Journal of Advanced Research (2014) 5, 175–182

Cairo University

Journal of Advanced Research

ORIGINAL ARTICLE

A simple analytical method to estimate all exit

parameters of a cross-ﬂow air dehumidiﬁer using

liquid desiccant

M.M. Bassuoni

*

Mechanical Power Engineering Department, Faculty of Engineering, Tanta University, Egypt

A R T I C L E

I N F O

Article history:

Received 16 December 2012

Received in revised form 5 February 2013

Accepted 23 February 2013

Available online 30 March 2013

Keywords:

Dehumidiﬁer

Regenerator

Liquid desiccant

Analytical solution

Structured packing bed

Desiccant cooling

A B S T R A C T

The dehumidiﬁer is a key component in liquid desiccant air-conditioning systems. Analytical

solutions have more advantages than numerical solutions in studying the dehumidiﬁer performance parameters. This paper presents the performance results of exit parameters from an analytical model of an adiabatic cross-ﬂow liquid desiccant air dehumidiﬁer. Calcium chloride is

used as desiccant material in this investigation. A program performing the analytical solution

is developed using the engineering equation solver software. Good accuracy has been found

between analytical solution and reliable experimental results with a maximum deviation of

+6.63% and À5.65% in the moisture removal rate. The method developed here can be used

in the quick prediction of the dehumidiﬁer performance. The exit parameters from the dehumidiﬁer are evaluated under the effects of variables such as air temperature and humidity, desiccant

temperature and concentration, and air to desiccant ﬂow rates. The results show that hot humid

air and desiccant concentration have the greatest impact on the performance of the dehumidiﬁer. The moisture removal rate is decreased with increasing both air inlet temperature and desiccant temperature while increases with increasing air to solution mass ratio, inlet desiccant

concentration, and inlet air humidity ratio.

ª 2013 Cairo University. Production and hosting by Elsevier B.V. All rights reserved.

Introduction

Ongoing increase in the air-conditioning load which is the sum

of the sensible and latent load represents 20–40% of the overall

energy consumption in a building [1]. Dehumidiﬁcation

* Tel.: +20 1005852335.

E-mail address: mahgoub.m@gmail.com

Peer review under responsibility of Cairo University.

Production and hosting by Elsevier

handles the latent load, while sensible cooling handles other

load portion. Traditional vapor compression equipment

overcools air-stream to provide cooling and dehumidiﬁcation.

Air-conditioning operates at a temperature colder than the

supply air dew-point temperature, so the supply air needs

reheating before entering the space to ensure indoor air

quality. Liquid desiccant dehumidiﬁer is used as an alternative

to the conventional air dehumidiﬁcation systems. An energy

savings, relative to conventional vapor compression systems,

of up to 40% can be achieved by using a desiccant assisted

air-conditioning system [2]. One-dimensional differential heat

and mass transfer models are well established and were

frequently used to study the performances of packed bed

dehumidiﬁers and regenerators. A theoretical model for a test

2090-1232 ª 2013 Cairo University. Production and hosting by Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.jare.2013.02.002

176

M.M. Bassuoni

Nomenclature

Cp

h

m_

P

T

X

y

speciﬁc heat at constant pressure, kJ/kg K

enthalpy, kJ/kg

mass ﬂow rate, kg/s

pressure, Pa

temperature, °C

desiccant solution concentration, kgd/kgs

air humidity ratio, kgv/kgda

Subscripts

da

dry air

a

air

column with LiBr solutions was developed by Factor and

Grossman [3]. The interface temperature and concentration

were assumed to be the bulk liquid temperature and concentration. Overall, heat and mass transfer coefﬁcients were utilized.

The model was validated with the experimental results. For

CaCl2, LiCl and cost effective liquid desiccant solutions

(CELD), the individual phase heat and mass transfer coefﬁcients were calculated and correlated for various packing materials [4,5]. Analytical expressions of the air and desiccant

parameters in the counter ﬂow dehumidiﬁer are provided by

Stevens et al. [6]. Within the model, the analytical solution of

the air enthalpy and liquid desiccant equivalent enthalpy,

which expressed the capability of the combined heat and mass

transfer process, is ﬁrst calculated. Then, the solutions of the

air humidity ratio and desiccant equivalent humidity ratio,

which expresses the capability of moisture transfer, are given.

Finally, the air and liquid desiccant temperature can be calculated according to the above enthalpy and humidity ratio calculated result. A method for ﬁnding the analytical solution of

the coupled heat and mass transfer performance for the dehumidiﬁer and regenerator was reported before [7,8]. Analytical

solutions of the air enthalpy and desiccant equivalent enthalpy

ﬁeld within the cross-ﬂow dehumidiﬁer/regenerator were given

[9,10], where the air and desiccant are not mixed breadthwise

(which means the transfer processes of the air and desiccant

are both two dimensional). The enthalpy ﬁeld gained from

the analytical solutions compares well with numerical solutions, and the analytical enthalpy efﬁciency compares well with

experimental results of the cross-ﬂow dehumidiﬁer.

Researchers [11–13] have developed mathematical models

of the coupled heat and mass transfer processes in the dehumidiﬁer or regenerator, and most of the models were solved

numerically. In Liu et al. [14], an experimental study of the

performance of the cross-ﬂow dehumidiﬁer was done, which

has been less studied than the counter ﬂow dehumidiﬁer,

although it is more applicable in practice. The moisture removal rate and dehumidiﬁer effectiveness were adopted as

the dehumidiﬁer performance indices. The effects of the dehumidiﬁer inlet parameters on the two indices were investigated.

Correlations have been proposed to predict the cross-ﬂow

dehumidiﬁer performance, which give results in good agreement with the present experimental ﬁndings. The results from

studying the performance of a counter ﬂow liquid desiccant

dehumidiﬁer were presented by Koronaki et al. [15]. A heat

and mass transfer theoretical model of an adiabatic packed

cond

d

eq

s

v

1

2

condensed

desiccant

equilibrium

desiccant solution

vapor

inlet

exit

Greek symbols

e

effectiveness

column has been developed, based on the Runge–Kutta ﬁxed

step method, to predict the performance of the device under

various operating conditions. Good agreement was found between experimental tests and the theoretical model. Davoud

and Meysam [16] presented a new analytical solution of heat

and mass transfer processes in a packed bed liquid desiccant

dehumidiﬁer. They results revealed that design variables such

as desiccant concentration, desiccant temperature, air ﬂow

rate, and air humidity ratio have the greatest impact on the

performance of the dehumidiﬁer. The liquid ﬂow rate and

the air temperature have not a signiﬁcant effect. Furthermore,

the effects of air and liquid desiccant ﬂow rate have been reported on the humidity effectiveness of the column.

Heat and mass transfer coefﬁcients were used to numerically solve most models in the literature. This paper proposed

a simple analytical model of the bulk heat and mass transfer

processes in a cross-ﬂow liquid desiccant air dehumidiﬁer.

An empirical correlation for calculating the dehumidiﬁer effectiveness introduced by Moon et al. [17] is used to perform the

analytical solution of the presented model with acceptable

accuracy. Comprehensively, this model is used for studying

the effect of operating parameters on the whole dehumidiﬁer

performance. The analytical solution shows good accuracy

when compared with reliable experimental data available in

the literature.

System description

Based on energy and mass laws of conservations, the proposed

analytical model has been developed as a tool for evaluating

the performance of a cross-ﬂow liquid desiccant air dehumidiﬁer. This model describes rationally the bulk coupled heat and

mass transfer processes taking place inside the dehumidiﬁer.

