RESULTS AND DISCUSSION

The models developed were initially verified by simple species and energy balances. The results were accurate within 1%.

(25)

(26)

For the constant thickness model, the results were compared to results available in the literature [10] for simulations using CaCl2-water as the liquid-desiccant solution, flowing in a co-current configuration. The authors defined average Nusselt and Sherwood numbers as follows:

It is not clear if the Cai* adopted by the authors was calculated at the wall temperature or the desiccant inlet temperature. The former was used in the present work. Table 1 presents the variables and properties used that were common to all simulations.

Table 1: properties and variables used in simulations.

CaCl2

Air

k

W/m2

0.525

0.02635

CP

J/kg K

2330

1.028 x 103

r

kg/m3

1394

1.172

kg/m s

1.19 x 10-2

1.83 x 10-5

D

m2/s

2.5 x 10"5

4.2 x 10-10

m

kg/s

7.0 x 10"3

1.23795 x 10-2

Ti

oC

25

35

Ci

kg/kg

0.6

0.02

hfa

J/kg K

2.448 x 106

Tw

oC

1 0

H

8 cx 2

Present work

Rahamah et al [10]

% Difference

m

m

Nu

Sh

Nu

Sh

Nu

Sh

4.0 x 10-1

2.6 x 10-3

2.42

2.08

2.32

1.92

4.1

7.7

4.0 x 10-1

3.0 x 10-3

2.79

2.42

2.68

2.25

3.9

7.0

4.0 x 10-1

3.5 x 10-3

3.20

2.80

3.08

2.67

3.8

4.6

4.0 x 10-1

4.0 x 10-3

3.56

3.15

3.44

2.95

3.4

6.3

4.0 x 10-1

3.3 x 10-3

3.04

2.65

2.93

2.50

3.6

5.7

5.0 x 10-1

3.3 x 10-3

2.56

2.20

2.45

2.07

4.3

5.9

6.0 x 10-1

3.3 x 10-3

2.18

1.88

2.08

1.75

4.6

6.9

7.0 x 10-1

3.3 x 10-3

1.98

1.63

1.84

1.51

7.1

7.4

8.0 x 10-1

3.3 x 10-3

1.73

1.40

1.65

1.32

4.6

5.7

Table 2: comparison between the results for Nu and Sh obtained in the present work and

Rahamah et al[10].

The results agree well, in special if one considers that the values used for the properties were not presented by Rahamah et al. This is particularly important for the air mass flow rate. The authors used a Reynolds number for the air flow of 1350, but did not inform the value used for air viscosity. Since the air flow rate has a significant impact on Nu and Sh, it would be difficult to obtain closer results, even if using the same numerical method and computer algorithms. For example, in the case of the 0.70 high channel, the one which presented the largest difference between the works, a 10% reduction in air mass flow rate causes a 9.6% reduction in the Nusselt number and a 9.8% reduction in the Sherwood number.

To compare the three models, another set of simulations was performed. All conditions were kept constant, with the exception of the desiccant mass flow. A co-current flow configuration was used, at this time with LiCl as the desiccant material. Table 3 presents the properties and variables used for the simulations.

Table 3: properties and

variables used in simulations for comparison between the three models.

LiCl

Air

k

(W/m2K)

0.558

0.0275

cp

(J/kg K)

3140

990

r

(kg/m3)

1394

1.11

P

(kg/m s)

1.86 x 10-3

1.9 x 10-5

D

(m2/s)

2.65 x 10-5

1.2 x 10-9

m

(kg/s)

0.01264

Ti

(oC)

25

30

Ci

(kg/kg)

0.6

0.015

hfg

(J/kg K)

2.430 x 106

Tw

(oC)

25

H

(m)

0.5

p cX 2

(m)

5.0 x 10-3

Table 4 and Fig. 5 present the results obtained with the simulations. It can be seen that the outlet air temperatures for the three models are relatively close, but the results for outlet water mass fraction in air differ significantly when the desiccant mass flow is reduced. The constant and variable thickness models give results that disagree by only 1.2%, when the air mass flow rate equals the desiccant mass flow rate.

Fig. 5: variation of outlet water mass fraction in air with desiccant solution mass flow. (conditions in Table 3).

For higher desiccant flow rates the variable and constant thickness model converge to the same results. However, for a desiccant flow rate 400 times lower than the air flow rate, the difference between the two models is 19%.In terms of the E Ca, the constant thickness model predicts a value 4 times smaller than the variable thickness model.

The variable thickness model was further tested against experimental data available in the literature. Keeling et al [11] made measurements with one single channel using LiCl as the desiccant and a counter-flow configuration.

