plate:

$$\left.m^{t}\_{\text{max}}\right|\_{\text{max}} = \frac{1}{R\_{tp}} \cdot \frac{t\_c - t\_s}{h\_{gl}}\tag{4}$$

$$R\_{tp} = \Delta \mathbf{x} \;/\; \mathcal{A}\_p \tag{5}$$

where *t*c is the temperature of the plate surface at the constant-temperature water side, *t*s is the temperature of the plate surface at the air-side, *h*gl is the latent heat of the vaporization of the water and λp is the thermal conductivity of the plate.

#### **3.2 Effect of thermal conductivity**

Figure 7 shows the variations in mass flux, temperature and relative humidity of the outlet air with respect to the air volumetric flow for porous plates having different thermal conductivities. The plate thickness and the height of the channel are 2 mm and 1 mm, respectively. In either high or low thermal conductivities of the porous plate, the mass flux first increases with the increase of the air volumetric flow, and then changes slightly when the air volumetric flow exceeds a threshold. This indicates that, as mentioned above, for the range in the low air volumetric flow, the factors controlling the moisture transport process are the moisture absorption capacity of the air and the resistances of the heat and mass transfer between the porous plate surface and the air, and those for the range in the high air volumetric flow are the thermal resistance and mass transport resistance inside the plate. In particular, in the range of the high air volumetric flow, the relative humidity and temperature in the outlet air are less remarkable than the saturation state or the temperature of the constant-temperature water, respectively. Therefore, for this range, it is remarkable that the moisture transport is controlled by the resistance of the heat and mass transfer inside the porous plate. Moreover, (1) the increase of the mass flux caused by the increase of the thermal conductivity of the porous plate is remarkable, and (2) although the thermal conductivity in the high-thermal-conductivity plate is approximately 11 times that in the low-thermal-conductivity plate, the mass flux in the former case less than twice that in the latter case. Therefore, it is thought that, the moisture transport is controlled by the mass transfer resistance inside the plate in the former case and by the thermal resistance inside the plate in the latter case. That is, for the former case, the maximum mass flux is limited to the maximum flux *m*<sup>f</sup> max of the liquid water through the porous plate determined by the mass transfer resistance inside the porous plate defined by equation (1), and, for the latter case, the maximum mass flux is limited to the maximum flux *m*<sup>t</sup> max of the water vaporization at the plate surface determined by the thermal resistance inside the porous plate defined by equation (4).

<sup>2</sup> *KDCD* (, ) ()

where σ is the surface tension of the water, *D* is the characteristic pore diameter of the

is a coefficient depending on the porosity of the plate. In addition, as mentioned above, most of the heat from the constant-temperature water to the air through the porous plate is used for the water evaporation at the air-side of the plate. Therefore, the maximum evaporation of the liquid water at the air side can be determined by the heat transfer resistance of the

*<sup>t</sup>* 1 *c s*

where *t*c is the temperature of the plate surface at the constant-temperature water side, *t*s is the temperature of the plate surface at the air-side, *h*gl is the latent heat of the vaporization of

Figure 7 shows the variations in mass flux, temperature and relative humidity of the outlet air with respect to the air volumetric flow for porous plates having different thermal conductivities. The plate thickness and the height of the channel are 2 mm and 1 mm, respectively. In either high or low thermal conductivities of the porous plate, the mass flux first increases with the increase of the air volumetric flow, and then changes slightly when the air volumetric flow exceeds a threshold. This indicates that, as mentioned above, for the range in the low air volumetric flow, the factors controlling the moisture transport process are the moisture absorption capacity of the air and the resistances of the heat and mass transfer between the porous plate surface and the air, and those for the range in the high air volumetric flow are the thermal resistance and mass transport resistance inside the plate. In particular, in the range of the high air volumetric flow, the relative humidity and temperature in the outlet air are less remarkable than the saturation state or the temperature of the constant-temperature water, respectively. Therefore, for this range, it is remarkable that the moisture transport is controlled by the resistance of the heat and mass transfer inside the porous plate. Moreover, (1) the increase of the mass flux caused by the increase of the thermal conductivity of the porous plate is remarkable, and (2) although the thermal conductivity in the high-thermal-conductivity plate is approximately 11 times that in the low-thermal-conductivity plate, the mass flux in the former case less than twice that in the latter case. Therefore, it is thought that, the moisture transport is controlled by the mass transfer resistance inside the plate in the former case and by the thermal resistance inside the plate in the latter case. That is, for the former case, the maximum mass flux is limited to