From Fig. 1, the strong desiccant solution is supplied to the

dehumidiﬁer at suitable concentration and temperature. At

the same time, process air ﬂows continuously across the dehumidiﬁer. Due to the vapor pressure difference between air and

desiccant solution, the process air is dehumidiﬁed. The dryer

the exit air is, the higher the rate of water vapor absorbed by

the strong desiccant solution which leads to weak desiccant

solution at the dehumidiﬁer exit. The following initial parameters should be assumed during calculation procedure: concentration and temperature of desiccant solution at dehumidiﬁer

inlet, mass ﬂow rate of inlet desiccant, humidity ratio, temperature, and mass ﬂow rate of inlet air.

Liquid desiccant cross ﬂow air dehumidiﬁer

177

where Cps is the speciﬁc heat of CaCl2 solution at constant

pressure in J/kgt°C, and it can be calculated in terms of its desiccant solution concentration X in kgd/kgs and temperature Ts

in °C from:

Desiccant solution inlet

ms1, Ts1, X1

Process air inlet

ma, ha1, ya1

Process air exit

ma, ha2, ya2

Cps ¼ 4027 þ 1:859Ts À 5354X þ 3240X2

ð4Þ

Mass balance equation for the desiccant solution

Since the mass of the desiccant material is constant during the

absorption process, the following equation can be written as:

Desiccant solution exit

ms2, Ts2, X2

m_ s1 X1 ¼ m_ s2 X2

Fig. 1 Control volume of a cross-ﬂow liquid desiccant air

dehumidiﬁer.

Mathematical model

A simple analytical method based on the nominal effectiveness

values of a cross-ﬂow liquid desiccant air dehumidiﬁer is introduced in this investigation. The schematic diagram of the control volume of the desiccant dehumidiﬁer is shown in Fig. 1. In

order to simplify the complexity of the governing equations,

the following assumptions are used in the calculations based

on the available heat and mass transfer models: adiabatic

cross-ﬂow air dehumidiﬁer, steady-state operation, the dehumidiﬁer effectiveness is used as a controlling variable in the calculation procedure, equilibrium properties of air are calculated

at the same conditions of the desiccant solution in the interface

area. The desiccant solution properties at the interface area are

calculated at the average conditions across the dehumidiﬁer.

The bulk heat and mass transfer balance equations which link

air and desiccant solution properties across the dehumidiﬁer

are introduced as follows:

m_ a ðha1 À ha2 Þ ¼ m_ s ðhs2 À hs1 Þ þ m_ a ðya1 À ya2 Þhfg

ð1Þ

where m_ a is the mass ﬂow rate of air in kg/s, ha1 and ha2 are the

inlet and exit air enthalpy across the dehumidiﬁer, respectively,

in kJ/kg, hs1 and hs2 are the inlet and exit solution enthalpy

across the dehumidiﬁer, respectively, in kJ/kgs, hfg is the latent

heat of vaporization in kJ/kgv, ya1, ya2 are the inlet and exit air

humidity ratio across the dehumidiﬁer, respectively, in kgv/

kgda, m_ s is the mass ﬂow rate of desiccant solution through

the dehumidiﬁer in kg/s. The left-hand side of the above equation represents the total heat transferred to the air. On the

right-hand side, the ﬁrst term represents the heat transferred

to or from the desiccant solution, and the second term represents the heat transferred through the condensation process inside the dehumidiﬁer. The enthalpy of air (ha) can be calculated

as follows:

ha ¼ 1:005Ta þ ya ð2501 þ 1:805Ta Þ

ð2Þ

where Ta is the air temperature in °C, and ya is the air humidity

ratio in kgv/kgda.The enthalpy of CaCl2 solution is calculated

from the following equations based on the desiccant solution

temperature and concentration [18].

hs ¼ Cps Ts

where m_ s1 and m_ s2 are the inlet and exit solution mass ﬂow rate

across the dehumidiﬁer, respectively, in kg/s, and X1 and X2

are the inlet (strong) and exit (weak) concentration across

the dehumidiﬁer, respectively, in kgd/kgs.

Mass balance equation for air water vapor

The rate of water vapor condensed from the process air and

absorbed by the strong desiccant solution inside the dehumidiﬁer, referred as moisture removal rate (MRR), is given by:

m_ cond ¼ MRR ¼ m_ a ðya1 À ya2 Þ ¼ m_ a Dya

ð3Þ

ð6Þ

where m_ cond is the rate of water condensed by the dehumidiﬁer

in kg/s. The rate of water vapor condensed from the process air

is transferred to the desiccant solution by process known as

absorption. Simply, the condensation rate represents the

amount by which the desiccant solution is diluted. So, Eq.

(5) can be formulated as follows:

m_ s1 X1 ¼ ðm_ s1 þ m_ a ðya1 À ya2 ÞÞX2

ð7Þ

With little arrangements, Eq. (7) can be written as follows:

1

X1

ð1 þ mm__s1a Dya Þ

X2 ¼

Energy balance equation across the dehumidiﬁer

ð5Þ

ð8Þ

The most common performance measures for evaluating

the dehumidiﬁer potential to dehumidify the process air are

both humidity and temperature effectiveness. An empirical

correlation of the humidity effectiveness (ey) has been given

by Moon et al. [17]. Also, ey is introduced as follows:

y À ya2

ð9Þ

ey ¼ a1

ya1 À yeq

where ey is the dehumidiﬁer humidity effectiveness based on

the air humidity ratio change, and yeq is the humidity ratio

of air in equilibrium with CaCl2 solution at the interfacial area.

It is calculated from the following equation:

yeq ¼

0:622 pv

1:013 Â 105 À pv

ð10Þ

where pv is the partial vapor pressure on the desiccant solution

surface in Pa. Also, the dehumidiﬁer thermal effectiveness (eT)

based on air temperature change across the dehumidiﬁer is given as follows:

eT ¼

Ta1 À Ta2

Ta1 À Teq

ð11Þ

where Ta1 and Ta2 are the inlet and exit air temperature across

the dehumidiﬁer, respectively, in °C and Teq is the temperature

178

M.M. Bassuoni

Table 1

Constants and operating range of Eq. (12).

Equation constants

Operating range

ao = 10.0624, a1 = 4.4674, bo = 739.828, b1 = 1450.96, C = 111.96

ao = 19.786, a1 = 1.21507, bo = 4758.1735, b1 = 1492.5857, C = 273

T = 10–65 (°C); X = 0.2–0.5 (kgd/kgs)

T = 60–100 (°C); X = 0.2–0.5 (kgd/kgs)

of air which in thermal equilibrium with CaCl2 solution at the

interfacial area in °C, and it is assumed to be equal to the desiccant solution temperature Ts.

The partial vapor pressure on the surface of CaCl2 solution

(pv) in mm Hg is calculated using the correlations introduced

by Gad et al. [19]. Constants of Eq. (12) and its operating

range are shown in Table 1.

lnðpv Þ ¼ ðao þ a1 XÞ À

ðbo þ b1 XÞ

Ts þ C

ð12Þ

Results and discussion

The above mentioned analysis shows the dependence of the

absorption process, air dehumidiﬁcation, on operational

parameters such as air inlet humidity and temperature, inlet

concentration and temperature of the desiccant solution, and

air to desiccant solution mass ﬂow rates. The proposed mathematical model is constituted from coupled algebraic equations integrated with the correlation from Moon et al. [17].

A program for the analytical solution is developed using the

engineering equation solver software. The inlet parameters

for both air and desiccant solutions are introduced into the

program, and then, the exit parameters of the desiccant solution and process air are calculated.

Before evaluating the effect of various operating parameters

on the performance of the adiabatic air dehumidiﬁer, the validation of the developed analytical model should be achieved.

For this purpose, reliable experimental data from Moon et al.

[17] were selected. A plot digitizer program is used to extract

point data from Moon et al. [17]. The obtained inlet desiccant

0.001

Moon et. al. [17]

Present study

MRR, kgv/s

0.0008

0.0006

ma/ms=0.64, Ta1=30°C

ya1=0.02157 kgv/kgda,

Ts1=30°C.

