Desalination 317 (2013) 152–159
Contents lists available at SciVerse ScienceDirect
Desalination
journal homepage: www.elsevier.com/locate/desal
Simulation of the vapor mixture condensation in the condenser of
seawater greenhouse using two models
T. Tahri a,⁎, M. Douani a, S.A. Abdul-Wahab b, M. Amoura a, A. Bettahar a
a
b
Faculty of Technology, Hassiba Ben Bouali University, P.O. Box 151, Chlef 02000, Algeria
College of Engineering, Sultan Qaboos University, P.O. Box 33, Al-khod 123, Oman
H I G H L I G H T S
• Simulation of the condenser of seawater greenhouse using heat transfer model
• Simulation of the condenser of seawater greenhouse using mass transfer model
• The effects of operational parameters
a r t i c l e
i n f o
Article history:
Received 9 February 2012
Received in revised form 28 February 2013
Accepted 28 February 2013
Available online 9 April 2013
Keywords:
Condenser
Modeling
Heat model
Mass model
Seawater greenhouse
Oman
a b s t r a c t
The aim of this paper is the development of a mathematical model, based on mass transfer, in order to compare the simulation results with those obtained by the model developed by Tahri et al. for the analysis of
the seawater greenhouse (SWGH) condenser operating. This last model was depending on heat balance
according to the thermodynamic model of Nusselt for simulating the physical process of condensation of
the humid air in the condenser of SWGH that is located in Muscat, Oman. The present model was a mathematical one that was based on mass balance development in order to improve the description of phenomena
in a humidification-dehumidification seawater greenhouse desalination system. The values of the predicted
condensate calculated by the two models were compared with those of the measured values. Using the
model developed in this work, the predicted mass condensate rates calculated by mass model was much
closer to the measured condensate rates than that calculated by the heat model. Furthermore, the effects
of relative humidity, dry bulb temperature, seawater temperature, humid air velocity and solar radiation
on condensate values are also discussed.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
The lack of potable water poses a big problem in arid regions of
the world where freshwater is becoming very scarce and expensive.
The areas with the severest water shortages are the warm arid
countries of the Middle East and North Africa (MENA) [1]. The consequences of water scarcity will be especially seen in arid and semiarid
areas of the planet. Currently, agriculture accounts for around 70% of
fresh water use. In arid countries, this figure can exceed up to 90%.
Scarcity of water is very detrimental to agriculture and it is expected
that the growth in world population will aggravate the situation
further. This goes above 85% in the MENA and it is about 94% in
Oman [2]. As expected, irrigation demands will put a considerable
pressure on the water resources that are going to lead to groundwater
scarcity. The economic and social consequences are apparent in many
coastal regions of arid countries, such as Oman, where the overuse of
⁎ Corresponding author. Tel.: +213 551591304; fax: +213 27721794.
E-mail address: [email protected] (T. Tahri).
0011-9164/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.desal.2013.02.025
groundwater has caused saline intrusion, which in turn has reduced
the ability to grow crops and resulted in agricultural land being
discarded [3]. As the resources of freshwater are limited, there is an
inexorable and continuous pressure to reduce the agricultural uses
of the water. Desalination has become the main source of freshwater
in many parts of the world, especially in the MENA countries. The
most widely used desalination technologies are thermal and reverse
osmosis [4]. Desalination is an appropriate way in coastal regions or
other locations where access to saline or brackish water is not a constraint. The high operational cost of desalination (multi-stage flash
and reverse osmosis) has not rendered these techniques feasible for
arid land agriculture [5].
Today most of the desalination systems are using fossil fuels, and
thus are contributing to the increased levels of greenhouse gases.