*tp gl t t*

λ

max of the liquid water through the porous plate determined by the

max of the water vaporization

mass transfer resistance inside the porous plate defined by equation (1), and, for the latter

at the plate surface determined by the thermal resistance inside the porous plate defined by

case, the maximum mass flux is limited to the maximum flux *m*<sup>t</sup>

*R h*

 ε

,*D*) is the permeability of the plate, Δ*x* is the thickness of the plate, and *C*(

= (3)

<sup>−</sup> = ⋅ (4)

(5)

ε)

ε

max

*m*

/ *R x tp p* = Δ

the water and λp is the thermal conductivity of the plate.

porous plate, *K*(

porous plate:

ε

**3.2 Effect of thermal conductivity** 

the maximum flux *m*<sup>f</sup>

equation (4).

Fig. 7. Effect of thermal conductivity of a porous plate on moisture transport (plate thickness: 2 mm)

Figure 8 shows the variations in mass flux, temperature and relative humidity of the outlet air with respect to the air volumetric flow for porous plates having different thermal conductivities and thickness of 1 mm. In the case of the low-thermal-conductivity plate, the mass flux increases with respect to the increase of the air volumetric flow when the air volumetric flow is less than 1.0×10-4m3/s, and the relative humidity in the outlet air is approximately 100%. However, the mass flux changes slightly when the air volumetric flow exceeds 1.0×10-4m3/s. The reason is as mentioned above. Moreover, as shown in Figure 8(a), for the case of the high-thermal-conductivity porous plate with a thickness of 1 mm, there is no range in which the mass flux changes slightly with the air volumetric flow. Furthermore, the temperature in the outlet air is less than the temperature of the constant-temperature water, and the difference exceeds 7 K. At the same time, the relative humidity in the outlet air is approximately 100% with the air volumetric flow. Therefore, it is thought that, in this

Moisture Transport Through a Porous Plate with Micro Pores 331

contrast, the value is approximately 6×10-5 kg/(m2s) for the case of the low-thermalconductivity porous plate with a thickness of 1mm. That is, when the thermal resistance and the mass transfer resistance inside the plate are the controlling factors, the mass flux doubled by halving the plate thickness. Furthermore, comparing the experimental results for the high-thermal-conductivity plate with a thickness of 2mm and the low-thermalconductivity plate with a thickness of 1 mm reveals that although the mass transfer resistance inside the plate for the latter is half that for the former, the mass flux in the latter is only 1.2 times the mass flux in the former. Therefore, as in the case for a low-thermalconductivity plate with a thickness of 2mm, for the case of the low-thermal-conductivity porous plate with a thickness of 1 mm, the mass flux is also controlled by the thermal

Equation (5). This is also understood by that fact that the relative humidity in the outlet air is approximately 100% for the case of the high-thermal-conductivity porous plate with a

Figures 9 and 10 show the effect of the porosity in the porous plate on the mass flux for plate thicknesses of 0.5mm and 2mm, respectively. The thermal conductivity of the plate is 20.2W/(mK). For the plate thickness of 0.5mm, under the condition of the present study, although the porosity varied from 12% to 30% and the variation range is more than one time, no difference was observed to be caused by the porosity. As mentioned above, since, in this case, the mass transport is controlled by the heat transfer between air and the plate surface, it is ineffective to the moisture transport by changing the mass transport resistance inside the plate. However, for the plate thickness of 2mm, since the mass transport is controlled by the mass transport resistance inside the plate, the mass flux increases with the increase of the porosity. The increase is remarkable in the range of the large air volumetric

10 20 30

Air volumetric flow *V* 10 m /s -5 3

plate thickness 0.5mm channel height 1mm

thermal conductivity 20.2 W/(mK) pore diameter 2 μm

max, as defined in

resistance inside the plate, and the maximum mass flux is limited to *m*<sup>t</sup>

thickness of 1 mm.

flow.

