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Water film cooling over the glass cover of a solar still including evaporation effects
Pergamon
WATER SOLAR
PII: S0360-5442(96)00088-6
FILM COOLING
OVER
STILL INCLUDING
THE GLASS
E n e r g y Vol. 22, No. 1, pp. 43-48, 1997 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0360-5442/97 $17.00 + 0.00
COVER
EVAPORATION
OF A
EFFECTS
B A S S A M A / K ABU-HIJLEW'* and H A S A N A. M O U S A ~ *Mechanical and §Chemical Engineering Departments, Jordan University of Science and Technology, P.O. Box 3030, Irbid - Jordan (Received 26 March 1996)
Abstract--The effect of water film cooling of the glass cover on the efficiency of a single-basin still has been investigated numerically. Proper use of the film-cooling parameters may increase the still efficiency by up to 20%. On the other hand, a poor combination of these parameters leads to a significant reduction in efficiency. The presence of the cooling film neutralizes the effect of wind speed on still efficiency. Only a small fraction of the cooling film evaporates as it passes over the glass cover. Copyright © 1996 Elsevier Science Ltd.
INTRODUCTION The use of solar stills as a cheap and easy method for providing clean water dates back to the 16th century. A resurgence of interest has occurred recently with work focused on methods for increasing still efficiency and production rate. The main focus in achieving high efficiency was the temperature difference between the water in the basin and the glass cover. Several improvements have been proposed such as the use of forced convection, I a dye, 2 an external condenser, 3 and distillate condensation on the back of a flat-plate solar collector. 4 Each method has some drawbacks, namely, the need for a controllable air supply, the effects of the dye on distillate quality, the need for an electrical power supply, and a low production rate, respectively. The current work is focused on the flow of a water film over the glass cover in order to reduce the glass temperature. The results are reduced convection and radiation energy losses to the ambient, as well as increased condensation rate on the inside of the glass cover. The presence of a water film with an intermediate index of refraction n = 1.33 between the air with n = 1 and glass with n = 1.52 reduces the fraction of the reflected incident light that is absorbed by the glass cover. The still efficiency is further improved by utilizing a part of the water used for cooling in the form of preheated makeup water to the still. In practice, the cooling film also performs the important function of continuous self cleaning of the glass cover. This is an important consideration given the climatic conditions where such stills are most likely to be employed. The presence of dirt and other types of filth on the glass cover greatly reduces the still efficiency. Continuous cleaning of the glass cover maintains high levels of efficiency and distilled water-production rates with little or no maintenance. MATHEMATICALMODEL An energy balance for the still is performed for the following four components: the basin, water in the basin, glass cover, and water in the cooling film. These energy balances are based on the average temperature for each component (Fig. 1). All equations are written per unit area of still. The areas of the glass cover and basin are assumed to be equal. The energy balance equations are mbCpb(dTb/dt) mwCpw(dTw/dt)
(1)
= (1 - G ) (1 - a s ) (1 -- a w ) I - qbw -- qb,, = ( 1 - G) ( 1 - ag) aJ
*Author for correspondence. 43
+ qbw -- q , ~ -- qcw
-
qe -- qmw,
(2)
44
B. A/K Abu-Hijleh and H. A. Mousa
1
I
\ 1 1 Xe
~---~
x,
rfl
Volf
rg
Fig. 1. Sketch of the solar still.
mgCpg(dTg/dt) = (1
-
rg) as.I+
q~
+ q ~ , + q~ -
h~c(T s -
Ty),
mFpc( dTcCdt ) = mr1( Cp,T~ - Cp2T~) + h4( Tg - Tf) - q~. - qrf- q~
(3) (4)
where T: is the average film temperature between T: and T:2. The suitability of the first three equations for predicting solar-still performance accurately has been well established. I-5 The last term in Eq. (3) represents convective heat transfer between the cooling film and glass cover and is calculated by using the equation for laminar flow over a flat plate, 6 which leads to the convective heat-transfer coefficient. hcf= 0.664 (kf/L) Re[/2 x Pr 1/3.