0.34

0.36

After the validation of the analytical model with the experimental results, an extensive theoretical investigation was conducted to examine the effect of various operating parameters

on the adiabatic dehumidiﬁer performance. The parametric

study includes the effect of air inlet humidity ratio and temperature, air to solution mass ratio, inlet desiccant concentration,

and temperature on the exit dehumidiﬁer parameters. Table 2

provides the operating conditions considered for all cases in

the parametric analysis. The effect of each ﬁve parameter is

studied, while the other parameters are held constant.

Effect of inlet air humidity ratio

Validation of mathematical model

0.0004

0.32

concentrations from the plot digitizer are fed to the presented

model, and the results are shown in Fig. 2. According to these

results, good agreement between the experimental data of

Moon et al. [17] and the analytical results of present study is

achieved. In all cases, the most of predicted values for MRR

are higher than the experimental values, and the discrepancy

may be due to the assumptions made in the analysis. However,

the maximum deviation in MRR is +6.63% and À5.65%.

0.38

0.4

0.42

0.44

The effect of inlet air humidity ratio (ya1) on the moisture removal rate, dehumidiﬁer effectiveness (MRR, ey; respectively),

and the exit parameters from the dehumidiﬁer; air humidity ratio, air temperature, solution concentration, and solution temperature (ya2, Ta2, X2, and Ts2, respectively) is shown in Fig. 3.

As illustrated, when the inlet air humidity ratio is increased,

MRR, ya2, and Ts2 are increased, while ey, Ta2, and X2 show

no signiﬁcant effect. To a great extent, the partial vapor pressure is the governing factor of the mass transfer occurs between process air and desiccant solution. As the inlet air

humidity ratio increases, the partial vapor pressure of air also

increases which in turn enhances the difference between the

partial vapor pressure in the inlet air-stream and that on the

desiccant solution surface resulting in an increase in the moisture absorbing capacity of desiccant solution. This increase

leads to high moisture removing capacity. On the other hand,

as ya1 is increased the increase in the numerator of Eq. (9) offsets, the increase in the denominator of the same equation results in slight decrease in the dehumidiﬁer effectiveness. This in

turn increases the exit humidity ratio ya2. Increasing ya1 in turn

increases the enthalpy of air at the dehumidiﬁer inlet which

rises the temperature of the solution at the exit. When ya1 is increased from 0.016 to 0.024 kgv/kgda, MRR, ya2, and Ts2 are

increased by 67.29%, 39.22%, and 13.39%, respectively.

Effect of inlet air temperature

X1, kgd/kgs

Fig. 2 Comparison of MRR at different X1 between present

study and Moon et al. [17].

Fig. 4 shows the effect of inlet air temperature (Ta1) on the

MRR, ey and the exit parameters from the dehumidiﬁer; ya2,

Ta2, X2, and Ts2. As Ta1 is increased, both MRR and ey are

Liquid desiccant cross ﬂow air dehumidiﬁer

Operating conditions for the cases considered in the parametric analysis.

Cases

Ta1 (°C)

X1 (kgd/kgs)

Ts1 (°C)

0.64

1

1

1

1

0.25–2

0.02157

0.016–0.026

0.018

0.018

0.018

0.018

30

40

26–40

40

40

40

0.33–0.43

0.43

0.43

0.33–0.43

0.43

0.43

30

20

20

20

26–36

20

38

0.3

34

32

Ta2 &T s2 , oC

36

0.016

0.012

30

εy &

0.4

MRR

R

ya2

Ta2

Ts2

X2

Ey

0.02

MRR*10

MRR

10, kg v /s & ya2 , kgv /kgda

0.5

εy

& X 2 , kg d /kg s

0.6

( a/m

(m

ms=1

1, Ta11=40°°C ,T

Ts1=2

20°C

C, X1=0.43

= 3)

0.008

28

0.0

016

0.02

2

0.0

024

ya1, kgv/kgda

Fig. 3

Effect of ya1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

MRR

ya2

Ta2

Ts2

X2

Ey

0.6

0.5

0.4

MRR*10, kg v /s & y a2 , kg v /kg da

0.7

& X 2 , kg d /kg s

2

3

4

5

6

7

ya1 (kgv/kgda)

εy

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Inlet values for the parametric analysis

ma/ms

0.016

36

32

28

0.012

T a2 &T s2 , oC

Table 2

179

24

(ma/ms=1, ya1=0.018 kgv/kgda ,Ts1=20°C, X1=0.43)

0.3

0.008

24

28

32

36

40

20

Ta1, oC

Fig. 4

Effect of Ta1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

180

M.M. Bassuoni

34

MR

RR

ya2

Ta

a2

Ts

s2

X2

2

Ey

y

0.4

4

MRR*10 kg

MRR*10,

k v/s

/ & y a2 , kg

k v/kg

/k da

εy & X2, kg d/kg s

0.5

5

0.013

32

0.012

30

Ta2 &T s2 , oC

0.014

0.6

6

0.011

(ma/ms=1, ya1=00.0188 kgv/kgda

d ,

0.0

01

28

Ts1=200°C, Ta1=40°C

C)

0.3

3

0.32

0.34

0.36

6

0.38

8

0.4

4

0.42

0.4

44

X1, kgd/kgs

Fig. 5

Effect of X1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

decreased, but Ta2, ya2, and Ts2 are increased, while X2 has no

signiﬁcant change. This may be explained as follows: as the inlet process air temperature is increased, the temperature of the

desiccant solution inside the dehumidiﬁer is increased which in

turn increases Ts2, Ta2 and the partial vapor pressure on the

desiccant surface. When the desiccant surface vapor pressure

increases, the potential of the absorption process is decreased

causing air to become more humid (i.e., low Dya) and in turn

low MRR. On the other hand, the reduction in Dya is greater

than the decrease in (ya1 À yeq) which leads to low ey. When

Ta1 is increased from 26 °C to 40 °C, both MRR and ey are decreased by about 11.6% and 11.8%, respectively, but Ta2, ya2,

and Ts2 are increased by a percentage of 31.58%, 9.5%, and

6.8%, respectively.

Effect of inlet desiccant concentration

Fig. 5 shows the effect of inlet desiccant concentration (X1) on

the MRR, ey and the exit parameters from the dehumidiﬁer;

ya2, Ta2, X2, and Ts2. When X1 is increased, MRR, Ts2, and

X2 are increased, but the dehumidiﬁer effectiveness and Ta2

are slightly changed. When X1 increases, vapor pressure on

the desiccant surface is reduced leading to low ya2 which in

turn increases MRR. As shown from Table 2, the inlet air temperature is higher than the inlet temperature of the desiccant

solution resulting in high Ts2. Both ya2 and yeq are decreased

but at different rates which means that the numerator of Eq.

(9) is to some extent smaller than its denominator; so, ey is

slightly reduced. Increasing X1 from 0.33 to 0.43, MRR, Ts2,

0.016

0.014

44

40

0.012

36

0.01

Ta2 &Ts2, o C

0.6

MRR*10, kgv /s & ya2, kgv /kgda

εy &X2, kgd/kgs

0.8

MRR

ya2

Ta2

Ts2

X2

Ey

(ma/ms=1, ya1=0.018 kgv/kgda,

X1=0.43, Ta1=40°C)

0.008

32

0.4

0.006

28

32

36

Ts1, oC

Fig. 6

Effect of Ts1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

Liquid desiccant cross ﬂow air dehumidiﬁer

181

0

0.5

MRR

R

ya2

Ta2

Ts2

X2

Ey

0.02

40

0

Ta2 &Ts2, oC

εy &X2, kgd/kgs

0

0.6

50

0

10, kgv/s & yaa22, kgv/kgda

MRR*10,

MRR

0

0.7

0.01

30

0

0

0.4

(X1=0.443, ya1=00.018 kgv/kgdaa, Ts1=20°°C, Ta1=440°C)

0

20

0

0

0.5

5

1

1.5

2

ma /m

ms , kga /kgs

Fig. 7

Effect of ma/ms on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

and X2 are increased by 39.13%, 10.33%, and 30%, respectively. On the other hand, both ya2 and ey are decreased by a

percentage of 15.64% and 1.66%, respectively.