There have been numerous voices inclined towards a more ecological
and safer approach to the problem proposing the use of renewable energy sources, fundamentally wind and solar, for small-scale seawater
desalination. Recently, a considerable attention has been given to the
use of renewable energy in desalination, especially in remote areas
T. Tahri et al. / Desalination 317 (2013) 152–159
Nomenclature
As
C
Cp
Cs
D
DAB
f
H
h
hfg
k
Le
L
m
_
m
N
P
Pr
Q
RH
Sc
St
T
heat transfer area
number
specific heat
humid heat
diameter
mass diffusivity
friction factor
absolute humidity
enthalpy
latent heat of vaporization
Thermal conductivity
Lewis number
length
mass
mass flux
number
pressure
Prandtl number
heat flux
relative humidity
Schmidt number
Stanton number
temperature
Greek symbols
α
Thermal diffusivities
ρ
density
153
on the amount of the condensed water, which can be gained at a certain
ambient condition and a certain type of crops.
Having noted discrepancies between the experimental results and
those obtained by the model of heat transfer presented by Douani et
al. [17], we developed the mass transfer model within the framework
of this study. Our task was focused on simulating the condenser of a
seawater greenhouse by using two models that were based on heat
and mass transfer. Application of both developed models using
FORTRAN was conducted to validate its theoretical development.
The effect of the relative humidity, the dry bulb temperature, the seawater temperature, the humid air velocity and the solar radiation on
condensate values were also addressed.
2. Methodology
2.1. Condenser process description
The condenser of the solar greenhouse is a heat exchanger where
seawater is the coolant and humid air is the hot fluid (Fig. 1). The
tubes are organized in such a way to ensure passage of the coolant
from one tube to another forming a row of coiled tubes.
Seawater is introduced, at a constant speed (usw) and at a known
temperature (Tswin), in the first line of the tube bundle to an exit
tube located upstream of the greenhouse after an increase in
temperature.
The condenser unit consists of a set of 302 rows of parallel tubes
which arranged semi-vertically at an angle of 30 degrees to the direction of the flow of moist air. Each line consists of 16 vertical tubes,
identical diameter (D) of 33 mm, and a height (L) of 1.8 m [9]. Values
of different design parameters of the condenser unit are listed in
Table 1.
2.2. Modeling of heat and mass exchange in the condenser
Subscripts
air
air
c
condensate
D
degrees of freedom
db
dry bulb
in
inner
sat
saturation
sw
seawater
swin
seawater inlet
swout
seawater outlet
vap
vapor
and islands. This is mainly because of the high cost of fossil fuels, the difficulties to obtain it taking account with their progressive scarcity, the
attempts to preserve it for future generations, while envisaging a contribution to the reduction of the atmospheric pollution related to the combustion rejects during the electrical energy generation [1]. Solar
desalination methods are well suited for the arid and sunny regions of
the world as in the Arabian Peninsula. In the desalination context, it is
relevant to use the technologies which facilitate more efficient water
in agriculture. The Seawater Greenhouse (SWGH) provides a perfect environment in which the transpiration loss from plants is minimized. At
the same time, sufficient water for its own use is produced through a
process of solar distillation [6]. Indeed, the projects of solar desalination
have been demonstrated in several locations around the world. The
humidification-dehumidification method was used in a greenhousetype structure for desalination and for crop growth as a pilot plant at
Al-Hail, Muscat, in the Sultanate of Oman [7,8]. Sablani et al. shown
that the dimension of the greenhouse had the greatest overall effect
on water production and energy consumption [21]. Among other parameters, cooling the condenser(s) of the SWGH has a direct impact
2.2.1. Heat transfer model
Steam condensation occurs when its temperature is reduced
below its saturation temperature at a given pressure. The presence
of non-condensable gases (air) in the gas mixture leads to a significant reduction in the heat flow and during condensation. This is because of the formation non-condensable gases, bind to the wall film
that will prevent the diffusion of vapor through the bulk liquid film
[11]. Analysis of the kinetics of heat transfer for film condensation
outside vertical tubes was originally treated for laminar film by
Nusselt in 1916 [12].
In this work, the simulation of the condenser of the seawater
greenhouse was done on the basis of a model that developed previously by Tahri et al. [9] at Al-Hail, Muscat. Data of dry bulb temperature of air together with its relative humidity are collected only at the
inlet and the exit of the condenser of the seawater greenhouse. However, simulation of the operation of the condenser requires that the
saturation temperature to be known at each tube of the condenser.