(5)
The Reynolds number was in the laminar regime for all cases included in this paper. Should turbulent flow conditiions arise, Eq. (5) must be replaced by the equation for turbulent flow over a fiat plate: The last term in Eq. (4) represents heat transfer due to water evaporation associated with cooling. It is calculated by using an analogy between heat and mass transfer over a flat plate, 7 viz.,
q./=
O.O37MairPa,m Sc2/3R h/g ~
Vy
[Patm~ Pv(Ta.wet)] In [ Patm -- Pu(Tf) J"
(7)
The mass-flow rate of the film is assumed to be constant. This assumption was later verified by calculating the mass fraction of cooling water evaporated from the cooling film. This mass fraction ranged from zero to a maximum of 0.5%. All film properties are evaluated at T:. The cooling water inlet temperature T~ was assumed to be equal to the ambient temperature T,. Equations (1--4) were evaluated numerically using a first-order backward difference formula. In the following section, the steady-state efficiency of the still 7/is compared with that of a conventional still operating under the same conditions. RESULTS AND DISCUSSION The following reference values were used for the parameters in all calculations except for the value of the parameter being investigated: solar radiation = I = 1000 W / m 2, wind speed = V, = 0 m/s, ambient temperature = T, = 35°C, film thickness = xz = 2E-4 m, volumetric flow rate of cooling water per unit
Water film cooling of a solar still
45
70
-o- C o n v e n t i o n a l c o o l i n g -~- Film c o o l i n g
/ 65
--
~'~60
~
iii
55
50
45 400
600
500
700
800
900
1,000 1,100 1,200 1,300 1,400
Solar radiation ( W / m 2) Fig. 2. Steady-state efficiency vs incident solar radiation. depth = Vol: = 2E-6 m3/s-m, and humidity ratio = ~b = 30%. Figures 2 and 3 show ~ vs 1 and T,,, respectively. Film cooling resulted in improved efficiency over the entire range of values of I and T~. The change in efficiency varied slightly with I but was very sensitive to T,. This is a direct result of the reduction in Tg, which is more sensitive to T~ than L Figure 4 shows an interesting feature of a still with film cooling. For a conventional still, rl increases at low V~ and then decreases. This finding is consistent with experimental results reported by Clark et al.l For the film-cooled still, rl remained relatively constant. The water film seems to have shielded the glass from the effects of wind speed. Temperature results showed both T~ and Tw to be insensitive to V~ when film cooling was used. Figure 5 shows the percentage change of "O with xy and Voly. The change in ~ increased initially
72
/ C o n v e n t i o n a l c o o l i n g - - Film c o o l i n g 1
70 68 ~o
66 64
.m_ 62 .o_ w 60 58 56
-
. . . . . . .
y
l
. . . . . . . . . . . . . . . . . . . . . . . . . .
54 0
15
20
25
30
35
40
45
A m b i e n t t e m p e r a t u r e (o(3) Fig. 3. Steady-state efficiency vs ambient temperature.
50
55
60
46
B. A/K Abu-Hijl~ and H. A. Mousa
65 64 63 62 61
._o 6 0 tl:: ill
59
58 57 56 0
1
2
3
4
5
6
7
8
9
0
Wind speed (m/s) Fig. 4. Steady-state efficiency vs wind speed.
15 10 5 o ~" .c_
-5
~ -10 I-
e-
-20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-25 -=- F,Im flow rate -I- F,Im t h m k n e s s -30 • , , 1 E-07 1 E-06 1 E-05 1 E-04
I 1 E-03
1 E-02
Film t h i c k n e s s (m) & flow rate (m 3/s-m) Fig. 5. Percentage change in the steady-state efficiency vs the cooling-film thickness and volumetric flow rate per unit glass area.
with Xf and Volf up to a maximum and then decreased rapidly. Decreasing xf and/or increasing Vol/ increases the water speed and thus h~f For moderate values of h e Ts decreases with little effect on Tw and, therefore, there is a higher temperature differential and thus enhanced distillate production and still efficiency at moderate xs and Volt A high value of h o, results in high energy loss from the glass and a substantial reduction in T8. A very low value of T8 leads to excessive convective heat loss from the water in the basin to the glass cover, which greatly reduces the fraction of I used to evaporate the water in the basin. A low distillate production rate translates into low ~. Increasing 4) from 0 to 100% results in a slight reduction in the percentage change of ~1 from 12.8
Water film cooling of a solar still
47
12.9 12.8
12.7 o~" 1 2 . 6
~" 12.5 .~_ a) t ~ 12.4 t-
r- 12.3 12.2
12.1
12
,
0
10
i
20
~
30
40
,
i
,
l
i
50
60
70
80
90
100
Humidity ratio (%) Fig. 6. Percentage change in the steady-state efficiency vs the ambient relative humidity.
