Theoretical validation model of a double slope still with forced convection

* Corresponding author.
1944-3994/1944-3986 © 2020 Desalination Publications. All rights reserved.
Desalination and Water Treatment
www.deswater.com
doi: 10.5004/dwt.2020.25722
192 (2020) 33–43
July
Theoretical validation model of a double slope still with forced convection
José Andrés Alanís Navarroa
, Beatriz Castillo-Téllezb
, Rachid Marzougb
,
Margarita Castillo Téllezc,
*
a
Universidad Politécnica del Estado de Guerrero, Taxco de Alarcón, Guerrero, México 40321, email: aalanis@upeg.edu.mx (J.A.A. Navarro)
b
Centro Universitario del Norte, Universidad de Guadalajara, Jalisco, México, emails: beatriz.castillo@academicos.udg.mx
(B. Castillo-Téllez), r.marzoug@cunorte.udg.mx (R. Marzoug)
c
Facultad de Ingeniería, Universidad Autónoma de Campeche, Campeche, Campeche, México, email: mcastill@uacam.mx (M.C. Téllez)
Received 19 June 2019; Accepted 20 February 2020
a b s t r a c t
The use of solar energy for water desalination becomes vital for sustainable water supply.
This paper aims to analyze the experimental behavior of double slope solar theoretically still
(DSSS). In this work, we proposed a theoretical model that can predict the DSSS performance. The
theoretical results of temperatures and the impact of wind speed on water production are in good
agreement with experimental findings. It is found that the temperature augments with augment-
ing the wind speed until a critical value, where the temperature starts to drop. In addition, water
production increases with increasing speed. In this way, we determined the optimum wind speed
to have maximum water production with minimum energy consumption simultaneously. The val-
idation of the theoretical model allows us to predict the DSSS production under different climatic
conditions and to scale DSSS dimensions according to the need of water. The salinity of the water
is not a determining factor in its production. The production at 4.2 kWh/m2
daily insolation was
0.58 L/d. The volume of distilled water reaches a maximum value (62.3% efficiency) when glass
and environment temperatures are similar. This phenomenon occurs at 5.5 m/s wind speed.
Keywords: Double slope solar still; Theoretical validation; Solar energy; Forced convection; Energy2D
1. Introduction
Given the water shortage situation around the world, a
significant number of countries have devoted much effort
to obtain fresh water from sources such as the sea, lagoons,
or brackish wells. The process of obtaining fresh water
from these sources is desalination. Its cost can be very high
in terms of energy consumption and environmental qual-
ity. The solar still is a straightforward and efficient system
that allows reproducing in an accelerated way the natural
water cycle. In this context, many studies have been real-
ized to increase the efficiency of this system, especially the
double slope solar still (DSSS) type. Rajaseenivasan et al. [1]
performed a comparative study on a double slope single
basin and double basin solar still; they used various water
depths and different materials. It is found that the double
basin production is 85% higher than the single basin still.
Morad et al. [2] studied the efficiency of a double solar
still with a flat-plate solar collector and different cooling
glass cover thickness. Wang et al. [3] proposed a design of
a novel solar distillation that can use seawater directly in
agricultural irrigation.
Also, the use of a double basin attached with vac-
uum tubes enhances the still performance, based on the
results obtained in [4]. Kumar et al. [5] improved the air
circulation and vapor condensation, introducing a fan and

