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Mathematical model of the solar still performance using forced convection with condensation process outside the still
Renewable Energy Vol. t, No. 5/6, pp. 709-712, 1991 Printed in Great Britain.
0960--1481/91 $3.00+.00 Pergamon Press plc
MATHEMATICAL MODEL OF THE SOLAR STILL PERFORMANCE USING FORCED CONVECTION WITH CONDENSATION PROCESS OUTSIDE THE STILL H. M. ALl Department of Mechanical Engineering, Amirkabir University of Technology, P.O. Box 15875/4413 Tehran, lran (Received 4 April 1990 ; accepted 5 February 1991)
Abstract--In this study a mathematical model is used to predict the performance of the solar still using forced convection inside the solar still to enhance the productivity of the still. Experimental study on the enhancement of solar still productivity using forced convection with condensation outside the still, shows that the productivity increases about 60% more than that of a natural convection solar still. The results of this theoretical study show that there is a relationship between the Reynolds number and the still productivity. Good agreement between the theoretical and experimental results is obtained. Enhancing mass transfer coefficients due to forced convection has a major role in the productivity enhancement.
MATHEMATICAL ANALYSIS
INTRODUCTION
The solar still is a device used to produce fresh water from saline water, where the heating source is a renewable energy, i.e. solar energy, the solar still is an airtight basin of rectangular shape made from galvanized iron or concrete, and covered by glass to trap the solar energy inside the still. The condensed vapour at the interior surface o1~ the glass is collected at the glass sheets bottom. The solar still, can be used efficiently in remote areas, since it is cheap and has a low technology. The main problem of the solar still is its low productivity. The yearly average output is about 3 litres per day in moderate climate areas. The forced convection in the solar still is generated by a fan in one side of the still moving the air-vapour mixture to a channel connected to the still in this side and leaving the still again in the other side. The experimental results (1), show that there is about 60% increase in the still productivity. In this theoretical study, parameters causing this increase are studied using a mathematical model. The results are compared to the results for the cases with natural convection and also with forced convection but with no condensation outside the the still. The results of these two cases are given in [2].
The total distilled water per unit time is given by : mt = mey + mec
(1)
meg is calculated by : me# = hm( C m - C#)
(2)
hrn = Sh D / d
(3)
hm is given by :
Sh is found from (3) Sh = 0.037 Re °'8 Sc °'33.
(4)
Equation (4) is found by making analogy to forced convection heat transfer between a main flow stream and a solid body : N u = 0.037 Re °'8 Pr °'33.
(5)
This analogy is found to be correct for Re up to 150,000 (3). Above this value the waves effect should be included. In this analysis eq. (4) is used since Re is less than 150,000. The wave action from another point of view is found to enhance the surface area by 5%, (4) Cm is given by :
The proofs of this article were corrected by the Editor in place of the author.
Cm = M m P m / R Tm
709
(6)
710
H.M. A u
cy is computed by :
:•::
c# = My Pg/R Ty.
se
For the range of temperature in solar still, the partial pressure is given by : p = C1 T+C2.
re/
withoutinsutoted
(~
wtth Insutat.ed ¢l~nnek 52 t - - Q ) ' ~
(8)
The free stream, glass water, bottom black layer and channel temperatures are found from energy balance nce equation :
I. Forced convection .itnout ir~ut, t~U chw~et
,,~
6o J-
(7)
' ~
I~
-I-
"b
It
cL
3, Noturol. convection
",\'t ',\l
Iq
'¢t
= ,, E I.i
Mm d Tm/dt = A w(Qcw + Qew) -
Ay(Qcg + Qe#) - Ac(Qcc + Qec)
My d Tg/dt = Ag(~g Hs + Qrw + Qcg + Q e g - Q r a - Qca)
(10)
,~' 26 ~ -
- ---x--
W ~ e r 'temp. G ~ s s temp.
24[--
___
~.ow temp.
22F' I'/'['lWOI~t chOnnettem~ Ili i IiI III
202
9 I01112131415 ml718 19~021~]~4
Mw dTw/dt = Aw[xw H s - Q r w - Qcw - Qew + hbw(Tb- Tw)]
(11)
xb Hs = hbw(Tb- T w ) + h b ( T b - Ta)
(12)
Mc dTc/dt = Ac[Qcc + Q e c - h c a ( T c - Ta)]
(13)
Qcw is given by : Qcw = h c ( T w - Tm).
111
III
I 2 ~ 4 5 6 7
Time (hr)
(14)
Fig. I. Temperature-time relationship.
ment. But it is seen from Fig. 1 that for acceptable approximation is the same for the three different cases. This may mean that the main reason for the enhancement of the produced water from the still is not due to the temperature role. Figures 2 shows that the theoretical free stream
In similar equation, Qcg and Qcc are found. Qcw is calculated by : Qew = m w L
(15) 60
in the similar way Qeg and Qec are calculated.
