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Theoretical and experimental analysis of a simply designed solar retrofitting heating and cooling system
RenewableEnergyVo|. 1, No. 3/4,pp. 513-518. 1991 Printed in Great Britain.
0960-1481/91 $3.00+.00 PergamonPressplc
TECHNICAL
NOTE
Theoretical and experimental analysis of a simply designed solar retrofitting heating and cooling system A. N. AYOOB and R. A. ATTALAGE Centre d'Energ6tique, Ecole Nationale Sup6rieure Des Mines de Paris, Rue Claude Daunesse, 06565 Valbonne, France
(Received 26 June 1990; accepted 31 January 1991) Abstraet--A new design of a solar heating and a passive cooling system was built and operated that uses a water pond as a day time collector in winter and as a night time radiator in summer. The system built incorporates the storage and water pond collector-radiator in a single unit. The heating or cooling effect is transferred to the building by means o f circulating air via ducts. A room size building was built to investigate experimentally the performance of the established heating and cooling system. An energy balance was established in order to obtain the governing equations which were utilised to model the system during its two modes of operation. The calculated and measured values of the water pond (thermal medium) temperature were compared. The system is compact and cheap and can be installed anywhere, especially in rural areas.
1. INTRODUCTION The manner in which heat is provided to the living space in buildings does not necessarily dictate the type o f solar heating and cooling system to be used, but convenience and economy may limit the options. The solar heating and cooling system can be divided into two main types. The first involves the heating of the fluid in a solar panel, its delivery to the storage and the heating medium used directly for heating via fan coil units in winter, or used to activise absorption chillers in summer. The second type, in limited experimental use, involves elimination of fluid circulation by combining the collector or radiator and the storage into a single unit located in or adjacent to the living space (roof pond system). This system uses a water pond with a movable cover as a roof in conventional buildings. The water is exposed to the atmosphere to loose heat through radiation and convection at night and covered at day time for summer cooling. The operation reverses for winter heating. This technique provides a year-round space conditioning with no or minimal use of fossil fuels. Hay and Yellot experimented on a room size building with a roof pond in Phoenix, Arizona and were able to maintain an indoor air temperature between 21 °C and 27°C throughout the year [1]. Another house with three bedrooms using roof pond system was built in Atascadero, California, the system supplied an indoor air temperature between 17°C and 26°C while the outdoor temperature varied from - 1 2 ° C to 43°C [2]. A year long experimental and theoretical study on a building with a roof pond system at Brisbane, Australia showed that it can supply an indoor temperature 18°C-26°C during the whole year. The average ambient temperature varied from 6°C to 37°C [3]. Another experimental summer cooling results for a test structure with roof pond system in Baghdad showed an indoor temperature between 25°C and 27°C when the ambient temperature varied between 35°C and 45°C [4].
In this study a retrofitting solar heating and radiative cooling is described and assessed. It is a combined collectorradiator and storage energy system in a single unit. Unlike a roof pond system this design can be installed at any place in the building. 2. THE DESIGN O F THE SYSTEM A practical air conditioning system utilising radiative cooling in summer and collecting solar radiation in winter has been designed and constructed to air-condition a test room. The collector-radiator and the thermal storage medium are combined in a single unit, Fig. 1. The unit consists of (2 x 1 × 0.2 m) galvanized iron black painted pond which contains a polyethylene bag designed to contain 200 liters of waters as the thermal medium. The buldglng of the base and the sides of the pond under the pressure of the water bag are reduced by using angle iron plates bolted on the sides of the frame. It is drawn as asides, that the water and the water polyethylene bag can absorb the solar radiation in the day time during the heating season, or to radiate to the night sky during the cooling season. The stored heat is conducted to or extracted from the base of the pond which acts as a heat exchanger with the circulated air between the system and the test room. The circulated air is forced via a 5 cm deep passage in the system by means of a small powered fan. A movable insulation cover is provided and located in a place over the structure to prevent night time losses or day time energy absorption during the heating and cooling seasons. The structure rests on settled earth which serves as the floor o f the building. 3. E X P E R I M E N T A L TESTS RESULTS Under actual conditions of sun shine and air velocity, performance of the retrofitting heating and cooling system was 513
514
Technical Note 8 Air streom passo~e 7 Heat e~chonger 6 Supports
. -G.I
.