J.A.A. Navarroa et al. / Desalination and Water Treatment 192 (2020) 33–43
34
external condenser. Somwanshi and Tiwari enhanced the
performance of a single basin solar with water flow from an
air cooler on the cover [6].
In [7], the authors studied a system that uses solar
energy as a pressure source for reverse osmosis (RO)
water desalination. Mashaly et al. [8] investigated the per-
formance of a solar desalination system using three differ-
ent types of feed water to reach near-zero liquid discharge
(ZLD) under the hyper-arid environment.
Many researchers aim to develop mathematical models
that represent the thermodynamic phenomena to optimize
the distillation process, especially to predict the volume of
distilled water. Johnson et al. [9] proposed a thermal model
for predicting the performance of a solar still with Fresnel
lens. They found that the Fresnel lens can help improve the
overall efficiency of the solar still. Thermal modeling of a
double slope active solar still has been carried out based
on the energy balance of east and west glass covers, water
mass, and basin liner under natural circulation mode [10].
Kalbasi et al. [11] formulated a mathematical model to pre-
dict the performance of single and double effect solar still
by using modified heat transfer correlations. Two similar
experimental desalination units (single and double effect)
were designed to validate the mathematical model. Wind
speed is an essential parameter for distillation since it con-
tributes significantly to the condensation process; thus,
the increase of efficiency [12].
Recently, a thermal analysis of double slope solar still
by using free software called Energy2D is reported [13].
In this work, a theoretical validation of previous experi-
mental studies [2] and analysis of forced convection effects
in double slope solar still is performed.
The paper is organized as follows: in section 2, we define
used materials and methods. In section 3, the results are
discussed, and some findings are reported. Finally, section 4
is dedicated to the conclusions.
2. Experimental study
Two identical double solar stills were designed and
manufactured, with a square tray-type solar collector. Their
bottom has a side of 0.5 m (0.25 m2
collection area), con-
structed using the 16-gauge copper sheet (1.61 mm thick).
This bottom was coated with matte black paint resistant to
high temperatures to increase solar radiation absorption.
The tray was thermally insulated by 0.10 m thickness poly-
urethane foam to ensure thermal insulation. Finally, this
foam was covered with metal to enhance the mechanical
structure.
The still’s cover is formed by 3 mm thick glass placed
at an inclination of 23°. Two aluminum channels with a
slight slope and a 0.635 cm perforation, transport, and col-
lect the condensed water. At the center of the DSSS, a con-
tainer distributes the water to the stills, maintaining a con-
stant level of brackish water to be treated using a 0.635 cm
hose. Each still has an independent condensate collector.
The brine is eliminated by a hole located at the base of the
tray, and the distilled water is continuously recorded (Fig. 1).
To analyze the influence of the wind speed on the evap-
oration–condensation process of water, a closed wind tunnel
constructed of plastic was designed and placed at the roof
of one still to control and stabilize the airflow at a differ-
ent speed. The wind speed is produced inside the tunnel
using three fans powered electrically with a variable voltage
source. The process of switching on and off is performed
automatically during the 8:00–20:00 h period.
The principal objective of this paper is the validation
of the experimental results with a theoretical model and
simulation that analyzes the influence of wind speed and
saline concentration on double slope solar still productiv-
ity. In our knowledge, this work has not been treated in
the literature.
2.1. Materials and methods
In one still, the air is injected over the glass cover, using
a 3 mm thick plate for its speed distribution and control. Air
follows the outer contour, forming a tunnel. The effect of
placing this double cover was considered in the efficiency
still analysis. Three fans (119 mm × 119 mm × 38 mm and
a 390 g of weight), with a 0.94 A supply and a variable
voltage from 0 to 60 V DC, helped to obtain the desired
wind. A digital display shows the voltage and the electri-
cal current consumed by the fans. Fig. 2 shows the detail of
the parallel interconnection.
The salted water is supplied during the night to each
basin for distillation during the day. The water depth is
constant (2 cm). The following variables are collected in
real-time: solar radiation, temperatures: ambient, inside of
the still, basin water, and wind speed. The distilled water
is measured by recording the weight in a precision bal-
ance. The measurement cycles are taken at 20:00 h each
day. In the beginning, the average wind speed is fixed.
To achieve the required speed, three fans of dimensions
(119 mm × 119 mm × 38 mm) were used. To measure the
mass of distilled water, we used a Tor-Rey electronic scale,
L-EQ 5/10 series, with an accuracy of 0.001 kg. A computer
records the information every 10 min.
We used two sensors for the recording of wind speed.
One integrated into a Skywatch Owners model Geos 11
portable weather station, (±4% accuracy) and a Cole Palmer
thermo-anemometer, model EW-10323-11 with a resolution
Fig. 1. General view of the experimental device.