Effect of inlet desiccant temperature

Fig. 6 shows the effect of inlet desiccant temperature (Ts1) on

the MRR, ey and the exit parameters from the dehumidiﬁer;

ya2, Ta2, X2, and Ts2. When Ts1 is increased, ya2, Ta2, ey, and

Ts2 are increased, however, the MRR is decreased and X2 is

unaffected. Increasing Ts1 increases the vapor pressure on

the desiccant surface which in turn decreases the moisture

absorption from the process air, and hence, MRR is decreased

but ya2 increases. When Ts1 increases, the difference between

(ya1 À ya2) is more than that of (ya1 À yeq) which in turn increases ey (see Eq. (9)). Increasing Ts1 from 26 °C to 36 °C results in increasing ya2, Ta2, ey, and Ts2 by 28.61%, 16.92%,

22.88%, and 12.2%, respectively, but MRR is decreased by

about 48.92%.

Conclusions

Air dehumidiﬁcation by using CaCl2 desiccant solution in a

cross-ﬂow liquid desiccant dehumidiﬁer is studied by proposing a simple analytical model. The developed analytical model

shows an excellent agreement with the available experimental

data from Moon et al. [17]. Thus, for a detailed study of the

absorption process, this model gives accurate performance prediction, minimizing the use of calculation and assumptions.

Operating variables found to have the greatest impact on the

dehumidiﬁer performance. The following conclusions from

the analytical results can be summarized: The moisture removal rate is decreased with increasing both air inlet temperature and desiccant temperature while increases with increasing

ma/ms, X1, and ya1. The dehumidiﬁer effectiveness increases

with the increase of Ts1, while it decreases with the increase

of Ta1 and ma/ms. Increasing Ta1, Ts1, and ya1 results in higher

ya2, however, low exit humidity ratio is obtained at lower inlet

desiccant concentration. The exit desiccant solution concentration remains unaffected by changing different operating parameters except X1.

Effect of air to solution mass ratio

Conﬂict of interest

Fig. 7 shows the effect of air to solution mass ratio (ma/ms) on

the MRR, ey and the exit parameters from the dehumidiﬁer;

ya2, Ta2, X2, and Ts2. When ma/ms is increased, both MRR

and Ts2 are increased, but ey is decreased, while Ta2 and ya2

are slightly increased, however, X2 is slightly decreased. The

potential capacity of the desiccant solution to carry over moisture from the process air is reduced by increasing ma/ms results

in higher outlet ya2 which in turn reduces ey. Increasing the

mass ﬂow rate of air leads to high heat capacity of air compared to solution which offset the temperature increase in

air-stream. Increasing ma/ms by 400% results in an increase

in both MRR and Ts2 by 611% and 81.6%, respectively. On

the other hand, ey is decreased by about 11.1%.

The author has declared no conﬂict of interest.

References

[1] Li Z, Liu XH, Jiang Y, Chen XY. New type of fresh air

processor with liquid desiccant total heat recovery. Energy Build

2005;37:587–93.

[2] Potnis SV, Lenz TG. Dimensionless mass-transfer correlations

for packed-bed liquid-desiccant contactors. Ind Eng Chem Res

1996;35(11):4185–93.

[3] Factor HM, Grossman G. A packed bed dehumidiﬁer/

regenerator for solar air conditioning with liquid desiccants.

Solar Energy 1980;24:541–50.

182

[4] Gandhidasan P, Kettleborough CF, Ullah MR. Calculation of heat

and mass transfer coefﬁcients in a packed tower operating with a

desiccant-air contact system. Solar Energy 1986;108(2):123–8.

[5] Ertas A, Anderson EE, Kavasogullari S. Comparison of mass

and heat-transfer coefﬁcients of liquid-desiccant mixtures in a

packed-column. J Energy Resour-ASME 1991;113(1):1–6.

[6] Stevens DI, Braun JE, Klein SA. An effectiveness model of

liquid desiccant system heat/mass exchangers. Solar Energy

1989;42(6):449–55.

[7] Ren CQ, Jiang Y, Zhang YP. Simpliﬁed analysis of coupled heat

and mass transfer processes in packed bed liquid desiccant-air

contact system. Solar Energy 2006;80(1):121–31.

[8] Lu ZF, Chen PL, Zhang X. Approximate analytical solution of

heat and mass transfer processes in packed-type cross-ﬂow

liquid desiccant system and its experimental veriﬁcation. J

Tongji Univ. 2001;29(2):149–53.

[9] Liu XH, Jiang Y, Qu KY. Analytical solution of combined heat

and mass transfer processes of cross-ﬂow dehumidiﬁer using

liquid desiccant. Taiyangneng Xuebao/Acta Energy Solar Sin.

2006;27(8):774–81.

[10] Liu XH, Jiang Y, Xia J, Chang X. Analytical solutions of coupled heat

and mass transfer processes in liquid desiccant air dehumidiﬁer/

regenerator. Energy Convers Manage 2007;48:2221–32.

[11] Dai YJ, Zhang HF. Numerical simulation and theoretical

analysis of heat and mass transfer in a cross ﬂow liquid

desiccant air dehumidiﬁer packed with honeycomb paper.

Energy Convers Manage 2004;45(9–10):1343–56.

M.M. Bassuoni

[12] Khan AY, Sulsona FJ. Modeling and parametric analysis of

heat and mass transfer performance of refrigerant cooled

liquid desiccant absorbers. Int J Energy Res 1998;22(9):

813–32.

[13] Liu XH, Jiang Y, Qu KY. Heat and mass transfer model of

cross-ﬂow liquid desiccant air dehumidiﬁer/regenerator. Energy

Convers Manage 2007;48(2):46–54.

[14] Liu XH, Zhang Y, Qu KY. Experimental study on mass transfer

performance of cross-ﬂow dehumidiﬁer using liquid desiccant.

Energy Convers Manage 2006;47(15–16):2682–92.

[15] Koronaki IP, Christodoulaki RI, Papaefthimiou VD, Rogdakis

ED. Thermodynamic analysis of a counter ﬂow adiabatic

dehumidiﬁer with different liquid desiccant materials. Appl

Therm Eng 2013;50(1):361–73.

[16] Davoud B, Meysam S. An analytical solution for air

dehumidiﬁcation by liquid desiccant in a packed column. Int

Commun Heat Mass 2009;36:969–77.

[17] Moon CG, Bansal PK, Sanjeev J. New performance data of a

cross ﬂow liquid desiccant dehumidiﬁcation system. Int J Refrig

2009;32:524–33.

[18] Adnan AK, Moustafa ME, Omar MA. Proposed energy

efﬁcient air-conditioning system using liquid desiccant. Appl

Therm Eng 1996;16(10):791–806.

[19] Gad HE, Hamed AM, El-Sharkawy II. Application of a solar

desiccant/collector system for water recovery from atmospheric

air. Renew Energy 2001;22:541–56.