5 Air Fan
. --
.
4 3 2 I
Air Ducts InsuLotion Cover of poor (movobte) Wooden frame !Item
G.I styropor Wood Wood Mot.
/•//•
,,~
reflector sheet
Fig. 1. Design drawing of the system.
established. Thermocouples points were inserted at various locations in the system. An electronic thermometer was used to record the data. Solar radiation was recorded by an electronic solar meter.
3.1. Heating mode The heating has been tested over the winter season for the evaluation of the thermal performance. The pond was exposed to solar radiation between sunrise and sunset to collect and absorb solar heating which was utilized for charging the circulated air after sunset. Samples of the results are presented in Fig. 2: Ambient and water temperatures, inlet and outlet circulated air temperatures were recorded. It car~ be seen that the water temperature in the polyethylene bag reached 36°C after few hours in a normal sunny day in winter in Baghdad where the test was carried out. This temperature is quite adequate for obtaining warm circulated air for the building.
3.2. Cooling mode Cooling performance of the system was observed in summer system. Figure 3 shows the results during two consecutive days in July. The pond of the system was exposed to the ambient after sunset and covered before sunrise every day. The water depth in the polyethylene bag was kept constant during the period of experimentation. It is clear from this figure that at a rate of 0.18 m 3 s -n of circulating air, the difference between the outlet and inlet system temperatures arranged between 0.5°C and 2.5°C throughout the day, and the test room temperature is always maintained between 27°C and 32°C.
4. ANALYSIS An analysis was carried out for the two principle operating modes, heating and cooling. In order to develop energy bal-
40-~ u m
30-
/
/\
20 - * t ° l I ~
8.0
SoLar r 0 d i o t . i o n
, Wo r
\Exit m "I.__
?,.~
16.0
/
l~
inLetqNb+*'°~..e"
24.0
8.0 T i m e (hr)
~lmls,,.
~
"o-o" ....
16.0
"~'t.+*.
24.0
8.0
Fig. 2. Measured thermal characteristics of the system in the heating mode for two consecutive days.
Technical Note
:50Fl /
•.•. ll"
\
",.
/
o
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""
3oL..+..-..+.,:,.,'++~ +++ + 4,.+,+ .i..i. ~
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. ~ . I . i . t , . i . i , # .e.i.i.#., I
4vi.##,i'i'i'~""
Water pond
-i-o-i-
"-,-",,--r
"i'i'i'i'i#
/ io/
l
I
I
I
I
I
80
16.0
24.0
8.0
16.0
24.0
8,0
Time (hr) Fig. 3. Measured thermal characteristics of the system in the cooling mode for two consecutive days.
ance equations of the water pond, the following assumptions have been made. (i) the system is horizontally installed in such a way that it sees only the sky ; (ii) the bulk mean temperature of water, and that of the polyethylene cover and of the G1 sheet at the bottom are the same at any particular instant after a period of continuous operation ; (iii) the heat capacity of those other than water is neglected ; (iv) side insulation is perfect ; (v) the net radiant heat exchange between the two GI sheets in the passage is neglected compared to other types of heat exchange ; (vi) the water pond is not stratified. In addition, the sky is considered as a blackbody at some equivalent temperature. In fact the atmosphere is not at a uniform temperature and it radiates only in certain wavelength bands (i.e. it is essentially transparent in 8-14 /~m band and has radiating bands covering much of the infrared spectrum). In order to evaluate the equivalent sky temperature the following relationship, proposed by Clark and Berdahl, was used in the analysis [5]. Tsky = f°'25(T~ +273)
(ii) Between sunrise and sunset. in the passage, mrCpf dTr L 2 dx
For the circulating air
hb(T, - Tr)
(3a)
this results, Tw - Tf
~ -- hbL2x]
(3b)
for the water pond, dTw fL, ( M C p ) w ~ - = -- =o h u ( T w - Tr)L2 d x
(4a)
using (3b), dTw dt
mfCpr (Tw-Tri) (MCp),
exp
- 1
(4b)
LmrCprJ
the solution of this equation for a time interval of 0 to t yields T~ = Tn0 + (Two - Tn0) exp (Qt)
(4c)
where mrCw {exp~-hbA'~
Q = (MCp)w
(1)
11.