35
of 0.1 m/s. One was used to measure the speed at the surface
of the glass cover, and others to measure the speed across
the wind tunnel. A picture and schematic diagram of the
location of the fans placed in the wind tunnel are shown
in Fig. 3.
2.2. Experimental procedure
For the preparation of seawater at the laboratory, we
used the salt concentration values reported by Werlinger
et al. [14].
The brackish water distribution vessel supplies over-
night for daytime operation, keeping the level in each of
the constant at 2 cm using the constant level burette. The
DSSS is exposed to solar radiation, and the variations in
temperatures inside and outside the still, brackish water,
the environment, solar radiation, and the selected speed
inside the wind tunnel are recorded. The amount of distilled
water is measured by recording its weight on the precision
balance. The measurement cycles are recorded at 20:00 h
of each day. In the beginning, average wind speed is set,
and the variations of the different parameters are recorded
through an automatic data acquisition system (DAS).
2.3. Instrumentation
The stills were instrumented using K-type thermo-
couples placed inside and outside the device to measure
the temperature; using these thermocouples and a DAS
Brand Campbell CR10 model, these temperatures were
measured daily; installed program extracts data every 10 min
through the serial interface that connects to a computer.
Moreover, daily climatological data was acquired:
solar irradiance, ambient temperature, wind speed, wind
direction, and relative humidity, which are continuously
recorded at the Institute of Renewable Energies in Temixco,
Morelos, México. Table 1 shows the accuracy and descrip-
tion values given by the manufacturers of the different
sensors used in this solarimetric station.
2.4. Experimental and theoretical analysis
The experimental study was carried out at the Institute
of Renewable Energies of the National Autonomous Uni
versity of Mexico, in Temixco, Morelos, México, located at
18°51’NL and 99°14’WL. The experimental device consists of
one DSSS with a copper tray coated with black paint (high
temperature resistant), 0.25 m2
of the solar collection area, and
12.5 ± 0.2 L of capacity. The cover is made of standard glass
(3 mm thickness) with an inclination of 23° and south-
oriented,
resulting in an optimal transmittance according to the local
latitude. The walls and the bottom were thermally insulated
with polyurethane foam (10 mm of thickness), which was
covered with a metallic protective shield. The cover and the
enclosure was sealed to prevent any vapor and condensate
loss. The water depth was 2 cm, which corresponds to a 5.0 L
capacity. Asecond still with the same characteristics with nat-
ural convection kept operating at the same time to compare
the performance of both. Moreover, the exterior air does not
influence the interior wind speed. Fig. 1 shows a general view
of the experimental equipment. The purpose of this paper is
to validate the experimental results with a theoretical model
analyzing the influence of wind speed on DSSS productivity.
2.5. Transient model
The solar irradiance (G) passing through a transparent
cover with a transmittance (t) that depends on the material
and its thickness (τg
G). Aportion of this radiation is absorbed
(αg
G) or reflected (ρg
G). The portion of G that reaches the
water surface (τg
G) again undergoes a decomposition due
to the optical characteristics of the water; reflected (ρw
τg
G),
absorbed (αw
τg
G) and transmitted (τw
τg
G). The most radia-
tion amount transmitted to the base of the tray is absorbed
(αb
τw
τg
G), and a small portion is reflected (ρb
τw
τg
G) because
Fig. 2. Detail view of the parallel interconnection of the fans.
Fig. 3. (a) Schematic diagram and (b) photograph of the location of the fans in the wind tunnel. (1) Fans, (2) glass cover, and (3) wind
tunnel.

36
the black color of the tray base has a high absorptance and
low reflectance. The energy absorption in the base of the
tray is the necessary energy to heat the water of the tray or
absorber. A portion is transmitted to the exterior by conduc-
tion through the tray thickness (Qk
). Another part is trans-
ferred to the water by convection (Qcw
), this heat gained
by water, reaches the glass cover from its surface by three
heat transfer phenomena: the first part is due to convection
through the internal air (Qc
), the second part constitutes the
latent heat which transports the vapor molecules that will
condense on the inner part of the glass cover (Qu
) which
represents precisely the amount of heat necessary to evap-
orate the water placed in the tray. The third phenomenon
is the radiative heat (Qr
) between the water surface and the
glass cover. This radiation produces the greenhouse effect.
The heat given to the glass is transferred to the exterior
due to the convection (Qca
). The overall optical and thermal
phenomena that occur in a solar still are illustrated in Fig. 4.
To calculate the still thermal efficiency (η) we used
the following equation:
η =
⋅
⋅ ⋅
V h
P H
fg
av
3 600
,
(1)
where V: distillate volume measured (L); hfg
: latent heat of
vaporization (J/kg). Its value was obtained considering
the maximum temperature obtained in the water to distill;
P: potency of the incidence of solar radiation on the absorber
surface (given by the product of the average irradiance
I of the day (W/m2
) by the surface S (m2
); H: total exposure
time or sun hours (h).
The product P·H·3,600 is the solar energy captured
by the absorber (J) [15,16]. The energy balance of the still
requires that solar radiation absorbed must be equal to the
transferred energy from the roof to the air plus the losses of
the bottom/walls and the stored energy in the system [17].
The corresponding equations are the following:
Eq. (2) gives the differential equation for the slope:
m
dT
dt
I I q q q q q
g g
g
g b g d r w g c g g r g c g
Cp ev air a
= +
( )+ + +
( )− +
− − − −
α α , , , , i
ir