**3.3 Effect of porosity** 

2

Mass flux

*m* 10 kg/(m・s)


 2

0

4

6

8

10

 porosity 12% 20% 30%

Fig. 9. Effect of porosity on mass flux (plate thickness: 0.5 mm)

case, the factor controlling the moisture transport is the heat transfer at the plate surface. That is, in the case in which the thin porous plate having a high thermal conductivity is used, it is best to promote the moisture transport that enhances the heat transfer at the plate surface facing the channel side.

Fig. 8. Effect of thermal conductivity of a porous plate on moisture transport (plate thickness: 1 mm)

Moreover, comparing the results shown in Figures 7 and 8, in the range of the large air volumetric flow in which the moisture absorption capacity is sufficient, the mass flux, which is almost constant at approximately 3×10-5 kg/(m2s) for the case of the low-thermalconductivity porous plate with a thickness of 2mm, and is approximately 5×10-5 kg/(m2s) for the case of the high-thermal-conductivity porous plate with a thickness of 2mm. In contrast, the value is approximately 6×10-5 kg/(m2s) for the case of the low-thermalconductivity porous plate with a thickness of 1mm. That is, when the thermal resistance and the mass transfer resistance inside the plate are the controlling factors, the mass flux doubled by halving the plate thickness. Furthermore, comparing the experimental results for the high-thermal-conductivity plate with a thickness of 2mm and the low-thermalconductivity plate with a thickness of 1 mm reveals that although the mass transfer resistance inside the plate for the latter is half that for the former, the mass flux in the latter is only 1.2 times the mass flux in the former. Therefore, as in the case for a low-thermalconductivity plate with a thickness of 2mm, for the case of the low-thermal-conductivity porous plate with a thickness of 1 mm, the mass flux is also controlled by the thermal resistance inside the plate, and the maximum mass flux is limited to *m*<sup>t</sup> max, as defined in Equation (5). This is also understood by that fact that the relative humidity in the outlet air is approximately 100% for the case of the high-thermal-conductivity porous plate with a thickness of 1 mm.

#### **3.3 Effect of porosity**

330 Mass Transfer - Advanced Aspects

case, the factor controlling the moisture transport is the heat transfer at the plate surface. That is, in the case in which the thin porous plate having a high thermal conductivity is used, it is best to promote the moisture transport that enhances the heat transfer at the plate

thermal conductivity W/(mK)


(c)

10 20 30

relative humidity = 1

(a)

(b)

Air volumetric flow *V* 10 m /s

 plate thickness 1mm channel height 1mm porosity 20% pore diameter 2 μm

Fig. 8. Effect of thermal conductivity of a porous plate on moisture transport (plate thickness:

Moreover, comparing the results shown in Figures 7 and 8, in the range of the large air volumetric flow in which the moisture absorption capacity is sufficient, the mass flux, which is almost constant at approximately 3×10-5 kg/(m2s) for the case of the low-thermalconductivity porous plate with a thickness of 2mm, and is approximately 5×10-5 kg/(m2s) for the case of the high-thermal-conductivity porous plate with a thickness of 2mm. In

1.7 20.2

surface facing the channel side.

0

80

40

1

0.5

Outlet air relative humidity *RH*

1 mm)

0

50

60

70

2

Mass flux

Outlet air temperature

*T*

℃

*m* 10 kg/(m・s)


 2

4

6

8

10

Figures 9 and 10 show the effect of the porosity in the porous plate on the mass flux for plate thicknesses of 0.5mm and 2mm, respectively. The thermal conductivity of the plate is 20.2W/(mK). For the plate thickness of 0.5mm, under the condition of the present study, although the porosity varied from 12% to 30% and the variation range is more than one time, no difference was observed to be caused by the porosity. As mentioned above, since, in this case, the mass transport is controlled by the heat transfer between air and the plate surface, it is ineffective to the moisture transport by changing the mass transport resistance inside the plate. However, for the plate thickness of 2mm, since the mass transport is controlled by the mass transport resistance inside the plate, the mass flux increases with the increase of the porosity. The increase is remarkable in the range of the large air volumetric flow.