Equations used in this work can be found in Sherwood and Comings
[13].
Saturation temperature (Tsat) was calculated for the first and the
last tube in the row of the condenser [10] according to Eq. (1):
H sat −H
C
¼− s
T sat −T db
hfg
ð1Þ
Cs is the mass humid heat (kJ/kg °C) [19] which was calculated
according to Eq. (2):
C s ¼ C pair þ H C pvap
ð2Þ
The temperature of seawater flowing inside the tubes of the condenser is only known at the entrance and exit of the condenser. In
154
T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 1. Process schematic of one vertical tube of the condenser unit.
this work, parabolic interpolations were used to find the temperature
of seawater at the entrance and the exit for each tube of the condenser by utilizing the information that are known at the entrance and the
exit of the condenser. As a basis of calculation, the temperature of
seawater at the entrance and the exit of intermediate tubes are unknown. To resolve this problem, linear profile of seawater temperature along the row of the condenser was adopted. The temperature
at the entrance of each tube was calculated according to Eq. (3):
T swin ðjÞ ¼
ðT swout ð16Þ−T swin ð1ÞÞ
ðj−1Þ þ T swin ð1Þ
16
ð3Þ
However, this hypothesis was subsequently corrected by introducing a coefficient of weighting [17] that was used to adjust the
value of the entrance seawater temperature for each tube. If the
total number of tubes in the condenser is Ntot, then the total flow of
condensate will be:
_ ctot ¼
m
NL X
NT
X
mij
ð4Þ
j¼1 i¼1
Moreover, it was considered that the outlet seawater temperature
of one tube of the row (Tswout) was equal to the inlet seawater temperature (Tsin) of the next tube. Also, it was assumed known both
the inner (TWin) and the outer wall (TWout) temperatures for the first
Table 1
Design parameters of the condenser unit [10].
Dimensions of condenser
Thickness of vertical tube (δ)
Height of vertical tube (L)
Diameter of vertical tube (Dout)
Number of longitudinal tubes (NL)
Number of transverse tubes (NT)
Total number of tubes (Ntot)
tube in the row of condenser. This value of TWout will be used in
Eq. (9) to find out the heat flux (Q).
The average heat transfer coefficient for a laminar film condensation over a vertical tube of height (L) was calculated [12] for each tube
of the condenser according to Eq. (5):
"
have ¼ 0:943
#1
4
ð5Þ
According to Çengel [14], Rohsenow [15] showed that the cooling
of a liquid below its saturation temperature can be accounted for
∗
, deby replacing hfg by the modified latent heat of vaporization hfg
fined as
hfg ¼ hfg þ 0:68 C pL ðT sat −T Wout Þ
ð6Þ
In the presence of noncondensble gases (e.g., air), the average heat
transfer coefficient for film condensation (have) was corrected (hvert)
according to the graph of Sacadura [16] as shown in Eq. (7). According
to Tahri et al. [12], correction is a function of the noncondensable gas
mass fraction (X)
hvert ¼ have f ðX Þ
ð7Þ
X is the mass fraction of the noncondensable gases (kg noncondensable
gas/kg humid air) which was calculated for each tube according to
Eq. (8):
X¼
(15 × 19 × 0.8)m
200 μm
1.8 m
33 mm
16
302
4832
3
g ρL ðρL −ρv ÞkL hfg
μ L ðT sat −T Wout ÞL
mNC
1
¼
mtot 1 þ H
ð8Þ
Calculation of Q
The heat flux (Q) in the film condensation was calculated for the
first tube according to Eq. (9):
Q ¼ hvert Aout ðT sat −T Wout Þ
ð9Þ
T. Tahri et al. / Desalination 317 (2013) 152–159
Calculation of hin
The inner heat transfer coefficient hin was calculated [10]
according to Eq. (10):
hin ¼
Nu ksw
Din
ð10Þ
Calculation of (TWout)cal
The outer wall temperature (TWout)cal was then calculated for the
first tube [14] according to Eq. (11):
Q ¼ 2 π L ktub
ðT Wout Þcal −ðT Win Þ
ln DDout
ð11Þ
in
Calculation of (TWin)cal
The inner wall temperature (TWin)cal was then calculated for the
first tube [10] according to Eq. (12):
Q ¼ hin Ain
ðT Win Þcal −T swin − ðT Win Þcal −T swout
ððT Þ −T Þ
ln ðT WinÞ cal−T swin
ð Win cal swout Þ
ð12Þ
Firstly, the values of (TWout)cal and (TWin)cal are calculated from
Eqs. (11) to (12) respectively. Their values were compared with the
guessed initial values of TWout and TWin. If the difference between
the compared values does not verify a criterion of convergence, the
values of (TWout)cal and (TWin)cal will be again used in Eqs. (5) and
(11) to calculate the new values of (TWout)cal and (TWin)cal. The process
was repeated until the values of (TWout)cal and (TWin)cal with successive trials did not change.