(2)
The heat transferred by evaporation between the water
and the cover (qev
) is based on [10]:
q h P P
c w g
ev
= −
( )
16 28
. (3)
And pw
y pg
:
P e
w
Tw
=
−
( )
25 317 5 144
. , /
(4)
P e
g
Tw
=
−
( )
25 317 5 144
. , /
(5)
hc
represents the heat transfer coefficient by convection
and is calculated by the following equation:
h T T
P P T
P
c w g
w g w
w
= −
( )+
−
( )
−
( )








( )
0 884
268 900
2
.
,
/
W m K (6)
The heat transfer from the water to the cover by radia-
tion is given by Stefan–Boltzmann Law, considering that
the emittance of the glass cover is 0.9:
q T T
r w g w g
,
.
−
= −
( )
0 9 4 4
σ (7)
This heat is due to the radiant exchange between the
water surface and the glass cover.
The heat transferred by convection between the
absorber and the glass cover consists of the convection of
Table 1
Characteristics and description of the measuring instruments used in this work
Parameter Description Model Calibration Maximum error
Global irradiation Pyranometer Eppley PSP Annual (IGF-UNAM)
(K = 7.68 Sensor Campbell)
±0.5 W/m2
Ambient temperature and
relative humidity
Sensor Campbell, CS500 1,000 ΩPRT,
DIN 43760B
Biannual ±0.4°C
±3%
Wind speed and direction Air Sentry mod 03002-5
R.M. Young Company
03002–5 Biannual ±0.3 m/s
±3°
Fig. 4. Phenomena involved in the performance of the solar still.

37
the air enclosed between the evaporating and condensing
surface and is called internal convection. The amount of
heat transferred by this phenomenon can be calculated by
the following expression, which is modeled by Newton’s
cooling Law:
q h T T
c w g c w g
, −
= −
( ) (8)
The heat lost by the cover towards the atmosphere by
radiation is calculated with the following expression:
q T T
r g g
,
.
−
= −
( )
air sky
0 9 4 4
σ (9)
The exterior temperature depends on the amount of
water vapor and dust in the atmosphere, which will be
manifested in an increase in the heat reflectance of the soil.
The used Eq. (10) to find this value is [18]:
T T T
sky air dp
= + ( )




0 74 0 006
0 25
. .
.
(10)
where Tdp
is the dew point temperature of the ambient air
and can be calculated by [19]:
T
K
T
T K
T
dp
amb
amb
am
=
∅ +
+






− ∅ +
237 3
17 27
237 3
17 27
17 27
. ln
.
.
. ln
. b
b
amb
T K
+






237 3
.
(11)
The heat transfer by convection between the glass cover
and the ambient air is given by:
q h T T
c g g g
, −
= −
( )
air air (12)
The following Eq. (13) calculates the coefficient of heat
transfer by convection between the booth and the air:
h k L
g L f g g
= +
( )
Nu Nu
1 3
/
/ (13)
The energy balance Eq. (14) for the absorber is
calculated by:
m
dT
dt
q q q q
b b
b
r b c w b k x
Cp = − − +
( )
−
, ,
(14)
The heat transfer coefficient for the equation that mod-
els this convection is calculated according to the following
equation:
q h T T
c w b b w b
, −
= −
( ) (15)
The heat transfer coefficient between the water and the
absorber (qc, w–b
), is calculated using the following Eq. (16) [20]:
h
k
L
b
w
b
= Nu (16)
The last term in the Eq. (17) represents the heat losses by
conduction of the base and sides of the absorber into ambient
air and is modeled by Fourier’s law:
q q
k T T
L
k x
b b
b
+
( ) =
−
( )
amb
(17)
The energy balance Eq. (18) for the insulation of the
absorber is:
m
dT
dt
q q q
k x
in in
in
loss
Cp = +
( )− (18)
The heat loss by the insulator can be written:
q U T T
loss in in air
= −
( ) (19)
The total heat transfer coefficient of the insulator Uin
is
calculated by:
U
L
k h
in
in
in in
= +