Cairo University

Journal of Advanced Research

ORIGINAL ARTICLE

A simple analytical method to estimate all exit

parameters of a cross-ﬂow air dehumidiﬁer using

liquid desiccant

M.M. Bassuoni

*

Mechanical Power Engineering Department, Faculty of Engineering, Tanta University, Egypt

A R T I C L E

I N F O

Article history:

Received 16 December 2012

Received in revised form 5 February 2013

Accepted 23 February 2013

Available online 30 March 2013

Keywords:

Dehumidiﬁer

Regenerator

Liquid desiccant

Analytical solution

Structured packing bed

Desiccant cooling

A B S T R A C T

The dehumidiﬁer is a key component in liquid desiccant air-conditioning systems. Analytical

solutions have more advantages than numerical solutions in studying the dehumidiﬁer performance parameters. This paper presents the performance results of exit parameters from an analytical model of an adiabatic cross-ﬂow liquid desiccant air dehumidiﬁer. Calcium chloride is

used as desiccant material in this investigation. A program performing the analytical solution

is developed using the engineering equation solver software. Good accuracy has been found

between analytical solution and reliable experimental results with a maximum deviation of

+6.63% and À5.65% in the moisture removal rate. The method developed here can be used

in the quick prediction of the dehumidiﬁer performance. The exit parameters from the dehumidiﬁer are evaluated under the effects of variables such as air temperature and humidity, desiccant

temperature and concentration, and air to desiccant ﬂow rates. The results show that hot humid

air and desiccant concentration have the greatest impact on the performance of the dehumidiﬁer. The moisture removal rate is decreased with increasing both air inlet temperature and desiccant temperature while increases with increasing air to solution mass ratio, inlet desiccant

concentration, and inlet air humidity ratio.

ª 2013 Cairo University. Production and hosting by Elsevier B.V. All rights reserved.

Introduction

Ongoing increase in the air-conditioning load which is the sum

of the sensible and latent load represents 20–40% of the overall

energy consumption in a building [1]. Dehumidiﬁcation

* Tel.: +20 1005852335.

E-mail address: mahgoub.m@gmail.com

Peer review under responsibility of Cairo University.

Production and hosting by Elsevier

handles the latent load, while sensible cooling handles other

load portion. Traditional vapor compression equipment

overcools air-stream to provide cooling and dehumidiﬁcation.

Air-conditioning operates at a temperature colder than the

supply air dew-point temperature, so the supply air needs

reheating before entering the space to ensure indoor air

quality. Liquid desiccant dehumidiﬁer is used as an alternative

to the conventional air dehumidiﬁcation systems. An energy

savings, relative to conventional vapor compression systems,

of up to 40% can be achieved by using a desiccant assisted

air-conditioning system [2]. One-dimensional differential heat

and mass transfer models are well established and were

frequently used to study the performances of packed bed

dehumidiﬁers and regenerators. A theoretical model for a test

2090-1232 ª 2013 Cairo University. Production and hosting by Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.jare.2013.02.002

176

M.M. Bassuoni

Nomenclature

Cp

h

m_

P

T

X

y

speciﬁc heat at constant pressure, kJ/kg K

enthalpy, kJ/kg

mass ﬂow rate, kg/s

pressure, Pa

temperature, °C

desiccant solution concentration, kgd/kgs

air humidity ratio, kgv/kgda

Subscripts

da

dry air

a

air

column with LiBr solutions was developed by Factor and

Grossman [3]. The interface temperature and concentration

were assumed to be the bulk liquid temperature and concentration. Overall, heat and mass transfer coefﬁcients were utilized.

The model was validated with the experimental results. For

CaCl2, LiCl and cost effective liquid desiccant solutions

(CELD), the individual phase heat and mass transfer coefﬁcients were calculated and correlated for various packing materials [4,5]. Analytical expressions of the air and desiccant

parameters in the counter ﬂow dehumidiﬁer are provided by

Stevens et al. [6]. Within the model, the analytical solution of

the air enthalpy and liquid desiccant equivalent enthalpy,

which expressed the capability of the combined heat and mass

transfer process, is ﬁrst calculated. Then, the solutions of the

air humidity ratio and desiccant equivalent humidity ratio,

which expresses the capability of moisture transfer, are given.

Finally, the air and liquid desiccant temperature can be calculated according to the above enthalpy and humidity ratio calculated result. A method for ﬁnding the analytical solution of

the coupled heat and mass transfer performance for the dehumidiﬁer and regenerator was reported before [7,8]. Analytical

solutions of the air enthalpy and desiccant equivalent enthalpy

ﬁeld within the cross-ﬂow dehumidiﬁer/regenerator were given

[9,10], where the air and desiccant are not mixed breadthwise

(which means the transfer processes of the air and desiccant

are both two dimensional). The enthalpy ﬁeld gained from

the analytical solutions compares well with numerical solutions, and the analytical enthalpy efﬁciency compares well with

experimental results of the cross-ﬂow dehumidiﬁer.

Researchers [11–13] have developed mathematical models

of the coupled heat and mass transfer processes in the dehumidiﬁer or regenerator, and most of the models were solved

numerically. In Liu et al. [14], an experimental study of the

performance of the cross-ﬂow dehumidiﬁer was done, which

has been less studied than the counter ﬂow dehumidiﬁer,

although it is more applicable in practice. The moisture removal rate and dehumidiﬁer effectiveness were adopted as

the dehumidiﬁer performance indices. The effects of the dehumidiﬁer inlet parameters on the two indices were investigated.

Correlations have been proposed to predict the cross-ﬂow

dehumidiﬁer performance, which give results in good agreement with the present experimental ﬁndings. The results from

studying the performance of a counter ﬂow liquid desiccant

dehumidiﬁer were presented by Koronaki et al. [15]. A heat

and mass transfer theoretical model of an adiabatic packed

cond

d

eq

s

v

1

2

condensed

desiccant

equilibrium

desiccant solution

vapor

inlet

exit

Greek symbols

e

effectiveness

column has been developed, based on the Runge–Kutta ﬁxed

step method, to predict the performance of the device under

various operating conditions. Good agreement was found between experimental tests and the theoretical model. Davoud

and Meysam [16] presented a new analytical solution of heat

and mass transfer processes in a packed bed liquid desiccant

dehumidiﬁer. They results revealed that design variables such

as desiccant concentration, desiccant temperature, air ﬂow

rate, and air humidity ratio have the greatest impact on the

performance of the dehumidiﬁer. The liquid ﬂow rate and

the air temperature have not a signiﬁcant effect. Furthermore,

the effects of air and liquid desiccant ﬂow rate have been reported on the humidity effectiveness of the column.

Heat and mass transfer coefﬁcients were used to numerically solve most models in the literature. This paper proposed

a simple analytical model of the bulk heat and mass transfer

processes in a cross-ﬂow liquid desiccant air dehumidiﬁer.

An empirical correlation for calculating the dehumidiﬁer effectiveness introduced by Moon et al. [17] is used to perform the

analytical solution of the presented model with acceptable

accuracy. Comprehensively, this model is used for studying

the effect of operating parameters on the whole dehumidiﬁer

performance. The analytical solution shows good accuracy

when compared with reliable experimental data available in

the literature.

System description

Based on energy and mass laws of conservations, the proposed

analytical model has been developed as a tool for evaluating

the performance of a cross-ﬂow liquid desiccant air dehumidiﬁer. This model describes rationally the bulk coupled heat and

mass transfer processes taking place inside the dehumidiﬁer.

From Fig. 1, the strong desiccant solution is supplied to the

dehumidiﬁer at suitable concentration and temperature. At

the same time, process air ﬂows continuously across the dehumidiﬁer. Due to the vapor pressure difference between air and

desiccant solution, the process air is dehumidiﬁed. The dryer

the exit air is, the higher the rate of water vapor absorbed by

the strong desiccant solution which leads to weak desiccant

solution at the dehumidiﬁer exit. The following initial parameters should be assumed during calculation procedure: concentration and temperature of desiccant solution at dehumidiﬁer

inlet, mass ﬂow rate of inlet desiccant, humidity ratio, temperature, and mass ﬂow rate of inlet air.