56
• "e"
~4
Qrw is found from :
/.C .,x
50
Qrw = (Tw 4 - Tg4)/(1/sw+ l/e,y- l)
(16)
Qra is calculated by : Qra = eg6(Tg+273)4-[(Ta - 12)+273) 4]
I. W a t e r temp.
2. GLass
£ ~46
temp.
3. FLow temp.
W(~f/x~]~xx~X 4. WottchonneL"temp.
,4 E
(17)
¢. ~oL ~ ."-./'~,~.-.
-,
Qca is given by (5) : Qca = hca[Tg- (4.5 + 2.9 V)].
(18) 26
RESULTS AND DISCUSSION It is seen from the theoretical analysis that the temperature of water, glass, free stream and channel has one of the main effects on the productivity enhance-
::L I011 121314151617181920212223241 Time (hr)
3 4 5 6 7
Fig. 2. Temperature-time relationship.
Mathematical model to predict solar still performance temperature is in good agreement to the experimental one. This shows that the assumed average temperature of the free stream in the whole of the system is correct. Good agreement is also seen from the figure for water, glass and channel, theoretical and experimental temperatures. Figure 3 gives clear picture to the parameters affecting the productivity enhancement. The results show that the heat and mass transfer coefficients have a major role in the enhancement of the productivity. Since there is a very large percentage of the noncondensable gas in the air-vapour mixture, hence forced convection is found to have very small effect in reducing the non-condensable gas amount in the condensation area, so that condensation cannot be improved (6). The Reynolds number with the productivity relationship is shown in Fig. 4. The figure shows that there is an optimum value to the productivity. Increasing the Reynolds number causes an increase in mass transfer coefficient, i.e. increasing productivity, but in same time this causes heat to be lost more from water and free stream. So that more heat is added to the glass and channel making the concentration difference less, and then the productivity which depends on this difference will be reduced. The figure shows that about 220% enhancement in the productivity is obtained with increasing Reynolds number. It is also seen from this figure that for low range of Reynolds number, the productivity
711
I. Forced convection without insulated channeL
~ j].i "
3
--
2
i
?_ Forced convection with insulated channel
I
I
I
I
I
I
I
2ooo -
ExperimentaL ¢ondensot ion outside
o,e'e
TheoreticaL condensation outside
/ \ / /+r+,.Q(" /]
~!
\~
"~
/
Experimental condensation inside
/
t5oo -
Effect
II ~ < / ~ " ~
~:
*o0o
/
/
of waves
Effect. of forced Natural convection
.E
5coI~/I%/III I I i I I I I e
9 I01112 13 141~ 16 171~19L:=021;>~24 1 2 3 4 5 Time (hr]
I 678
Fig. 3. Water productivity during daily hours.
I
Fig. 4. Productivity of forced to natural convection ratio-Reynolds number.
with forced convection is less than that with natural one. The mass and heat transfer coefficients with low Reynolds number are smaller than that for natural convection.
NOMENCLATURE j
I
10'300 21100 31700 4~E)0 52800 63~0 ?3E~ 84400 Re I I I I I I I I 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.3 u[m/s)
A a b C Ca
c C1, C2 D d e g h L M Nu m m P Pr Q R Re ra
Sc Sh
area air bottom surface concentration convection with air channel constants coefficient hydraulic diameter evaporation glass heat transfer convection coefficient latent heat thermal mass Nusselt number free stream rate of condensed mass pressure Prandtl number heat transferred gas constant Reynolds number radiation Schmidtnumber Sherwood number
712
H. M. ALl T v w 6 e z
temperature velocity water Stefan-Boltzman emissivity absorptance.
3.
4.
REFERENCES 1. H. M. Ali, Experimental study on the air motion effect inside the solar still on the still performance. Proceedings of The North Sun 88 Conference, Borlange, Sweden, 2931 August (1988). 2. H. M. Ali and A. Ardakani, Effect of the forced convection inside solar still on heat and mass transfer
5. 6.
coefficients. Proceedings of CSME Mechanical Engineering Forum, Toronto, Canada (1990). T. Kumada, T. Hirota, N. Tamura and R. Ishiguro, Heat and mass transfer with liquid evaporation into a turbulent air stream. J. Heat Trans. Transaction of the ASME, Vol. 108 (1986). N. C. G. Markatous, Phenomenological correlation for heat and mass transfer through wavy interfaces. La Termotecnica 111(2), (1979). J. Duffle and W. Beckman, Solar Thermal Processes. John Wiley, New York (1974). V. E. Denny, A. F. Mills and V. J. Jusionis, Laminar film condensation from a stream-air mixture undergoing forced flow down a vertical surface. J. Heat Trans. Transactions of the ASME, Paper No. 71-HT-E (1971).