The mass flux of condensate for the first tube was determined by
Eq. (13):
_ c1 ¼
m
hvert Aout ðT sat −T Wout Þ
hfg
ð13Þ
The heat flux transferred from humid air to seawater (Qsw) was
calculated in the first tube according to Eq. (14):
2
Q sw ¼ ρsw usw C P sw π
ðDin Þ
ðT swout −T swin Þ
4
ð14Þ
The enthalpy of air (Hair) was calculated at the entrance of the first
tube according to Eq. (15):
ðH air Þin ¼ C Pair
0
T db þ H C Pvap T db þ hfg
ð15Þ
The heat flux of air (Qair) was calculated at the entrance of the first
tube according to Eq. (16):
_ air
ðQ air Þin ¼ ðHair Þin m
ð16Þ
The heat flux of air (Qair) was calculated at the outlet of the first
tube according to Eq. (17):
ðQ air Þout ¼ ðQ air Þin −Q−Q sw
ð17Þ
The humidity of air (H) at the dry bulb temperature was calculated
at the outlet of the first tube according to Eq. (18):
_ c1
m
H out ¼ Hin −
_ air
m
ð18Þ
155
The dry bulb temperature Tdb was calculated at the outlet of the
first tube according to Eq. (19):
T dbout ¼
ðQ air Þout
_ air −
m
Hout h0fg
C Pair þ H out C Pvap
ð19Þ
The calculated humidity of air (Hout)cal from Eq. (18) and dry bulb
temperature (Tdbout)cal from Eq. (19) in outlet first tube were used in
Eq. (1) to set the saturation temperature (Tsat) of the second tube in
the row of the condenser. Simulation of the condenser operation required that the saturation temperature to be known at each tube in
the condenser. For this purpose, Eqs. (1)–(19) were repeated for
_ c1tot Þcal from
each tube. Next, the total mass flow calculated ðm
_ ctot Þm
Eq. (4) was compared with the measured total mass flow ðm
on the day of 25 December 2005. If the model was not valid, then
new values were proposed for the coefficients of weighting of parabolic interpolation for seawater temperature at different tubes in
the condenser [17]. The trial was repeated until the values of
_ c1tot Þcal and ðm
_ ctot Þm did not change with successive trials.
ðm
2.2.2. Mass transfer model
For this model, Eqs. (1)–(12) were repeated for the first tube to
defined (Tsat) and (TWout).
The Reynolds analogy is very useful relation, and it is certainly desirable to extend it to a wider range of Pr and Sc number. Several attempts were done in this regards, but the simplest and the best know
was the one suggested by Chilton and Colburn in 1934 as [18]:
f
2=3
2=3
¼ StPr ¼ St mass Sc
2
ð20Þ
For 0.6 b Pr > 60 and 0.6 b Sc > 3000. This equation is known as
the Chilton–Colburn analogy. Using the definition of heat and mass
Stanton numbers, the analogy between heat and mass transfer was
expressed more conveniently as:
2=3
hvert
Sc
¼ ρair C pair
Pr
hmass
ð21Þ
For air-vapor mixtures at 298 K, the mass and thermal diffusivities
were D = 2.5 10 −5 m 2/s and α = 2.18 10 −5 m 2/s, respectively.