Liquid desiccant cross ﬂow air dehumidiﬁer

177

where Cps is the speciﬁc heat of CaCl2 solution at constant

pressure in J/kgt°C, and it can be calculated in terms of its desiccant solution concentration X in kgd/kgs and temperature Ts

in °C from:

Desiccant solution inlet

ms1, Ts1, X1

Process air inlet

ma, ha1, ya1

Process air exit

ma, ha2, ya2

Cps ¼ 4027 þ 1:859Ts À 5354X þ 3240X2

ð4Þ

Mass balance equation for the desiccant solution

Since the mass of the desiccant material is constant during the

absorption process, the following equation can be written as:

Desiccant solution exit

ms2, Ts2, X2

m_ s1 X1 ¼ m_ s2 X2

Fig. 1 Control volume of a cross-ﬂow liquid desiccant air

dehumidiﬁer.

Mathematical model

A simple analytical method based on the nominal effectiveness

values of a cross-ﬂow liquid desiccant air dehumidiﬁer is introduced in this investigation. The schematic diagram of the control volume of the desiccant dehumidiﬁer is shown in Fig. 1. In

order to simplify the complexity of the governing equations,

the following assumptions are used in the calculations based

on the available heat and mass transfer models: adiabatic

cross-ﬂow air dehumidiﬁer, steady-state operation, the dehumidiﬁer effectiveness is used as a controlling variable in the calculation procedure, equilibrium properties of air are calculated

at the same conditions of the desiccant solution in the interface

area. The desiccant solution properties at the interface area are

calculated at the average conditions across the dehumidiﬁer.

The bulk heat and mass transfer balance equations which link

air and desiccant solution properties across the dehumidiﬁer

are introduced as follows:

m_ a ðha1 À ha2 Þ ¼ m_ s ðhs2 À hs1 Þ þ m_ a ðya1 À ya2 Þhfg

ð1Þ

where m_ a is the mass ﬂow rate of air in kg/s, ha1 and ha2 are the

inlet and exit air enthalpy across the dehumidiﬁer, respectively,

in kJ/kg, hs1 and hs2 are the inlet and exit solution enthalpy

across the dehumidiﬁer, respectively, in kJ/kgs, hfg is the latent

heat of vaporization in kJ/kgv, ya1, ya2 are the inlet and exit air

humidity ratio across the dehumidiﬁer, respectively, in kgv/

kgda, m_ s is the mass ﬂow rate of desiccant solution through

the dehumidiﬁer in kg/s. The left-hand side of the above equation represents the total heat transferred to the air. On the

right-hand side, the ﬁrst term represents the heat transferred

to or from the desiccant solution, and the second term represents the heat transferred through the condensation process inside the dehumidiﬁer. The enthalpy of air (ha) can be calculated

as follows:

ha ¼ 1:005Ta þ ya ð2501 þ 1:805Ta Þ

ð2Þ

where Ta is the air temperature in °C, and ya is the air humidity

ratio in kgv/kgda.The enthalpy of CaCl2 solution is calculated

from the following equations based on the desiccant solution

temperature and concentration [18].

hs ¼ Cps Ts

where m_ s1 and m_ s2 are the inlet and exit solution mass ﬂow rate

across the dehumidiﬁer, respectively, in kg/s, and X1 and X2

are the inlet (strong) and exit (weak) concentration across

the dehumidiﬁer, respectively, in kgd/kgs.

Mass balance equation for air water vapor

The rate of water vapor condensed from the process air and

absorbed by the strong desiccant solution inside the dehumidiﬁer, referred as moisture removal rate (MRR), is given by:

m_ cond ¼ MRR ¼ m_ a ðya1 À ya2 Þ ¼ m_ a Dya

ð3Þ

ð6Þ

where m_ cond is the rate of water condensed by the dehumidiﬁer

in kg/s. The rate of water vapor condensed from the process air

is transferred to the desiccant solution by process known as

absorption. Simply, the condensation rate represents the

amount by which the desiccant solution is diluted. So, Eq.

(5) can be formulated as follows:

m_ s1 X1 ¼ ðm_ s1 þ m_ a ðya1 À ya2 ÞÞX2

ð7Þ

With little arrangements, Eq. (7) can be written as follows:

1

X1

ð1 þ mm__s1a Dya Þ

X2 ¼

Energy balance equation across the dehumidiﬁer

ð5Þ

ð8Þ

The most common performance measures for evaluating

the dehumidiﬁer potential to dehumidify the process air are

both humidity and temperature effectiveness. An empirical

correlation of the humidity effectiveness (ey) has been given

by Moon et al. [17]. Also, ey is introduced as follows:

y À ya2

ð9Þ

ey ¼ a1

ya1 À yeq

where ey is the dehumidiﬁer humidity effectiveness based on

the air humidity ratio change, and yeq is the humidity ratio

of air in equilibrium with CaCl2 solution at the interfacial area.

It is calculated from the following equation:

yeq ¼

0:622 pv

1:013 Â 105 À pv

ð10Þ

where pv is the partial vapor pressure on the desiccant solution

surface in Pa. Also, the dehumidiﬁer thermal effectiveness (eT)

based on air temperature change across the dehumidiﬁer is given as follows:

eT ¼

Ta1 À Ta2

Ta1 À Teq

ð11Þ

where Ta1 and Ta2 are the inlet and exit air temperature across

the dehumidiﬁer, respectively, in °C and Teq is the temperature

178

M.M. Bassuoni

Table 1

Constants and operating range of Eq. (12).

Equation constants

Operating range

ao = 10.0624, a1 = 4.4674, bo = 739.828, b1 = 1450.96, C = 111.96

ao = 19.786, a1 = 1.21507, bo = 4758.1735, b1 = 1492.5857, C = 273

T = 10–65 (°C); X = 0.2–0.5 (kgd/kgs)

T = 60–100 (°C); X = 0.2–0.5 (kgd/kgs)

of air which in thermal equilibrium with CaCl2 solution at the

interfacial area in °C, and it is assumed to be equal to the desiccant solution temperature Ts.

The partial vapor pressure on the surface of CaCl2 solution

(pv) in mm Hg is calculated using the correlations introduced

by Gad et al. [19]. Constants of Eq. (12) and its operating

range are shown in Table 1.

lnðpv Þ ¼ ðao þ a1 XÞ À

ðbo þ b1 XÞ

Ts þ C

ð12Þ

Results and discussion

The above mentioned analysis shows the dependence of the

absorption process, air dehumidiﬁcation, on operational

parameters such as air inlet humidity and temperature, inlet

concentration and temperature of the desiccant solution, and

air to desiccant solution mass ﬂow rates. The proposed mathematical model is constituted from coupled algebraic equations integrated with the correlation from Moon et al. [17].

A program for the analytical solution is developed using the

engineering equation solver software. The inlet parameters

for both air and desiccant solutions are introduced into the

program, and then, the exit parameters of the desiccant solution and process air are calculated.

Before evaluating the effect of various operating parameters

on the performance of the adiabatic air dehumidiﬁer, the validation of the developed analytical model should be achieved.

For this purpose, reliable experimental data from Moon et al.

[17] were selected. A plot digitizer program is used to extract

point data from Moon et al. [17]. The obtained inlet desiccant

0.001

Moon et. al. [17]

Present study

MRR, kgv/s

0.0008

0.0006

ma/ms=0.64, Ta1=30°C

ya1=0.02157 kgv/kgda,

Ts1=30°C.

0.34

0.36

After the validation of the analytical model with the experimental results, an extensive theoretical investigation was conducted to examine the effect of various operating parameters

on the adiabatic dehumidiﬁer performance. The parametric

study includes the effect of air inlet humidity ratio and temperature, air to solution mass ratio, inlet desiccant concentration,

and temperature on the exit dehumidiﬁer parameters. Table 2

provides the operating conditions considered for all cases in

the parametric analysis. The effect of each ﬁve parameter is

studied, while the other parameters are held constant.