0960--1481/91 $3.00+.00 Pergamon Press plc
MATHEMATICAL MODEL OF THE SOLAR STILL PERFORMANCE USING FORCED CONVECTION WITH CONDENSATION PROCESS OUTSIDE THE STILL H. M. ALl Department of Mechanical Engineering, Amirkabir University of Technology, P.O. Box 15875/4413 Tehran, lran (Received 4 April 1990 ; accepted 5 February 1991)
Abstract--In this study a mathematical model is used to predict the performance of the solar still using forced convection inside the solar still to enhance the productivity of the still. Experimental study on the enhancement of solar still productivity using forced convection with condensation outside the still, shows that the productivity increases about 60% more than that of a natural convection solar still. The results of this theoretical study show that there is a relationship between the Reynolds number and the still productivity. Good agreement between the theoretical and experimental results is obtained. Enhancing mass transfer coefficients due to forced convection has a major role in the productivity enhancement.
MATHEMATICAL ANALYSIS
INTRODUCTION
The solar still is a device used to produce fresh water from saline water, where the heating source is a renewable energy, i.e. solar energy, the solar still is an airtight basin of rectangular shape made from galvanized iron or concrete, and covered by glass to trap the solar energy inside the still. The condensed vapour at the interior surface o1~ the glass is collected at the glass sheets bottom. The solar still, can be used efficiently in remote areas, since it is cheap and has a low technology. The main problem of the solar still is its low productivity. The yearly average output is about 3 litres per day in moderate climate areas. The forced convection in the solar still is generated by a fan in one side of the still moving the air-vapour mixture to a channel connected to the still in this side and leaving the still again in the other side. The experimental results (1), show that there is about 60% increase in the still productivity. In this theoretical study, parameters causing this increase are studied using a mathematical model. The results are compared to the results for the cases with natural convection and also with forced convection but with no condensation outside the the still. The results of these two cases are given in [2].
The total distilled water per unit time is given by : mt = mey + mec
(1)
meg is calculated by : me# = hm( C m - C#)
(2)
hrn = Sh D / d
(3)
hm is given by :
Sh is found from (3) Sh = 0.037 Re °'8 Sc °'33.
(4)
Equation (4) is found by making analogy to forced convection heat transfer between a main flow stream and a solid body : N u = 0.037 Re °'8 Pr °'33.
(5)
This analogy is found to be correct for Re up to 150,000 (3). Above this value the waves effect should be included. In this analysis eq. (4) is used since Re is less than 150,000. The wave action from another point of view is found to enhance the surface area by 5%, (4) Cm is given by :
The proofs of this article were corrected by the Editor in place of the author.
Cm = M m P m / R Tm
709
(6)
710
H.M. A u
cy is computed by :
:•::
c# = My Pg/R Ty.
se
For the range of temperature in solar still, the partial pressure is given by : p = C1 T+C2.
re/
withoutinsutoted
(~
wtth Insutat.ed ¢l~nnek 52 t - - Q ) ' ~
(8)
The free stream, glass water, bottom black layer and channel temperatures are found from energy balance nce equation :
I. Forced convection .itnout ir~ut, t~U chw~et
,,~
6o J-
(7)
' ~
I~
-I-
"b
It
cL
3, Noturol. convection
",\'t ',\l
Iq
'¢t
= ,, E I.i
Mm d Tm/dt = A w(Qcw + Qew) -
Ay(Qcg + Qe#) - Ac(Qcc + Qec)
My d Tg/dt = Ag(~g Hs + Qrw + Qcg + Q e g - Q r a - Qca)
(10)
,~' 26 ~ -
- ---x--
W ~ e r 'temp. G ~ s s temp.
24[--
___
~.ow temp.
22F' I'/'['lWOI~t chOnnettem~ Ili i IiI III
202
9 I01112131415 ml718 19~021~]~4
Mw dTw/dt = Aw[xw H s - Q r w - Qcw - Qew + hbw(Tb- Tw)]
(11)
xb Hs = hbw(Tb- T w ) + h b ( T b - Ta)
(12)
Mc dTc/dt = Ac[Qcc + Q e c - h c a ( T c - Ta)]
(13)
Qcw is given by : Qcw = h c ( T w - Tm).
111
III
I 2 ~ 4 5 6 7
Time (hr)
(14)
Fig. I. Temperature-time relationship.
ment. But it is seen from Fig. 1 that for acceptable approximation is the same for the three different cases. This may mean that the main reason for the enhancement of the produced water from the still is not due to the temperature role. Figures 2 shows that the theoretical free stream
In similar equation, Qcg and Qcc are found. Qcw is calculated by : Qew = m w L
(15) 60
in the similar way Qeg and Qec are calculated.