Fig. 9. Effect of porosity on mass flux (plate thickness: 0.5 mm)

Moisture Transport Through a Porous Plate with Micro Pores 333

Figure 11 presents the variation of the mass flux for different pore diameters in plates having thicknesses of 1 mm and 3.5 mm. The thermal conductivity of the plate is 1.7 W/(mK). Similar values were observed for pore diameters of 5 μm and 14 μm. However, a comparatively low value was observed for a pore diameter of 2 μm. The difference increases with the increase in air volumetric flow, and the largest differences are approximately 25% and 60% for the plate thicknesses of 1 mm and 3.5 mm, respectively. This is thought to be caused by the remarkable resistance to the flow within the porous media for small pore diameters or thick plates. That is, in this moisture transport process, we suppose that the mass transfer resistance at the surface of a porous plate became small and the influence of

> channel height mm 0.5 1.0 1.5

plate thickness 1mm

porosiy 20% pore diameter 2 μm

Fig. 12. Effect of channel height on moisture transport for a plate of high thermal conductivity

thermal conductivity 20.2 W/(mK)

Air volumetric flow *V* 10 m /s

3-5

(a)

(b)

(c)

10 20 30

**3.4 Effect of pore diameter** 

flowing resistance inside the plate became strong.

80

40

1

0.5

Outlet air relative humidity *RH*

0

50

60

70

Mass flux

Outlet air temperature

*T*

℃

*m* 10 kg/(m・s)


 2

Fig. 10. Effect of porosity on mass flux (plate thickness: 2 mm)

Fig. 11. Effect of pore diameter on mass flux for porous plates of different thickness

#### **3.4 Effect of pore diameter**

332 Mass Transfer - Advanced Aspects

thermal conductivity 20.2 W/(mK)

Air volumetric flow *V* 10 m /s 3-5

plate thickness 1mm

plate thickness 3.5mm

Fig. 11. Effect of pore diameter on mass flux for porous plates of different thickness

channel height 1 mm thermal conductivity 1.7 W/(mK) porosity 30%

plate thickness 2mm channel height 1mm

pore diameter 2 μm

2

Mass flux

*m* 10 kg/(m s)


 2

0

0

2

4

100

6

8

Mass flux

*m* 10 kg/(m s)


 2

2

4

6

8

10

Fig. 10. Effect of porosity on mass flux (plate thickness: 2 mm)

4

6

8

10

10 20 30

 porosity 20% 30%

3-5

 pore diameter <sup>2</sup><sup>μ</sup>m 5<sup>μ</sup><sup>m</sup> 14μm

(b)

(a)

10 20 30

Air volumetric flow *V* 10 m /s

Figure 11 presents the variation of the mass flux for different pore diameters in plates having thicknesses of 1 mm and 3.5 mm. The thermal conductivity of the plate is 1.7 W/(mK). Similar values were observed for pore diameters of 5 μm and 14 μm. However, a comparatively low value was observed for a pore diameter of 2 μm. The difference increases with the increase in air volumetric flow, and the largest differences are approximately 25% and 60% for the plate thicknesses of 1 mm and 3.5 mm, respectively. This is thought to be caused by the remarkable resistance to the flow within the porous media for small pore diameters or thick plates. That is, in this moisture transport process, we suppose that the mass transfer resistance at the surface of a porous plate became small and the influence of flowing resistance inside the plate became strong.