to 12.0% (Fig. 6). This small change in efficiency suggests that the heat loss due to water evaporation from the cooling film is small and supports the assumptions made when writing Eq. (4). CONCLUSIONS Film cooling of the glass cover was used to reduce the glass temperature and provide preheated make-up water to the still. A proper combination of cooling film parameters enhanced the still efficiency by up to 20%. On the other hand, a poor choice of the parameters resulted in a reduction in still efficiency. The best combination of film-cooling parameters was x: = 5 E - 4 m and Vol: = 1E-6 m3/s m. rl increased monotonely with increasing I and To but decreased slightly with 4). 7/was not sensitive to Va. REFERENCES 1. 2. 3. 4. 5. 6. 7.
Clark, J., Schrader, J., Grayson, A. and Abu-Hijleh, B. ASME Winter Annual Meeting, Miami Beach, FL, 1985. Lawrence, S., Gupla, S. and Tiwari, G. International Journal of Solar Energy 1988, 6, 291. Nijegorodov, N., Jain, P. and Carlsson, S. Renewable Energy, 1994, 4, 123. Badran, A. and Hamdan, M. International Journal of Solar Energy, 1995, 17, 1. Malik, M., Tiwari, G. N., Kumar, A. and Sodha, M. Solar Distillation. Pergamon Press, Oxford, 1982. Incropera, F. and DeWitt, D. Fundamentals of Heat Transfer. John Wiley & Sons, New York, 1981. Sherwood, T. K., Pigford, R. L. and Wilke, C. H. Mass Transfer. McGraw Hill, New York, 1975. NOMENCLATURE Cp = Heat capacity (J/kg - °C)
he/= Convection heat-transfer coefficient between the glass and film (W/m 2 -
°C)
hyg = Latent heat of vaporization (J/kg) I = Solar radiation normal to the glass cover (W/m:) k:= Thermal conductivity of water used for film cooling (W/m - °C)
M~ir = Molecular weight of air (kg/kmol) m = Mass per unit basin area (kg/m 2) mr/= Cooling water mass-flow rate per unit glass depth (kg/s-m) P = Pressure (Pa) P~(T) = Vapor pressure at T (Pa) Pr = Prandtl number qba = Heat transfer from the basin to the ambient (W/m 2)
48
B. A/K Abu-Hijleh and H. A. Mousa
qbw = Heat transfer from the basin to water in the basin ( W / m 2) qc~ = Heat transfer from the film to the ambient (W/mE) qcg = Heat transfer from the glass to the ambient ( W / m 2) qcw = Heat transfer from water in the basin to the glass (W/m 2) qe = Heat transfer due to evaporation ( W / m 2) qe:= Heat transfer due to evaporation from the cooling film (J/kg) qmw = Heat required to heat make-up water to the basin temperature ( W / m 2) q,: = Radiation heat transfer from the film to the ambient ( W / m 2) qrg = Radiation heat transfer from the glass to the ambient ( W / m 2) q,~ -- Radiation heat transfer from water in the basin to the glass ( W / m 2) R = Universal gas constant (8314 J/kmoI-K) r = Refraction coefficient ReL = Reynolds number based on L
Sc = Schmidt number T = Temperature (°C) t = Time (s) V-- Velocity (m/s) Vol: = Volumetric flow rate of the cooling water per unit depth (m3/s-m) xr= Cooling-film thickness (m) Greek letters a = E= = p= th =
Absorptivity Emissivity Still efficiency (%) Density ( k g / m 3) Relative humidity (%)
Subscripts a = Ambient b -- Basin f = Average value of the film f l = Film inlet f2 = Film exit g = Glass w = Water in the basin wet = Wet bulb temperature
WATER SOLAR
PII: S0360-5442(96)00088-6
FILM COOLING
OVER
STILL INCLUDING
THE GLASS
E n e r g y Vol. 22, No. 1, pp. 43-48, 1997 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0360-5442/97 $17.00 + 0.00
COVER
EVAPORATION
OF A
EFFECTS
B A S S A M A / K ABU-HIJLEW'* and H A S A N A. M O U S A ~ *Mechanical and §Chemical Engineering Departments, Jordan University of Science and Technology, P.O. Box 3030, Irbid - Jordan (Received 26 March 1996)
Abstract--The effect of water film cooling of the glass cover on the efficiency of a single-basin still has been investigated numerically. Proper use of the film-cooling parameters may increase the still efficiency by up to 20%. On the other hand, a poor combination of these parameters leads to a significant reduction in efficiency. The presence of the cooling film neutralizes the effect of wind speed on still efficiency. Only a small fraction of the cooling film evaporates as it passes over the glass cover. Copyright © 1996 Elsevier Science Ltd.