56
• "e"
~4
Qrw is found from :
/.C .,x
50
Qrw = (Tw 4 - Tg4)/(1/sw+ l/e,y- l)
(16)
Qra is calculated by : Qra = eg6(Tg+273)4-[(Ta - 12)+273) 4]
I. W a t e r temp.
2. GLass
£ ~46
temp.
3. FLow temp.
W(~f/x~]~xx~X 4. WottchonneL"temp.
,4 E
(17)
¢. ~oL ~ ."-./'~,~.-.
-,
Qca is given by (5) : Qca = hca[Tg- (4.5 + 2.9 V)].
(18) 26
RESULTS AND DISCUSSION It is seen from the theoretical analysis that the temperature of water, glass, free stream and channel has one of the main effects on the productivity enhance-
::L I011 121314151617181920212223241 Time (hr)
3 4 5 6 7
Fig. 2. Temperature-time relationship.
Mathematical model to predict solar still performance temperature is in good agreement to the experimental one. This shows that the assumed average temperature of the free stream in the whole of the system is correct. Good agreement is also seen from the figure for water, glass and channel, theoretical and experimental temperatures. Figure 3 gives clear picture to the parameters affecting the productivity enhancement. The results show that the heat and mass transfer coefficients have a major role in the enhancement of the productivity. Since there is a very large percentage of the noncondensable gas in the air-vapour mixture, hence forced convection is found to have very small effect in reducing the non-condensable gas amount in the condensation area, so that condensation cannot be improved (6). The Reynolds number with the productivity relationship is shown in Fig. 4. The figure shows that there is an optimum value to the productivity. Increasing the Reynolds number causes an increase in mass transfer coefficient, i.e. increasing productivity, but in same time this causes heat to be lost more from water and free stream. So that more heat is added to the glass and channel making the concentration difference less, and then the productivity which depends on this difference will be reduced. The figure shows that about 220% enhancement in the productivity is obtained with increasing Reynolds number. It is also seen from this figure that for low range of Reynolds number, the productivity
711
I. Forced convection without insulated channeL
~ j].i "
3
--
2
i
?_ Forced convection with insulated channel
I
I
I
I
I
I
I
2ooo -
ExperimentaL ¢ondensot ion outside
o,e'e
TheoreticaL condensation outside
/ \ / /+r+,.Q(" /]
~!
\~
"~
/
Experimental condensation inside
/
t5oo -
Effect
II ~ < / ~ " ~
~:
*o0o
/
/
of waves
Effect. of forced Natural convection
.E
5coI~/I%/III I I i I I I I e
9 I01112 13 141~ 16 171~19L:=021;>~24 1 2 3 4 5 Time (hr]
I 678
Fig. 3. Water productivity during daily hours.
I
Fig. 4. Productivity of forced to natural convection ratio-Reynolds number.
with forced convection is less than that with natural one. The mass and heat transfer coefficients with low Reynolds number are smaller than that for natural convection.
NOMENCLATURE j
I
10'300 21100 31700 4~E)0 52800 63~0 ?3E~ 84400 Re I I I I I I I I 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.3 u[m/s)
A a b C Ca
c C1, C2 D d e g h L M Nu m m P Pr Q R Re ra
Sc Sh
area air bottom surface concentration convection with air channel constants coefficient hydraulic diameter evaporation glass heat transfer convection coefficient latent heat thermal mass Nusselt number free stream rate of condensed mass pressure Prandtl number heat transferred gas constant Reynolds number radiation Schmidtnumber Sherwood number
712
H. M. ALl T v w 6 e z
temperature velocity water Stefan-Boltzman emissivity absorptance.
3.
4.
REFERENCES 1. H. M. Ali, Experimental study on the air motion effect inside the solar still on the still performance. Proceedings of The North Sun 88 Conference, Borlange, Sweden, 2931 August (1988). 2. H. M. Ali and A. Ardakani, Effect of the forced convection inside solar still on heat and mass transfer
5. 6.
coefficients. Proceedings of CSME Mechanical Engineering Forum, Toronto, Canada (1990). T. Kumada, T. Hirota, N. Tamura and R. Ishiguro, Heat and mass transfer with liquid evaporation into a turbulent air stream. J. Heat Trans. Transaction of the ASME, Vol. 108 (1986). N. C. G. Markatous, Phenomenological correlation for heat and mass transfer through wavy interfaces. La Termotecnica 111(2), (1979). J. Duffle and W. Beckman, Solar Thermal Processes. John Wiley, New York (1974). V. E. Denny, A. F. Mills and V. J. Jusionis, Laminar film condensation from a stream-air mixture undergoing forced flow down a vertical surface. J. Heat Trans. Transactions of the ASME, Paper No. 71-HT-E (1971).