Fig. 12. Effect of channel height on moisture transport for a plate of high thermal conductivity

Moisture Transport Through a Porous Plate with Micro Pores 335

Figure 13 shows the variation in the mass flux with respect to the air volumetric flow using the low-thermal-conductivity plate for channel heights of 0.5, 1.0, and 1.5 mm. In contrast to the case for the high-thermal-conductivity plate, the mass flux increased when the channel height was varied from 1.5 mm to 1.0 mm, but it did not change much with air volumetric flow for channel heights between 1.0 mm and 0.5 mm. This is thought to be caused by that the main factors controlling the moisture transport are the thermal resistance inside the plate and the resistances of the heat and mass transfer at the plate surface next to the channel for a channel height of 1.5mm, and, the controlling factor just is the thermal

Based on these results, to increase the moisture transport, a smaller apparatus would be

Figure 14 shows the variation of pressure drop in air with respect to the air volumetric flow for the experimental conditions shown in Figure 13. The solid line represents the air pressure drop in the tube for a laminar flow obtained using the Hagen-Poiseuille equation

> <sup>32</sup> 2 Re *<sup>e</sup> <sup>L</sup> P v D*

where *L* is the channel length, *D*e is the equivalent diameter of the channel, *v* is the air

channel height decreases, and the experimental results are higher than the calculation results for any channel height. This is thought to be due to the effect of the roughness of the porous plate surface and the water vaporization at the plate surface. In addition, the existence of the air volumetric flow that the mass flux varies only slightly with the air flow, as shown in Figure 13, indicates that a proper air volumetric flow (when the air volumetric flow exceeds the value the mass flux increases only slightly but the pressure drop increases. For example, approximately 10×10-5 m3/s for channel heights of 1 mm) is favorable to

<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>10</sup>

Air volumetric flow *V* 10 m /s

Fig. 14. Variation of pressure decrease with air volumetric flow for different channel heights


ρ

is the density of the air. The pressure drop increases rapidly when the

(6)

used under the condition in which the pressure drop is less than a limited range.

Δ= ⋅

channel height mm 0.5 1.0 1.5

resistance inside the plate for the channel height of less than 1mm.

(Welty et al., 1976), as follows:

ρ

50 100

Pressure drop

Δ*P* Pa

500 1000

5000

velocity, and

#### **3.5 Effect of channel height**

As mentioned above, the heat transfer and the mass transfer at the plate surface strongly affect the moisture transport through the porous plate. Consequently, the variations of the heat and mass transfer at the plate surface and the moisture absorption capacity of air caused by the variation in the quantity or the velocity of the airflow channel are projected. However, the variation of the mass flux cannot be easily predicted.

Figure 12 shows the variation in mass flux, temperature, and relative humidity in the outlet air with respect to the air volumetric flow using the high-thermal-conductivity plate for channel heights of 0.5, 1.0, and 1.5 mm. The mass flux increased when the channel height was varied from 1.5 mm to 1.0 mm and from 1.0 mm to 0.5 mm. As shown in Figure 12(b), over the entire range of the air volumetric flow, when the channel height was reduced, the heat transfer at the porous plate surface was promoted, resulting in an increase in the air temperature in the outlet air. This means that the moisture absorption capacity of air increased when the channel height was reduced. In addition, from Figure 12(c), the relative humidity of the air in the outlet air was approximately 100%, irrespective of the channel height and the air volumetric flow. This result has two implications. One is that there was sufficient water supplied from the constant-temperature water to the plate surface next to the air. The other implication is that mass transfer due to gas convection or diffusion at the plate surface has not hampered moisture transport under the experimental conditions. In other words, the results shown in Figure 12 confirmed that the controlling factor for the moisture transport through the porous plate under the experimental conditions is the heat transfer at the plate surface near the air channel and is not the thermal resistance or the mass transport resistance inside the plate. This result agrees with the discussion in Section 3.2. that is, in the case of the thin porous plate with high thermal conductivity, the factor controlling the moisture transport is the heat transfer resistance at the plate surface next to the channel.

Fig. 13. Effect of channel height on moisture transport for a plate of low thermal conductivity

As mentioned above, the heat transfer and the mass transfer at the plate surface strongly affect the moisture transport through the porous plate. Consequently, the variations of the heat and mass transfer at the plate surface and the moisture absorption capacity of air caused by the variation in the quantity or the velocity of the airflow channel are projected.