−
1
1
(20)
In the same way as in the previous two Eqs. (19) and
(20), the convection coefficient (hin
) is calculated by the
Dunkle [15]:
h
k
L
in in
air
in
Nu
= (21)
The energy balance Eq. (22) of water is calculated by:
m
dT
dt
I q q q q
L
w w
w
w g c w b r w g c w g
w w w
Cp
Cp
ev
=
+
( )− + +
( )




− − −
α τ
ρ
, , ,
(22)
kw
is the water thermal conductivity and Lb
is the charac-
teristic length of the copper plate, evaluating both the base
and the height of the basin.
2.5.1. Numerical solution and computational model
The theoretical study presented is based on the experi-
mental results carried out in a DSSS. An acrylic sheet 3 mm
thickness was adapted on the glass cover with an opti-
cal transmission in the visible interval of 80.7% to create a
“wind tunnel” and the greenhouse effect. Three fans were
placed symmetrically to ensure a uniform air flux through-
out the inner surface of the roof (forced convection). This
airstream over the hot sheet enhances the heat convection
phenomenon. The parameters that affect the equations
of gain and loss of the energy in the solar still depends on
the climatic conditions during the day, Fig. 5. To evaluate
these equations, different heat values that depend on the
temperatures must be determined. The modeling process
begins with a proposed value for each temperature of the
glass cover Tg,t
, absorber Tb,t
insulator Tin,t
and water Tw,t
. The
ambient temperature is considered as a starting point for

38
all equations. To solve these equations, we used the finite
difference method [21]. Eqs. (6)–(9) were discretized and
Access software was used as a computational tool to imple-
ment the solution. The simulation was performed using 1 h
between two successive iterations ∆t = 1 h.
T
t
S G q q q
q
g t t
g g
t
t r w g t c w g t
r g t
,
, , , , ,
, ,
+
− −
−
=
( ) + + +
( )
( )
−
∆
∆
α α ev
amb
−
−








+
−
q
m
T
c g t
g g
g t
, ,
,
amb
Cp
(23)
T
t q q q q
m
T
b t t
b t c w b t k x t
b b
b t
,
, , ,
,
+
− ′
=
+
( )− +
( )



 +
∆
∆
Cp
(24)
T
t q q q
m c
T
t t
k x t
t
t
in
loss
in in
in
, ,
+
′
=
+
( ) −



 +
∆
∆
(25)
T
t S I q q q q
w t t
w g d
t
c w b t r w g t c w g t t
,
, , , , , , ,
+
− − −
=
( ) +
( )− + +
( )

∆
∆ α τ ev






ρw w w
L
Cp
(26)
To calculate the instantaneous distilled water for time t,
we used the following equation:
Pro ev
fg
=
Q
h
(27)
A table with real-time temperature values of the cover,
absorber, insulator, and water, is also introduced into the
program. These initial temperatures are used to solve the
equations of each heat transfer type (radiation, convection,
and evaporation). The obtained heats are utilized in each
new discretized equation.
2.5.2. Physical model
The experimental results it was complemented by per-
formed simulations using the computational fluid dynamics
technique, with a general-purpose commercial computing
program Fluent from the company ANSYS (Headquartered
in the United States, South of Pittsburgh in Canonsburg,
Pennsylvania) [22]. This software includes design tools in
three dimensions (3D), the solution of the mathematical
equations that represent the phenomena studied, such as
heat transfer, etc., is obtained by the finite volume method
(FVM), through a process of discretization finding approx-
imate solutions of partial differential equations [23]. The
simulation consists of four stages: (i) design and definition
of properties of the materials, (ii) mesh or sub-division of
the 3D space, (iii) solution of the equations by the FVM [24],
and (iv) presentation of results and analysis (flow chart of
Fig. 6 [25]). This simulation is useful to know the speed and
temperature fields inside solar water still. The design was
made according to the physical dimensions and materials of
the manufactured still. For the mesh of the still, 405,970 vol-
umes of the tetrahedron type was used (Fig. 7). The elements
quality of the mesh was evaluated using the parameter of
“angle bias” and the equiangular and equi-size skew. These
two parameters are less than 0.5 for 92% and less than 0.25
for 51% of the elements; a value = 1 means a high bias of the
elements, which causes erroneous results.
3. Results and discussions
In order to analyze the production of distilled water,
experiments with two solar stills working with seawater and
drinking water, natural convection, and functioning simulta-
neously. Fig. 8 shows the water production obtained in each
still. It can be seen that regardless of the solar energy received,
daily production decreases as the salt concentration increases.
However, salt concentration has no significant influence on
the final amount of distilled water. Therefore, with a solar
resource of 4.2 kWh/m2
, the average water production is 0.58
and 0.56 L, while for a solar resource of 3.6 kWh/m2
, 0.49 and
0.47 L are obtained with fresh seawater, respectively. These
values are in good agreement with the literature [26,27].
For the brackish water case, initial concentration
was 24 ± 0.1 g/L, and remaining not distilled water has a
27.4 ± 0.1 g/L concentration. These results are consistent
with those obtained by [28,29].
Fig. 5. Climatological parameters affecting distillation.