Hence, Lewis number was calculated from Eq. (22):
Le ¼
α
¼ 0:872
D
ð22Þ
Next, (α/D)2/3 = 0.872 2/3 was calculated as 0.913, where the value
was close to unity. The Lewis number was relatively insensitive to variations in temperature. Therefore, for air–water vapor mixture, the relation between heat and mass transfer coefficients was expressed with a
good accuracy as:
hmass ≅
hvert
ρair C pair
ð23Þ
where ρair and Cpair are the density and specific heat of air at film temperature. The film temperature (Tfilm) was given by [14] according to
Eq. (24):
T film ¼
T db þ T Wout
2
ð24Þ
The condensate rate of fresh water produced for the first tube was
calculated by the following relation:
_ c2 ¼ hmass π Dout L ρvapdb −ρvapWout
m
ð25Þ
156
T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 2. Comparison of the diurnal measured and calculated mass condensate rate of condenser.
where ρvapdb and ρvapWout are the density of vapor at dry bulb and external wall temperature which were calculated by Eq. (26), according
to [20]:
ρsat ðT Þ ¼
2910 expð9:48654−3892:7=ðT−42:6776ÞÞ
8314 T
ð26Þ
Where
ρvapdb ¼ ρsat T vapdb
ρvapWout ¼ ρsat T vapWout
_ c2tot Þcal from Eq. (4) which is compared with the meacalculated ðm
_ ctot Þm on the day of 25 December 2005. If
sured total mass flow ðm
the model is not valid, then new values are proposed for the coefficients of weighting of parabolic interpolation for seawater temperature at different tubes in the condenser [17]. The trial calculation is
_ c2tot Þcal and ðm
_ ctot Þm don’t change.
repeated until the values of ðm
3. Results and discussion
ð27Þ
3.1. Comparison between the measured and predicted mass condensate
rate
The simulation of the condenser operation requires that the saturation temperature to be known at each tube in the condenser. To this
end and knowing the dry air properties (Hdry, Tdb), we use the Eq. (1)
to determinate it for each tube. For all the tubes, the total mass flow
Fig. 2 illustrates the calculated and measured mass condensate
rates according to the hours of a one day period. It can be seen that
there was a time gap between the calculated [9] and the measured
condensate rates. This gap was attributed to the tipping bucket
Fig. 3. Comparison of the diurnal mass condensate rate and the solar radiation inside the SWGH.
T. Tahri et al. / Desalination 317 (2013) 152–159
157
Fig. 4. Comparison of the diurnal mass condensate rate and the inlet dry bulb temperature in the condenser.
gauge which did not register outflow from the condenser due to the
low production rate of condensate. Formation of the water droplets
on the tubes of the condensers were observed, but only a small fraction of the droplets made their way to the gutter collecting the condensate. It should be noted that the measured condensate mass
rates were taken from the freshwater tank by the tipping bucket
gauge, whereas the predicted condensate mass rates were calculated
directly as droplets formed at the outer surface of the tubes of
the condenser [9]. Therefore it was observed that the trend of the predicted and the measured mass condensate rates were close, a gap was
clearly seen between them.
The trend of the predicted mass condensate rates calculated in this
work by mass model was much closer to the measured condensate
rates than that calculated by heat model.
3.2. Impact of the meteorological variables on mass condensate rates
Fig. 3 shows the variation of the measured and predicted mass
condensate rates together with solar radiation values of a one day period. It can be seen that the solar radiation values were observed only
during the interval from 08:00 to 18:00 and it was zero during the
night time. Hence, the trend of the calculated and measured mass
condensate rates went hand-in-hand with solar radiation.