Figure 12 shows the variation in mass flux, temperature, and relative humidity in the outlet air with respect to the air volumetric flow using the high-thermal-conductivity plate for channel heights of 0.5, 1.0, and 1.5 mm. The mass flux increased when the channel height was varied from 1.5 mm to 1.0 mm and from 1.0 mm to 0.5 mm. As shown in Figure 12(b), over the entire range of the air volumetric flow, when the channel height was reduced, the heat transfer at the porous plate surface was promoted, resulting in an increase in the air temperature in the outlet air. This means that the moisture absorption capacity of air increased when the channel height was reduced. In addition, from Figure 12(c), the relative humidity of the air in the outlet air was approximately 100%, irrespective of the channel height and the air volumetric flow. This result has two implications. One is that there was sufficient water supplied from the constant-temperature water to the plate surface next to the air. The other implication is that mass transfer due to gas convection or diffusion at the plate surface has not hampered moisture transport under the experimental conditions. In other words, the results shown in Figure 12 confirmed that the controlling factor for the moisture transport through the porous plate under the experimental conditions is the heat transfer at the plate surface near the air channel and is not the thermal resistance or the mass transport resistance inside the plate. This result agrees with the discussion in Section 3.2. that is, in the case of the thin porous plate with high thermal conductivity, the factor controlling the moisture transport is the heat transfer resistance at the plate surface next to

10 20 30

channel height mm 0.5 1.0 1.5


Air volumetric flow *V* 10 m /s

Fig. 13. Effect of channel height on moisture transport for a plate of low thermal conductivity

thermal conductivity 1.7 W/(mK)

porosity 30% pore diameter 5 μm plate thickness 1.0 mm

However, the variation of the mass flux cannot be easily predicted.

**3.5 Effect of channel height** 

the channel.

2

Mass flux

*m* 10 kg/(m s)


0

4

6

8

10

 2 Figure 13 shows the variation in the mass flux with respect to the air volumetric flow using the low-thermal-conductivity plate for channel heights of 0.5, 1.0, and 1.5 mm. In contrast to the case for the high-thermal-conductivity plate, the mass flux increased when the channel height was varied from 1.5 mm to 1.0 mm, but it did not change much with air volumetric flow for channel heights between 1.0 mm and 0.5 mm. This is thought to be caused by that the main factors controlling the moisture transport are the thermal resistance inside the plate and the resistances of the heat and mass transfer at the plate surface next to the channel for a channel height of 1.5mm, and, the controlling factor just is the thermal resistance inside the plate for the channel height of less than 1mm.

Based on these results, to increase the moisture transport, a smaller apparatus would be used under the condition in which the pressure drop is less than a limited range.

Figure 14 shows the variation of pressure drop in air with respect to the air volumetric flow for the experimental conditions shown in Figure 13. The solid line represents the air pressure drop in the tube for a laminar flow obtained using the Hagen-Poiseuille equation (Welty et al., 1976), as follows:

$$
\Delta P = \frac{32}{\text{Re}} \cdot \frac{L}{D\_e} v^2 \rho \tag{6}
$$

where *L* is the channel length, *D*e is the equivalent diameter of the channel, *v* is the air velocity, and ρ is the density of the air. The pressure drop increases rapidly when the channel height decreases, and the experimental results are higher than the calculation results for any channel height. This is thought to be due to the effect of the roughness of the porous plate surface and the water vaporization at the plate surface. In addition, the existence of the air volumetric flow that the mass flux varies only slightly with the air flow, as shown in Figure 13, indicates that a proper air volumetric flow (when the air volumetric flow exceeds the value the mass flux increases only slightly but the pressure drop increases. For example, approximately 10×10-5 m3/s for channel heights of 1 mm) is favorable to

Fig. 14. Variation of pressure decrease with air volumetric flow for different channel heights

Moisture Transport Through a Porous Plate with Micro Pores 337

Figure 16 shows the variations in the moisture absorption rate with respect to the air volumetric flow using the high-thermal-conductivity plate for channel heights of 0.5, 1.0, and 1.5 mm. As mentioned in Section 3.5, the moisture transport increased with decreasing channel height because the heat transfer at the plate surface next the channel is promoted, so that the moisture absorption rate increased with the decrease of the channel height. In particular, the moisture absorption rate shows a high value that exceeds 90% for the case of an air volumetric flow of less than 6.7×10-5 m3/sand a channel height of 0.5mm. That is, a high moisture recovery rate can be expected for a suitable working condition for the device