Effect of inlet air humidity ratio

Validation of mathematical model

0.0004

0.32

concentrations from the plot digitizer are fed to the presented

model, and the results are shown in Fig. 2. According to these

results, good agreement between the experimental data of

Moon et al. [17] and the analytical results of present study is

achieved. In all cases, the most of predicted values for MRR

are higher than the experimental values, and the discrepancy

may be due to the assumptions made in the analysis. However,

the maximum deviation in MRR is +6.63% and À5.65%.

0.38

0.4

0.42

0.44

The effect of inlet air humidity ratio (ya1) on the moisture removal rate, dehumidiﬁer effectiveness (MRR, ey; respectively),

and the exit parameters from the dehumidiﬁer; air humidity ratio, air temperature, solution concentration, and solution temperature (ya2, Ta2, X2, and Ts2, respectively) is shown in Fig. 3.

As illustrated, when the inlet air humidity ratio is increased,

MRR, ya2, and Ts2 are increased, while ey, Ta2, and X2 show

no signiﬁcant effect. To a great extent, the partial vapor pressure is the governing factor of the mass transfer occurs between process air and desiccant solution. As the inlet air

humidity ratio increases, the partial vapor pressure of air also

increases which in turn enhances the difference between the

partial vapor pressure in the inlet air-stream and that on the

desiccant solution surface resulting in an increase in the moisture absorbing capacity of desiccant solution. This increase

leads to high moisture removing capacity. On the other hand,

as ya1 is increased the increase in the numerator of Eq. (9) offsets, the increase in the denominator of the same equation results in slight decrease in the dehumidiﬁer effectiveness. This in

turn increases the exit humidity ratio ya2. Increasing ya1 in turn

increases the enthalpy of air at the dehumidiﬁer inlet which

rises the temperature of the solution at the exit. When ya1 is increased from 0.016 to 0.024 kgv/kgda, MRR, ya2, and Ts2 are

increased by 67.29%, 39.22%, and 13.39%, respectively.

Effect of inlet air temperature

X1, kgd/kgs

Fig. 2 Comparison of MRR at different X1 between present

study and Moon et al. [17].

Fig. 4 shows the effect of inlet air temperature (Ta1) on the

MRR, ey and the exit parameters from the dehumidiﬁer; ya2,

Ta2, X2, and Ts2. As Ta1 is increased, both MRR and ey are

Liquid desiccant cross ﬂow air dehumidiﬁer

Operating conditions for the cases considered in the parametric analysis.

Cases

Ta1 (°C)

X1 (kgd/kgs)

Ts1 (°C)

0.64

1

1

1

1

0.25–2

0.02157

0.016–0.026

0.018

0.018

0.018

0.018

30

40

26–40

40

40

40

0.33–0.43

0.43

0.43

0.33–0.43

0.43

0.43

30

20

20

20

26–36

20

38

0.3

34

32

Ta2 &T s2 , oC

36

0.016

0.012

30

εy &

0.4

MRR

R

ya2

Ta2

Ts2

X2

Ey

0.02

MRR*10

MRR

10, kg v /s & ya2 , kgv /kgda

0.5

εy

& X 2 , kg d /kg s

0.6

( a/m

(m

ms=1

1, Ta11=40°°C ,T

Ts1=2

20°C

C, X1=0.43

= 3)

0.008

28

0.0

016

0.02

2

0.0

024

ya1, kgv/kgda

Fig. 3

Effect of ya1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

MRR

ya2

Ta2

Ts2

X2

Ey

0.6

0.5

0.4

MRR*10, kg v /s & y a2 , kg v /kg da

0.7

& X 2 , kg d /kg s

2

3

4

5

6

7

ya1 (kgv/kgda)

εy

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Inlet values for the parametric analysis

ma/ms

0.016

36

32

28

0.012

T a2 &T s2 , oC

Table 2

179

24

(ma/ms=1, ya1=0.018 kgv/kgda ,Ts1=20°C, X1=0.43)

0.3

0.008

24

28

32

36

40

20

Ta1, oC

Fig. 4

Effect of Ta1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

180

M.M. Bassuoni

34

MR

RR

ya2

Ta

a2

Ts

s2

X2

2

Ey

y

0.4

4

MRR*10 kg

MRR*10,

k v/s

/ & y a2 , kg

k v/kg

/k da

εy & X2, kg d/kg s

0.5

5

0.013

32

0.012

30

Ta2 &T s2 , oC

0.014

0.6

6

0.011

(ma/ms=1, ya1=00.0188 kgv/kgda

d ,

0.0

01

28

Ts1=200°C, Ta1=40°C

C)

0.3

3

0.32

0.34

0.36

6

0.38

8

0.4

4

0.42

0.4

44

X1, kgd/kgs

Fig. 5

Effect of X1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

decreased, but Ta2, ya2, and Ts2 are increased, while X2 has no

signiﬁcant change. This may be explained as follows: as the inlet process air temperature is increased, the temperature of the

desiccant solution inside the dehumidiﬁer is increased which in

turn increases Ts2, Ta2 and the partial vapor pressure on the

desiccant surface. When the desiccant surface vapor pressure

increases, the potential of the absorption process is decreased

causing air to become more humid (i.e., low Dya) and in turn

low MRR. On the other hand, the reduction in Dya is greater

than the decrease in (ya1 À yeq) which leads to low ey. When

Ta1 is increased from 26 °C to 40 °C, both MRR and ey are decreased by about 11.6% and 11.8%, respectively, but Ta2, ya2,

and Ts2 are increased by a percentage of 31.58%, 9.5%, and

6.8%, respectively.

Effect of inlet desiccant concentration

Fig. 5 shows the effect of inlet desiccant concentration (X1) on

the MRR, ey and the exit parameters from the dehumidiﬁer;

ya2, Ta2, X2, and Ts2. When X1 is increased, MRR, Ts2, and

X2 are increased, but the dehumidiﬁer effectiveness and Ta2

are slightly changed. When X1 increases, vapor pressure on

the desiccant surface is reduced leading to low ya2 which in

turn increases MRR. As shown from Table 2, the inlet air temperature is higher than the inlet temperature of the desiccant

solution resulting in high Ts2. Both ya2 and yeq are decreased

but at different rates which means that the numerator of Eq.

(9) is to some extent smaller than its denominator; so, ey is

slightly reduced. Increasing X1 from 0.33 to 0.43, MRR, Ts2,

0.016

0.014

44

40

0.012

36

0.01

Ta2 &Ts2, o C

0.6

MRR*10, kgv /s & ya2, kgv /kgda

εy &X2, kgd/kgs

0.8

MRR

ya2

Ta2

Ts2

X2

Ey

(ma/ms=1, ya1=0.018 kgv/kgda,

X1=0.43, Ta1=40°C)

0.008

32

0.4

0.006

28

32

36

Ts1, oC

Fig. 6

Effect of Ts1 on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

Liquid desiccant cross ﬂow air dehumidiﬁer

181

0

0.5

MRR

R

ya2

Ta2

Ts2

X2

Ey

0.02

40

0

Ta2 &Ts2, oC

εy &X2, kgd/kgs

0

0.6

50

0

10, kgv/s & yaa22, kgv/kgda

MRR*10,

MRR

0

0.7

0.01

30

0

0

0.4

(X1=0.443, ya1=00.018 kgv/kgdaa, Ts1=20°°C, Ta1=440°C)

0

20

0

0

0.5

5

1

1.5

2

ma /m

ms , kga /kgs

Fig. 7

Effect of ma/ms on dehumidiﬁer parameters (MRR, ey, ya2, Ta2, Ts2, X2).

and X2 are increased by 39.13%, 10.33%, and 30%, respectively. On the other hand, both ya2 and ey are decreased by a

percentage of 15.64% and 1.66%, respectively.