Fig. 4 shows the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the dry bulb temperature for one day period. It can be noted that the two plots of
the measured and predicted mass condensate rates follow the same
trend of the diurnal variations of dry bulb temperature. We note
that its shapes are typically Gaussian which reach its maximum at
Fig. 5. Comparison of the diurnal mass condensate rate and inlet relative humidity in the condenser.
158
T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 6. Comparison of the diurnal mass condensate rate and the inlet seawater temperature in the condenser.
12 h 00. In any rigor, we mention that the mass condensate rate is
strongly influenced by the pinch of temperature (Tsat–Tdb) according
to Eq. (1). For a condenser, where the condensation of vapor place inside the tubes bank immersed in a tank, filled by seawater [20], the
results of the operating analysis show that the trends of Tdb, and
_ ctot Þcal versus the time confirm the results obtained by the model
ðm
developed within the framework of this work. Indeed, the maximum
values are also reached at 12 h 00.
Fig. 5 depicts the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the relative humidity of a one day period. It can be seen that the relative humidity values
were high (100%) between 08:00 and 14:00, while their lower values
(RH = 65%) were seen during the rest of the day. It should be noted
that in the interval extended from 08:00 to 14:00, the seawater
greenhouse produce 98% of the total daily freshwater. This result
is in perfect agreement with the conditions of condensation of
the water vapor which require a preliminary saturation of the air
(100%). However, the tiny quantities of condensate appear beyond
14:00 where the air is unsaturated.
Fig. 6 depicts the variation of the measured and predicted mass
condensate rates together with the inlet seawater temperature values
to condenser for one day period. It shows that the condensation of
steam in the condenser happened between 08:00 and 18:00 with an
average temperature of cold fluid (seawater) below 20 °C. The quantity of the condensate is the consequence of the interference of the installation operating parameters so that it is impossible to obtain an
obvious conclusion for a variation of the inlet seawater temperature
in such a restricted interval (20 to 24 °C) which is an exterior uncontrollable parameter, dictated by ambient condition.
Fig. 7 depicts the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the air speed values
of a one day period. In our experiences, the air speed is selected
according to the degree of saturation of the air in order to favorite
the mass transfer. From previous results, these selected air speeds
Fig. 7. Comparison of the diurnal mass condensate rate and air speed inside the SWGH.
T. Tahri et al. / Desalination 317 (2013) 152–159
are maximum within the interval time 09:00 to 17:00. We see that
the measured and predicted mass condensate rates went hand-inhand with the air speed values inside SWGH whereas the seawater
greenhouse produced 98% of the total daily freshwater during this period when air speed was maximum (7 m/s).
4. Conclusions
This paper discussed the modeling of the heat and mass exchange
in the condenser of a seawater greenhouse (SWGH) at Al Hail in
Muscat, Oman. In this work, two theoretical models were developed
in order to describe the process of condensation by using model of
heat and mass transfer equations. A comparison was made between
the mass condensate rates values calculated by the two models. The
predicted values were also compared with that of the measured
values. The trend of the predicted mass condensate rates calculated
by mass model in this work was found much closer to the measured
mass condensate rates. The results indicated that the comparison
was more consistent with the mass model used in this work. The
effect of solar radiation, relative humidity, dry bulb temperature,
seawater temperature, and air speed was also discussed to see their
effects on the condensate.
Acknowledgments
The first author would like to acknowledge the valuable assistance
of his advisors: Prof. Dr. Sabah Ahmed Abdul-Wahab, (College of
Engineering, Sultan Qaboos University) and Prof. Dr Bettahar Ahmed
(College of Engineering, Chlef University). The first author would
like also to thank Dr. Douani Mustapha (College of Engineering,
Chlef University) for his assistance in describing the models.
References
[1] H.M. Qiblawey, F. Banat, Solar thermal desalination technologies, Desalination
220 (2008) 633–644.
[2] C. Paton, P. Davies, The seawater greenhouse cooling, fresh water and fresh produce from seawater, The 2nd International Conference on Water Resources in
Arid Environments, Riyadh, 2006.