[mrCof j -
(b) Heating mode (i) Between sunrise and sunset. For the circulating air in the passage,
where f = 0.77+0.045 Tdp. (a) Cooling mode (i) Between sunset and sunrise. For the water pond,
mrCpf dTr dx - hb(T'~- Tr)
(5a)
T w - Tr _ exp ~-hbL,X~_ - _
(5b)
L,
this results, +eaA{(Tw + 273)'-(T~ky)'}
the solution of this equation for a time interval of 0 to t yields, Tw = T~0 + (Two - T~0) exp
(--Pot)
(2)
where A
[/
Lt.,+
hb'~ .
{(T~ + 273) ' -- (T~ky0)'}-] ( ~ - - T:0) J"
Tw--Tn
( mrCpfJ
for the water pond, dT~ (MCv),~ ~ = hlA -- htA(Tw - 7".) - etrA {(Tw + 273) 4
-- (Tsky)4} -
hb(Tw-Tf)L2dx =0
(6a)
516
Technical Note 40 -
*...3O P
25 E2o
--D-- measured - e - cotcuLat.ed
Heat.in(] mode I0 8.0
I
I
I
I
I
I
16.0
24.0
8.0
160
24.0
8.0
Time (Hrs)
Fig. 4. Comparison of measured and calculated values of the water pond temperatures in the heating mode for two consecutive days.
40 -
CooLing mode
55 *-.--50
~
25
20
15 _
-0-- Measured - e - caLcuLated
io 8.0
[
I
I
-I
I
I
16.0
24.0
8.0
16.0
24.0
8.0
Time
(Hrs)
Fig. 5. Comparison of measured and calculated values o f the water pond temperature in the cooling mode for two consecutive days.
dt
A [
(ii) Between sunset and sunrise. For the circulating air in the passage, as derived in (i) o f the heating mode,
(MCp)w Iq--ht(T*--T~)--ea{(T*+273)4
T , - Tf
-- hbA
Tw - Tn
the solution of this equation for a time interval of 0 to t yields 7". = Ta0 + (Two- Tao) exp (Rot)
Ro =
(7)
for the water pond,
dT,
fL~ =ohb(Tw-Tr)L2dx
(8a)
d~ = mfCpf(Tw- Tr,) exp (mrCpr j - 1
(8b)
(MCp), ~
= --
(6c)
l (Two 1"=o) ht-~o {(Two + 273) 4 - (T,~yo)4} (Two -- T~o)
~ (r~o-r~,____~f
~-hbL~x~ exp ( mrCp-------~j
the solution of this equation for a time interval of 0 to t yields,
Tw = Tr,o+ (Two-- Trio)exp (St)
f--hbA]
mfcpf(r.o_r.o) ~eXP~m---7~r;-1}]
where
(8c)
517
Technical Note
(MCp)w
(rnrCprJ
different air mass flow rates circulated through the system during the heating mode. The calculated thermal system effÉciencywhich is defined as the amount of heat taken by the circulating air over absorbed solar heat by the water pond at its heating mode at different mass flow rates are shown in Fig. 6. The coefficient of performance (C.O.P.) of the system in the cooling mode was determined from the total cooling provided by the system over the maximum potential of the water pond to absorb heat from the circulating air are presented in Fig. 7.