39
The use of a conductivity meter Thermo Scientific Orion
Star A212 brand provided information to determine the
salinity of seawater (range from 0.001 to 3,000 µS, 0.001 µS,
and accuracy of 0.5%).
Fig. 9 shows a comparison between the irradiance and
temperatures measured in the black tray at the different
air velocities analyzed. It can be seen that at 6.9 m/s speed,
ambient temperature is higher than the outside glass because
the glass cools, inferring that under these conditions, there
will be less condensation and, consequently, a decrease
in water production.
3.1. Comparison of the theoretical model with the
experimental data
Fig. 10 shows experimental and theoretical temperatures
as a function of time. For all temperatures (Tb
, Tg
, Tw,
and
Tin
), simulation and experimental results are similar. When
the irradiance is lower, all these temperatures are almost
the same. However, at midday (high irradiance) where the
temperature reaches its maximum, the difference between
them is significant.
Fig. 11 presents a comparison between the measured
irradiance and water production. In this case, the tempera-
ture rises and enhances the evaporation, which augments
the still efficiency. Also, is presented the experimental
results of distilled water and the estimated production
by the theoretical model on the same day at 3.5 m/s wind
speed. The maximum water yield is obtained approxi-
mately at 13:00 h in both cases. Moreover, the theoretical
and experimental curves have almost the same qualitative
and quantitative behavior. The average deviation was
±0.052 L/h. The impact of the wind speed on the produc-
tion of distilled water is directly related to the temperature
difference between the glass and the water to be distilled.
It increases with the decrease in the temperature of the
roof. The heat transfer by convection from the deck to the
ambient air increases when the heat transfer by evaporation
and convection between the water and the house increases.
These results are consistent with those reported in [30].
Table 2 shows data obtained in the still with different
wind speeds. During test days, the average maximum irra-
diance (800 W/m2
) was presented at noon, corresponding
to 5.53 kWh/m2
daily, and the amount of distilled water
obtained was 0.7 L.
3.2. Simulation
For the simulation of the solar stills behavior, it is nec-
essary to consider the properties of the used materials in
the experiments, such as mass density, specific heat, ther-
mal conductivity, among others, not to underestimate or
overestimate the obtained results. It is necessary to reach
the number of iterations until the solution of the equations
converges to a fixed value, usually is 0.001 for the continuity
and momentum conservation equations and 1 × 10–6
for the
energy equations. Once this value is reached, it is possible
Fig. 6. Flow chart of the finite volume method. Adapted from [20].
Fig. 7. Isometric view of the still’s design with the mesh.
Fig. 8. Water production based on the solar energy received in
the collector.