159
[3] J.S. Perret, A.M. Al-Ismaili, S.S. Sablani, Development of humidification–dehumidification system in a quonset greenhouse for sustainable crop production in arid
regions, Biosyst. Eng. 91 (2005) 349–359.
[4] M.F.A. Goosen, S.S. Sablani, W.H. Shayya, C. Paton, H. Al-Hinai, Thermodynamic
and economic considerations in solar desalination, Desalination 129 (2000)
63–89.
[5] M.F.A. Goosen, H. Al-Hinai, S.S. Sablani, Capacity building strategies for desalination: activities, facilities and educational programs in Oman, Desalination 141
(2001) 181–190.
[6] P.A. Davies, C. Paton, The Seawater Greenhouse in the United Arab Emirates: thermal modelling and evaluation of design options, Desalination 173 (2005)
103–111.
[7] C. Paton, A. Davis, The seawater greenhouse for arid lands, Proc. Mediterranean
Conf. on Renewable Energy Sources for Water Production, Santorini, 10–12
June, 1996.
[8] B. Dawoud, Y.H. Zurigat, B. Klitzing, T. Aldoss, G. Theodoridis, On the possible
techniques to cool the condenser of seawater greenhouse, Desalination 195
(2006) 119–140.
[9] T. Tahri, S.A. Abdul-Wahab, A. Bettahar, M. Douani, H. Al-Hinai, Y. Al-mulla,
Simulation of the condenser of the seawater greenhouse. Part II: application of
the developed theoretical model, J. Therm. Anal. Calorim. 96 (2009) 43–47.
[10] N.K. Maheshwari, D. Saha, R.K. Sinha, M. Aritomiet, Investigation on condensation
in presence of a noncondensable gas for a wide range of Reynolds number, Nucl.
Eng. Des. 227 (2004) 219–238.
[11] W. Nusselt, Die oberflachen Kondensation des Wasserdampes, Z. Ver. Deut. Ing.
60 (2) (1916) 541–546.
[12] T. Tahri, S.A. Abdul-Wahab, A. Bettahar, M. Douani, H. Al-Hinai, Y. Al-mulla,
Simulation of the condenser of the seawater greenhouse. Part I: theoretical development, J. Therm. Anal. Calorim. 96 (2009) 35–42.
[13] T.K. Sherwood, E.W. Comings, An experimental study of the wet bulb hygrometer,
Trans. Am. Inst. Chem. Eng. 28 (1932) 88.
[14] Y.A. Çengel, Heat Transfer: a practical approach, second ed. McGrRAW-HILL, New
York, 2003.
[15] W.M. Rohsenow, A method of correlating heat transfer data for surface boiling of
liquid, ASME Trans. 74 (1952) 969–975.
[16] J.F. Sacadura, Initition aux transferts thermiques, Edit, Techniques et documentation, 1982.
[17] M. Douani, T. Tahri, S.A. Abdul-Wahab, A. Bettahar, H. Al-Hinai, Y. Al-mulla,
Modeling heat exchange in the condenser of a seawater greenhouse in Oman,
Chem. Eng. Commun. 198 (2011) 1–15.
[18] Y.A. Çengel, Heat Transfer: A Practical Approach, second ed. McGraw-Hill, New
York, 2003. 754–759.
[19] Perry's Chemical Engineers' Handbook, McGraw-Hill, 1999, p. 3 (Section 12).
[20] H. Mahmoudi, N. Spahis, S. Abdul-Wahab, S.S. Sablani, F.A. Goosen, Improving the
performance of a Seawater Greenhouse desalination system by assessment of
simulation models for different condensers, Renew. Sustain. Energy Rev. 14
(2010) 2182–2188.
[21] S.S. Sablani, M.F.A. Goosen, C. Paton, W.H. Shayya, H. Al-Hinai, Simulation of fresh
water production using a humidification–dehumidification seawater greenhouse,
Desalination 159 (2003) 283–288.