INTRODUCTION The use of solar stills as a cheap and easy method for providing clean water dates back to the 16th century. A resurgence of interest has occurred recently with work focused on methods for increasing still efficiency and production rate. The main focus in achieving high efficiency was the temperature difference between the water in the basin and the glass cover. Several improvements have been proposed such as the use of forced convection, I a dye, 2 an external condenser, 3 and distillate condensation on the back of a flat-plate solar collector. 4 Each method has some drawbacks, namely, the need for a controllable air supply, the effects of the dye on distillate quality, the need for an electrical power supply, and a low production rate, respectively. The current work is focused on the flow of a water film over the glass cover in order to reduce the glass temperature. The results are reduced convection and radiation energy losses to the ambient, as well as increased condensation rate on the inside of the glass cover. The presence of a water film with an intermediate index of refraction n = 1.33 between the air with n = 1 and glass with n = 1.52 reduces the fraction of the reflected incident light that is absorbed by the glass cover. The still efficiency is further improved by utilizing a part of the water used for cooling in the form of preheated makeup water to the still. In practice, the cooling film also performs the important function of continuous self cleaning of the glass cover. This is an important consideration given the climatic conditions where such stills are most likely to be employed. The presence of dirt and other types of filth on the glass cover greatly reduces the still efficiency. Continuous cleaning of the glass cover maintains high levels of efficiency and distilled water-production rates with little or no maintenance. MATHEMATICALMODEL An energy balance for the still is performed for the following four components: the basin, water in the basin, glass cover, and water in the cooling film. These energy balances are based on the average temperature for each component (Fig. 1). All equations are written per unit area of still. The areas of the glass cover and basin are assumed to be equal. The energy balance equations are mbCpb(dTb/dt) mwCpw(dTw/dt)
(1)
= (1 - G ) (1 - a s ) (1 -- a w ) I - qbw -- qb,, = ( 1 - G) ( 1 - ag) aJ
*Author for correspondence. 43
+ qbw -- q , ~ -- qcw
-
qe -- qmw,
(2)
44
B. A/K Abu-Hijleh and H. A. Mousa
1
I
\ 1 1 Xe
~---~
x,
rfl
Volf
rg
Fig. 1. Sketch of the solar still.
mgCpg(dTg/dt) = (1
-
rg) as.I+
q~
+ q ~ , + q~ -
h~c(T s -
Ty),
mFpc( dTcCdt ) = mr1( Cp,T~ - Cp2T~) + h4( Tg - Tf) - q~. - qrf- q~
(3) (4)
where T: is the average film temperature between T: and T:2. The suitability of the first three equations for predicting solar-still performance accurately has been well established. I-5 The last term in Eq. (3) represents convective heat transfer between the cooling film and glass cover and is calculated by using the equation for laminar flow over a flat plate, 6 which leads to the convective heat-transfer coefficient. hcf= 0.664 (kf/L) Re[/2 x Pr 1/3.