40
to find the variables information. The distribution of the
wind speed vectors inside the double slope is presented at
the left of Fig. 12. The bottom temperature of the wind tun-
nel is higher, which decreases the air density in this region;
thus, the wind speed augments. The increasing of the forced
convection decreases the solar still temperature, as shown at
the right of Fig. 12. Hence, this effect accelerates heat transfer
from the absorber to the top, and then the water temperature
is reduced.
The effect of wind speed on the temperature distribution
on the surface of the absorber was also analyzed. The initial
temperature of the absorber is 80°C. It is evident that the tem-
perature on the surface of the absorber decreases with higher
speed; these results are shown in Fig. 13. However, the area
that is interesting to cool, that is, the glass cover, would allow
a higher rate of water vapor condensation, and this should
be reflected directly in an increase in the efficiency of water
distillation.
Nevertheless, another satisfying result of this investi-
gation shows the dependence of water production on wind
speed, as shown in Fig. 14. For low wind speed v ≤ 5.5 m/s,
the water production increases with increasing wind speed.
After this critical speed, water production does not exhibit
a linear relationship with wind speed. In this case, water
production shrinks with the augmentation of wind speed.
Furthermore, we can have maximum production with
two speeds; 5.5 and 3.5 m/s. Nevertheless, this last wind
speed is the optimum one because we can have maximum
water production with a minimum energy consumption.
This theoretical result is in good agreement with experi
mental findings in [12].
Fig. 9. Comparison between the irradiance and temperatures
in the black tray at 2.5, 3.5, 5.5, and 6.9 m/s.
Fig. 10. Theoretical and experimental temperatures during
the day.
Fig. 11. Experimental and theoretical water production during
the day.
Table 2
Comparison of the production of distilled water at different wind speed concerning the solar radiation received.
Average speed
(m/s)
Average irradiation
(kWh/m2
)
Solar energy received
in the collector (kWh)
Distilled water*
obtained (L/d)
h (%)
2.5 5.22 0.860 0.61 46.4
3.5 5.18 0.854 0.75 58.0
5.5 4.91 0.810 0.76 62.3
6.9 5.10 0.842 0.62 48.9
*Manufacturer specified error (scales Tor-Rey): ±0.05 kg

41
4. Conclusions
The thermal behavior of two stills built working with
natural convection was analyzed. It is found that under
the conditions in which the experiment was conducted,
the water production is not affected by the salinity. With
a typical solar resource of 4.2 kWh/m2
, the analyzed
house still is capable to produce 0.58 L/d in the winter. By
increasing the wind speed from 0 to 6.9 m/s, the volume
of distilled water is increased to a maximum value that is
reached when the glass cover has the same temperature
as the environment. This result is achieved when wind
speed is 5.5 m/s. Moreover, the volume of water obtained
was 0.76 L at 4.9 kWh/m2
. The efficiency obtained for
these values is 62.3%, which is higher than the researcher
Fig. 12. Vectors speed in the double slope (left). Temperature profiles inside the house and the absorber at different speed (right):
(a) 2.5 m/s, (b) 3.5 m/s, (c) 5.5 m/s, and (d) 6.9 m/s.
Fig. 13. Temperature distribution at the base of the absorber for different wind speed: (a) 2.5 m/s, (b) 3.5 m/s, (c) 5.5 m/s, and (d) 6.9 m/s.

42
Cooper estimate for single-house distillers without the
influence of roof cooling. For higher speed, the glass tem-
perature was lower than that of the environment, which
decreases the volume of distilled water.
Acknowledgments
The authors are grateful for the academic and finan-
cial support to develop this research to the Universidad
Politécnica del Estado de Guerrero, and M.C. Guadalupe
Manuel Estrada Segovia, Director of the Facultad de
Ingeniería of the Universidad Autónoma de Campeche.
Symbol
a — Absorbance, 1
h — Efficiency, 1
ρ — Mass density, kg/m3
t — Transmittance, 1
cp
—
Specific heat, J/kg/K
h —
Convective heat transfer coefficient, W/m2
/K
hfg
—
Latent heat of vaporization, J/kg
H —
Total exposure time, h
I, G — Solar irradiance, W/m2
k —
Thermal conductivity, W/m/K
L —
Length, thickness, depth, m
m —
Mass, kg
Nu — Nusselt number, 1
P —
Solar power, W
Pro — Production of distilled water, L
q —
Heat rate transfer, W
Q —
Energy transfer, J
S —
Surface of tray, m2
t —
Time, S
T —
Temperature, K
U —
Total heat transfer coefficient, m2
/K/W
V —
Distillate volume, L
Subscripts
a, air — Air
amb — Ambient
b — Basin or tray
c — Convective
d — Diffuse
dp — Dew point
ev — Evaporative
g — Glass
in — Insulator
k — Vertical tray thickness
loss — Losses
r — Radiative
u — Upper
w — Water
x — Horizontal tray thickness
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