10 20 30


pore diameter 2 μm porosity 20% plate thickness 1mm

thermal conductivity 20.2 W/(mK)

Air volumetric flow *V* 10 m /s

The present study attempted to clarify the characteristics of the heat and moisture transport in the process of moisture recovery from the exhaust gas of fuel cell vehicles using a porous plate having extremely small pores. As a first step, the moisture transport from constanttemperature water to dry air through the porous plate was measured. The general characteristics of moisture and the effects of the thermal conductivity, porosity and pore diameter in the porous plate, and the height of the channel of flowing air on the performance of moisture transport were examined experimentally. The results are summarized as

1. For the process of moisture transport from constant-temperature water to dry air through a porous media plate, the mass flux increases with the increase of air volumetric flow, and the heat transport in this process is caused primarily by the

2. The thermal conductivity of the porous plate is a very important factor and the controlling factor for moisture transport is different for the high- and low-thermalconductivity plates. That is, for a plate thickness of 1 mm, the controlling factor is the

design.

0.5

Moisture absorptoin rate

**4. Conclusion** 

follows:

η

0

Fig. 16. Effect of channel height on moisture absorption rate

transport of latent heat accompanying the mass transport.

channel height

 0.5mm 1.0mm

1.5mm

1

moisture recovery for the channel height is fixed. As same, the fact that the increase in the pressure drop with respect to the increasing air flow and decreasing channel height, as shown in Figure 14, shows that a proper channel height (the mass flux increase hardly if even the channel height is decreased further. For example, approximately 1.0 mm for the conditions of the channel length 100 mm and the pressure drop 200 Pa) is favorable to moisture recovery for the pressure drop is limited.

#### **3.6 Moisture absorption rate**

In order to evaluate the utilization degree of the moisture absorption capacity of the air, the moisture absorption rate η, which is the ratio of the increase in the absolute humidity to the maximum moisture absorption of the air, is introduced and is given by

$$
\eta = (d\_{\rm out} - d\_{\rm in}) / (d\_{\rm w} - d\_{\rm in}) \tag{7}
$$

where *d*out and *d*in are the absolute humidities of the air at the exit and entrance, respectively, of the channel in which the air is flowing, and *d*w is the absolute humidity of saturated air at the temperature of the constant-temperature water.

Figure 15 shows the variations in moisture absorption rate with respect to the air volumetric flow for porous plates having different thermal conductivities. This figure shows that the moisture absorption rate decreases as the air volumetric flow increases, and the values for both the high- and low-thermal-conductivity plates were approximately the same and exceeded 80% at an air volumetric flow of 3.3×10-5 m3/s. However, as the air volumetric flow increases, the moisture absorption rates of the high- and low-thermal-conductivity plates gradually diverge, and at a volumetric flow rate of 24.7×10-5 m3/s, the moisture absorption rate for the low-thermal-conductivity plate is 26%, while that for the highthermal-conductivity plate is 40%, approximately 1.5 times that for the low-thermalconductivity plate. That is, from the standpoint of the moisture recovery, it is effective to use the high-thermal-conductivity plate for the case of the large air volumetric flow.

Fig. 15. Effect of thermal conductivity of the porous plate on moisture absorption rate

Figure 16 shows the variations in the moisture absorption rate with respect to the air volumetric flow using the high-thermal-conductivity plate for channel heights of 0.5, 1.0, and 1.5 mm. As mentioned in Section 3.5, the moisture transport increased with decreasing channel height because the heat transfer at the plate surface next the channel is promoted, so that the moisture absorption rate increased with the decrease of the channel height. In particular, the moisture absorption rate shows a high value that exceeds 90% for the case of an air volumetric flow of less than 6.7×10-5 m3/sand a channel height of 0.5mm. That is, a high moisture recovery rate can be expected for a suitable working condition for the device design.

Fig. 16. Effect of channel height on moisture absorption rate