(5)
The Reynolds number was in the laminar regime for all cases included in this paper. Should turbulent flow conditiions arise, Eq. (5) must be replaced by the equation for turbulent flow over a fiat plate: The last term in Eq. (4) represents heat transfer due to water evaporation associated with cooling. It is calculated by using an analogy between heat and mass transfer over a flat plate, 7 viz.,
q./=
O.O37MairPa,m Sc2/3R h/g ~
Vy
[Patm~ Pv(Ta.wet)] In [ Patm -- Pu(Tf) J"
(7)
The mass-flow rate of the film is assumed to be constant. This assumption was later verified by calculating the mass fraction of cooling water evaporated from the cooling film. This mass fraction ranged from zero to a maximum of 0.5%. All film properties are evaluated at T:. The cooling water inlet temperature T~ was assumed to be equal to the ambient temperature T,. Equations (1--4) were evaluated numerically using a first-order backward difference formula. In the following section, the steady-state efficiency of the still 7/is compared with that of a conventional still operating under the same conditions. RESULTS AND DISCUSSION The following reference values were used for the parameters in all calculations except for the value of the parameter being investigated: solar radiation = I = 1000 W / m 2, wind speed = V, = 0 m/s, ambient temperature = T, = 35°C, film thickness = xz = 2E-4 m, volumetric flow rate of cooling water per unit
Water film cooling of a solar still
45
70
-o- C o n v e n t i o n a l c o o l i n g -~- Film c o o l i n g
/ 65
--
~'~60
~
iii
55
50
45 400
600
500
700
800
900
1,000 1,100 1,200 1,300 1,400
Solar radiation ( W / m 2) Fig. 2. Steady-state efficiency vs incident solar radiation. depth = Vol: = 2E-6 m3/s-m, and humidity ratio = ~b = 30%. Figures 2 and 3 show ~ vs 1 and T,,, respectively. Film cooling resulted in improved efficiency over the entire range of values of I and T~. The change in efficiency varied slightly with I but was very sensitive to T,. This is a direct result of the reduction in Tg, which is more sensitive to T~ than L Figure 4 shows an interesting feature of a still with film cooling. For a conventional still, rl increases at low V~ and then decreases. This finding is consistent with experimental results reported by Clark et al.l For the film-cooled still, rl remained relatively constant. The water film seems to have shielded the glass from the effects of wind speed. Temperature results showed both T~ and Tw to be insensitive to V~ when film cooling was used. Figure 5 shows the percentage change of "O with xy and Voly. The change in ~ increased initially
72
/ C o n v e n t i o n a l c o o l i n g - - Film c o o l i n g 1
70 68 ~o
66 64
.m_ 62 .o_ w 60 58 56
-
. . . . . . .
y
l
. . . . . . . . . . . . . . . . . . . . . . . . . .
54 0
15
20
25
30
35
40
45
A m b i e n t t e m p e r a t u r e (o(3) Fig. 3. Steady-state efficiency vs ambient temperature.
50
55
60
46
B. A/K Abu-Hijl~ and H. A. Mousa
65 64 63 62 61
._o 6 0 tl:: ill
59
58 57 56 0
1
2
3
4
5
6
7
8
9
0
Wind speed (m/s) Fig. 4. Steady-state efficiency vs wind speed.
15 10 5 o ~" .c_
-5
~ -10 I-
e-
-20
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-25 -=- F,Im flow rate -I- F,Im t h m k n e s s -30 • , , 1 E-07 1 E-06 1 E-05 1 E-04
I 1 E-03
1 E-02
Film t h i c k n e s s (m) & flow rate (m 3/s-m) Fig. 5. Percentage change in the steady-state efficiency vs the cooling-film thickness and volumetric flow rate per unit glass area.
with Xf and Volf up to a maximum and then decreased rapidly. Decreasing xf and/or increasing Vol/ increases the water speed and thus h~f For moderate values of h e Ts decreases with little effect on Tw and, therefore, there is a higher temperature differential and thus enhanced distillate production and still efficiency at moderate xs and Volt A high value of h o, results in high energy loss from the glass and a substantial reduction in T8. A very low value of T8 leads to excessive convective heat loss from the water in the basin to the glass cover, which greatly reduces the fraction of I used to evaporate the water in the basin. A low distillate production rate translates into low ~. Increasing 4) from 0 to 100% results in a slight reduction in the percentage change of ~1 from 12.8
Water film cooling of a solar still
47
12.9 12.8
12.7 o~" 1 2 . 6
~" 12.5 .~_ a) t ~ 12.4 t-
r- 12.3 12.2
12.1
12
,
0
10
i
20
~
30
40
,
i
,
l
i
50
60
70
80
90
100
Humidity ratio (%) Fig. 6. Percentage change in the steady-state efficiency vs the ambient relative humidity.