Effect of inlet desiccant temperature

Fig. 6 shows the effect of inlet desiccant temperature (Ts1) on

the MRR, ey and the exit parameters from the dehumidiﬁer;

ya2, Ta2, X2, and Ts2. When Ts1 is increased, ya2, Ta2, ey, and

Ts2 are increased, however, the MRR is decreased and X2 is

unaffected. Increasing Ts1 increases the vapor pressure on

the desiccant surface which in turn decreases the moisture

absorption from the process air, and hence, MRR is decreased

but ya2 increases. When Ts1 increases, the difference between

(ya1 À ya2) is more than that of (ya1 À yeq) which in turn increases ey (see Eq. (9)). Increasing Ts1 from 26 °C to 36 °C results in increasing ya2, Ta2, ey, and Ts2 by 28.61%, 16.92%,

22.88%, and 12.2%, respectively, but MRR is decreased by

about 48.92%.

Conclusions

Air dehumidiﬁcation by using CaCl2 desiccant solution in a

cross-ﬂow liquid desiccant dehumidiﬁer is studied by proposing a simple analytical model. The developed analytical model

shows an excellent agreement with the available experimental

data from Moon et al. [17]. Thus, for a detailed study of the

absorption process, this model gives accurate performance prediction, minimizing the use of calculation and assumptions.

Operating variables found to have the greatest impact on the

dehumidiﬁer performance. The following conclusions from

the analytical results can be summarized: The moisture removal rate is decreased with increasing both air inlet temperature and desiccant temperature while increases with increasing

ma/ms, X1, and ya1. The dehumidiﬁer effectiveness increases

with the increase of Ts1, while it decreases with the increase

of Ta1 and ma/ms. Increasing Ta1, Ts1, and ya1 results in higher

ya2, however, low exit humidity ratio is obtained at lower inlet

desiccant concentration. The exit desiccant solution concentration remains unaffected by changing different operating parameters except X1.

Effect of air to solution mass ratio

Conﬂict of interest

Fig. 7 shows the effect of air to solution mass ratio (ma/ms) on

the MRR, ey and the exit parameters from the dehumidiﬁer;

ya2, Ta2, X2, and Ts2. When ma/ms is increased, both MRR

and Ts2 are increased, but ey is decreased, while Ta2 and ya2

are slightly increased, however, X2 is slightly decreased. The

potential capacity of the desiccant solution to carry over moisture from the process air is reduced by increasing ma/ms results

in higher outlet ya2 which in turn reduces ey. Increasing the

mass ﬂow rate of air leads to high heat capacity of air compared to solution which offset the temperature increase in

air-stream. Increasing ma/ms by 400% results in an increase

in both MRR and Ts2 by 611% and 81.6%, respectively. On

the other hand, ey is decreased by about 11.1%.

The author has declared no conﬂict of interest.

References

[1] Li Z, Liu XH, Jiang Y, Chen XY. New type of fresh air

processor with liquid desiccant total heat recovery. Energy Build

2005;37:587–93.

[2] Potnis SV, Lenz TG. Dimensionless mass-transfer correlations

for packed-bed liquid-desiccant contactors. Ind Eng Chem Res

1996;35(11):4185–93.

[3] Factor HM, Grossman G. A packed bed dehumidiﬁer/

regenerator for solar air conditioning with liquid desiccants.

Solar Energy 1980;24:541–50.

182

[4] Gandhidasan P, Kettleborough CF, Ullah MR. Calculation of heat

and mass transfer coefﬁcients in a packed tower operating with a

desiccant-air contact system. Solar Energy 1986;108(2):123–8.

[5] Ertas A, Anderson EE, Kavasogullari S. Comparison of mass

and heat-transfer coefﬁcients of liquid-desiccant mixtures in a

packed-column. J Energy Resour-ASME 1991;113(1):1–6.

[6] Stevens DI, Braun JE, Klein SA. An effectiveness model of

liquid desiccant system heat/mass exchangers. Solar Energy

1989;42(6):449–55.

[7] Ren CQ, Jiang Y, Zhang YP. Simpliﬁed analysis of coupled heat

and mass transfer processes in packed bed liquid desiccant-air

contact system. Solar Energy 2006;80(1):121–31.

[8] Lu ZF, Chen PL, Zhang X. Approximate analytical solution of

heat and mass transfer processes in packed-type cross-ﬂow

liquid desiccant system and its experimental veriﬁcation. J

Tongji Univ. 2001;29(2):149–53.

[9] Liu XH, Jiang Y, Qu KY. Analytical solution of combined heat

and mass transfer processes of cross-ﬂow dehumidiﬁer using

liquid desiccant. Taiyangneng Xuebao/Acta Energy Solar Sin.

2006;27(8):774–81.

[10] Liu XH, Jiang Y, Xia J, Chang X. Analytical solutions of coupled heat

and mass transfer processes in liquid desiccant air dehumidiﬁer/

regenerator. Energy Convers Manage 2007;48:2221–32.

[11] Dai YJ, Zhang HF. Numerical simulation and theoretical

analysis of heat and mass transfer in a cross ﬂow liquid

desiccant air dehumidiﬁer packed with honeycomb paper.

Energy Convers Manage 2004;45(9–10):1343–56.

M.M. Bassuoni

[12] Khan AY, Sulsona FJ. Modeling and parametric analysis of

heat and mass transfer performance of refrigerant cooled

liquid desiccant absorbers. Int J Energy Res 1998;22(9):

813–32.

[13] Liu XH, Jiang Y, Qu KY. Heat and mass transfer model of

cross-ﬂow liquid desiccant air dehumidiﬁer/regenerator. Energy

Convers Manage 2007;48(2):46–54.

[14] Liu XH, Zhang Y, Qu KY. Experimental study on mass transfer

performance of cross-ﬂow dehumidiﬁer using liquid desiccant.

Energy Convers Manage 2006;47(15–16):2682–92.

[15] Koronaki IP, Christodoulaki RI, Papaefthimiou VD, Rogdakis

ED. Thermodynamic analysis of a counter ﬂow adiabatic

dehumidiﬁer with different liquid desiccant materials. Appl

Therm Eng 2013;50(1):361–73.

[16] Davoud B, Meysam S. An analytical solution for air

dehumidiﬁcation by liquid desiccant in a packed column. Int

Commun Heat Mass 2009;36:969–77.

[17] Moon CG, Bansal PK, Sanjeev J. New performance data of a

cross ﬂow liquid desiccant dehumidiﬁcation system. Int J Refrig

2009;32:524–33.

[18] Adnan AK, Moustafa ME, Omar MA. Proposed energy

efﬁcient air-conditioning system using liquid desiccant. Appl

Therm Eng 1996;16(10):791–806.

[19] Gad HE, Hamed AM, El-Sharkawy II. Application of a solar

desiccant/collector system for water recovery from atmospheric

air. Renew Energy 2001;22:541–56.

## Tài liệu THE VALUE OF IMPROVED PUBLIC SERVICES: AN APPLICATION OF THE CHOICE EXPERIMENT METHOD TO ESTIMATE THE VALUE OF IMPROVED WASTEWATER TREATMENT INFRASTRUCTURE IN INDIA docx

## Agent-based and analytical modeling to evaluate the eﬀectiveness of greenbelts potx

## WHAT IS BETA GLUCAN? A Concise Guide to the Benefits and Uses of the Most Powerful Natural Im- mune Enhancer Known to Science ppt

## intech-a method for project member role assignment in open source software development using self organizing maps

## intech-a method for project member role assignment in open source software development using self organizing maps

## A guide to the project management body of knowledge 4th

## hacking vim a cookbook to get the most out of the latest vim editor

## peer-to-peer harnessing the benefits of a disruptive technology

## analytical method validation and instrument performance verification

## Báo cáo hóa học: " Bias analysis applied to Agricultural Health Study publications to estimate non-random sources of uncertainty" doc

Tài liệu liên quan