Variable Thickness Model

Constant Thickness Model

Simplified Model

md

Tao ( C)

Cao

Tao

Cao

Tao

Cao

(kg/s)

(x10-3kgw/kgair)

(oC)

(x10-3kgw/kgair)

(oC)

(x10-3kgw/kgair)

ma

25.87

5.83

25.86

5.90

26.13

6.24

ma/2.5

25.86

5.93

25.86

6.13

26.13

6.37

ma/5

25.86

6.07

25.86

6.46

26.13

6.57

ma/10

25.86

6.32

25.85

7.08

26.13

6.96

ma/20

25.86

6.76

25.85

8.18

26.13

7.66

ma/30

25.86

7.15

25.85

9.08

26.13

8.25

ma/40

25.86

7.50

25.85

9.80

26.13

8.75

ma/50

25.86

7.81

25.85

10.4

26.13

9.18

ma/60

25.86

8.09

25.85

10.9

26.13

9.56

ma/70

25.86

8.34

25.85

11.2

26.13

9.88

ma/80

25.86

8.57

25.85

11.6

26.13

10.2

ma/90

25.86

8.78

25.85

11.8

26.13

10.4

ma/100

25.86

8.98

25.85

12.0

26.13

10.7

ma/150

25.86

9.73

25.85

12.8

26.13

11.5

ma/200

25.86

10.3

25.86

13.3

26.13

12.1

ma/250

25.87

10.7

25.86

13.6

26.13

12.5

ma/300

25.87

11.0

25.86

13.8

26.13

12.8

ma/350

25.87

11.2

25.86

14.0

26.13

13.0

ma/400

25.87

11.4

25.86

14.1

26.13

13.2

Table 4: comparison between the ^results obtained with the three different models.

The model was adapted for the water cooling channel employed in the experiment, that used a cross-flow configuration. In this configuration, for every 50 mm along the channel, there was 10 mm with no water flow. Therefore, the boundary condition for the regions with no water flow was changed to adiabatic, instead of isothermal. The regions with water flow were considered isothermal at a temperature equals to the average between the measured inlet and outlet water cooling temperatures. In the experiments, the water flow was kept high enough that the maximum increase in the water cooling temperature was

0. 4 oC. The channel was 0.46 m high and 5.5 mm deep, and the desiccant solution had an inlet water mass fraction of 59.8% for all experiments. The results are presented in Table

5. The outlet air temperature results agree very well, with less than 1.5% difference between the model and the experimental results. For the outlet water mass fraction in air the results agree very well for the lower desiccant mass flow rates. The difference increases for higher desiccant flow rates, reaching 13% for the case with the highest flow rate. It is not clear, however, what could cause such discrepancies. The desiccant mass flow range is still in the laminar smooth region, therefore, it is unlike that a wavy flow could have caused the difference. The values of uncertainty for the experiments published by the authors are bellow the difference obtained. Therefore, it remains to be investigated the causes for the discrepancies for the higher desiccant flow rates. For lower desiccant flow rates, the results agree very well. Although the use of the constant thickness model was not tested against the data from Keeling et al, the results would not likely be better, since the constant thickness model predicts a lower level of dehumidification than the variable thickness model.

Table 5: comparison between the results obtained with the variable thickness model and Keeling et ^ al[11]. ___________________________________________

ma

md

Tai

Tw

Cai

Tao

Cao

x 10-3 kg/s

x 10-3 kg/s

oC

oC

x 10-3 kgw/kgair

oC

x 10-3 kgw/kgair

1

12.64

0.621

24.5

24.3

14.2

Exp.

25.4

5.3

Model

25.1

6.1

2

12.64

0.327

24.8

24.3

14.3

Exp.

25.6

5.7

Model

25.3

6.4

3

12.64

0.187

24.6

24.3

14.3

Exp.

25.5

6.4

Model

25.3

6.8

4

12.64

0.115

24.4

24.3

14.3

Exp.

25.4

7.1

Model

25.3

7.4

5

12.64

0.085

24.4

24.3

14.3

Exp.

25.4

7.7

Model

25.3

7.8

6

12.64

0.071

24.1

24.3

14.3

Exp.

25.3

7.9

Model

25.3

8.1

7

12.64

0.058

23.9

24.2

14.2

Exp.

25.3

8.4

Model

25.2

8.4

CONCLUSIONS

Numerical models were developed for simultaneous heat and mass transfer in parallel — plate dehumidifiers. The model with variable film thickness was compared to experimental results available in the literature. The results for temperature agree well for all cases tested. The results for water mass fraction agree within 6% for desiccant flow rates more than 34 times lower than the air mass flow, considering desiccant flow on both sides of channel, i. e., 2 x md. For higher desiccant flow rates the discrepancies between the experimental and numerical results increase. Further investigation should be conducted to better explain the reasons for such discrepancies.

The constant thickness and simplified model under-predict the dehumidification, in special for low desiccant flow rates. The numerical model can be adapted for non-isothermal conditions, with the introduction of the cooling water flow equations.

NOMENCLATURE

C water mass fraction in solution (kg/kg)

Cp specific heat (J/kg K)

D diffusivity (m2/s)

dh hydraulic diameter (m)

g gravity acceleration (m/s2)

hh heat transfer coefficient (W/m2K)

hm mass transfer coefficient (m/s)

hfg latent heat of vaporization (J/kg)

ka heat conduction coefficient (W/mK)

m mass flow rate (kg/s)

Nu Nusselt number

p pressure (Pa)

pw water vapour pressure (Pa)

T temperature (oC)

u velocity (m/s)

x coordinate in the direction across the channel (m)

y coordinate in the direction along the channel (m)

Greek characters

a thermal diffusivity (m2/s)

g kinematic viscosity (m2/s)

dd film thickness (m)

dc channel half depth (m)

p. dynamic viscosity (kg/ms)

Subscripts

a

d

o

w

air-water

water-salt solution inlet

outlet

wall