to 12.0% (Fig. 6). This small change in efficiency suggests that the heat loss due to water evaporation from the cooling film is small and supports the assumptions made when writing Eq. (4). CONCLUSIONS Film cooling of the glass cover was used to reduce the glass temperature and provide preheated make-up water to the still. A proper combination of cooling film parameters enhanced the still efficiency by up to 20%. On the other hand, a poor choice of the parameters resulted in a reduction in still efficiency. The best combination of film-cooling parameters was x: = 5 E - 4 m and Vol: = 1E-6 m3/s m. rl increased monotonely with increasing I and To but decreased slightly with 4). 7/was not sensitive to Va. REFERENCES 1. 2. 3. 4. 5. 6. 7.
Clark, J., Schrader, J., Grayson, A. and Abu-Hijleh, B. ASME Winter Annual Meeting, Miami Beach, FL, 1985. Lawrence, S., Gupla, S. and Tiwari, G. International Journal of Solar Energy 1988, 6, 291. Nijegorodov, N., Jain, P. and Carlsson, S. Renewable Energy, 1994, 4, 123. Badran, A. and Hamdan, M. International Journal of Solar Energy, 1995, 17, 1. Malik, M., Tiwari, G. N., Kumar, A. and Sodha, M. Solar Distillation. Pergamon Press, Oxford, 1982. Incropera, F. and DeWitt, D. Fundamentals of Heat Transfer. John Wiley & Sons, New York, 1981. Sherwood, T. K., Pigford, R. L. and Wilke, C. H. Mass Transfer. McGraw Hill, New York, 1975. NOMENCLATURE Cp = Heat capacity (J/kg - °C)
he/= Convection heat-transfer coefficient between the glass and film (W/m 2 -
°C)
hyg = Latent heat of vaporization (J/kg) I = Solar radiation normal to the glass cover (W/m:) k:= Thermal conductivity of water used for film cooling (W/m - °C)
M~ir = Molecular weight of air (kg/kmol) m = Mass per unit basin area (kg/m 2) mr/= Cooling water mass-flow rate per unit glass depth (kg/s-m) P = Pressure (Pa) P~(T) = Vapor pressure at T (Pa) Pr = Prandtl number qba = Heat transfer from the basin to the ambient (W/m 2)
48
B. A/K Abu-Hijleh and H. A. Mousa
qbw = Heat transfer from the basin to water in the basin ( W / m 2) qc~ = Heat transfer from the film to the ambient (W/mE) qcg = Heat transfer from the glass to the ambient ( W / m 2) qcw = Heat transfer from water in the basin to the glass (W/m 2) qe = Heat transfer due to evaporation ( W / m 2) qe:= Heat transfer due to evaporation from the cooling film (J/kg) qmw = Heat required to heat make-up water to the basin temperature ( W / m 2) q,: = Radiation heat transfer from the film to the ambient ( W / m 2) qrg = Radiation heat transfer from the glass to the ambient ( W / m 2) q,~ -- Radiation heat transfer from water in the basin to the glass ( W / m 2) R = Universal gas constant (8314 J/kmoI-K) r = Refraction coefficient ReL = Reynolds number based on L
Sc = Schmidt number T = Temperature (°C) t = Time (s) V-- Velocity (m/s) Vol: = Volumetric flow rate of the cooling water per unit depth (m3/s-m) xr= Cooling-film thickness (m) Greek letters a = E= = p= th =
Absorptivity Emissivity Still efficiency (%) Density ( k g / m 3) Relative humidity (%)
Subscripts a = Ambient b -- Basin f = Average value of the film f l = Film inlet f2 = Film exit g = Glass w = Water in the basin wet = Wet bulb temperature