"
In developing the energy balance equations it was implicitly assumed that the system operates in a 'quasi-steady state' manner i.e. the conditions remain steady during one time step at the end of which they change abruptly and remain steady during the second time step. This is the reason for which 8Tr/Sxis replaced by dTddx in the energy balance. 5. NUMERICAL RESULTS AND DISCUSSION The water pond temperature Tw was modelled on an hourly basis for the two modes of operation, using hourly values of solar insolation, ambient and inlet air temperatures. As the system was assumed to behave in a quasi-steady state manner the calculated value of Tw at the end of a particular hour was taken as the initial for the succeeding hour. In order to model the water pond temperature the following parameters e = 0.9 and ~t = 0.85, were used in addition to the empirical correlations given in the Appendix to calculate the necessary heat transfer coefficients. Calculated and measured water pond temperature values are shown in Figs 4 and 5 for the two modes, from which it is seen that they are in good agreement. Figure 6 shows the calculated exit air temperature with that of the measured for
6. CONCLUSION The designed solar heating and radiative cooling system is an attractive way of heating and cooling in the rural areas. The system built incorporates the storage volume and the collector-radiator in a single unit. The important features of the system are : It is easy to use and operate. The system is free from welding, soldering joints, bends etc. It has a low cost and easy to fabricate. The efficiency of the system is quite good for the intended purposes. It is easy to install anywhere around the building.
25
40 --O- meosured
,£
--55
•- ~ - - c a l c u l a t e d T e m p e r o t u re
~2o
__2obJ
Efficiency
W
- - 15
0,6
I
o.,8
I
020 Air flow
I
I
022 ra{e
I
o.24
°26
o12~°
(M3/S)
Fig. 6. Measured and calculated exit air temperatures and efficiency at different air flow rates.
b.O - -
~. Q5 U
Qo '8
i
I
Io
IZ
I
I
I
I
14
16
le
2o
Time (hr)
Fig. 7. The coefficient of performance of the system.
518
Technical Note
The low powered circulated air fan can be easily operated by solar cells if the rural area is without electricity. The theoretical model established could be utilized to characterize the heating and cooling performance of the system. NOMENCLATURE Ta ambient temperature (°C) Tw bulk mean temperature of the water pond (°C) Tf temperature of the circulating air at a distance x from the passage inlet (°C) Ta inlet temperature of air to the passage (°C) Tsky equivalent blackbody sky temperature (K) Tap ambient dew point temperature (°C) /h convective heat transfer coefficient of the top surface of the water pond (Win-2 K-t) hb convective heat transfer coefficient of the bottom surface of the water pond (Wm- 2K - ~) (MCp)w heat capacity of the water pond (JK -~) m r mass flow rate of air through the passage (kgs-~) Cpr specific heat of air circulating through the passage (Jkg-I K -I ) A area of the water pond perpendicular to the heat transfer (m 2) L~, L2 length and breadth of the water pond (m) 1 hourly global irradiance on a horizontal plane (Wh m -2) e emmisivity of the water pond for long wave radiation ~/ mean optical efficiency of the water pond for short wave radiation tr Stephan-Boltzman constant (Win-2 K-4).
Subscripts 0
initial value for a particular time interval for the parameter concerned.
3. I. Ahmad, The roof pool and its influence on the internal thermal environment, Ph.D. Thesis submitted to the University of Queensland, Australia (1977). 4. I. Ahmad and A. N. Ayoob, Summer performance a roof pond system in hot and arid climates, Energy Xconference, Canada, 1982. 5. D. O. Hall and J. Morton, Solar WorldForum Vol. 3, pp. 1789--1791, Pergamon Press (1982). 6. J. A. Duffle and W. Beckman, Solar Engineering of Thermal Processes, Wiley Interscience publication (1980). 7. S. P. Sukhatme, Solar Energy, Tata McGraw Hill (1984). APPENDIX The convective heat transfer coefficient of the top surface of the water pond was given by [6] h t = 2.8+3.0V where V is the wind velocity in m s-~ and h t in Wm -2 K -~ . The evaluation of the convective heat transfer coefficient of the bottom surface of the water pond was done using one of the following expressions. --for the case in which there was a forced circulation of air in the passage, assuming a fully developed turbulent flow with one side heated and the other side insulated, the relationship between the average Nusselt number (Nu) and Reynolds number (Re) was given by [6]. Nu = 0.0158 Re °'8 for which the hydraulic diameter d, is given by
do
4 x flow area wetted perimeter
--for the case in which there was no circulation of air in the passage the heat transfer coefficient between inclined parallel surfaces was given by [7]. Nu = 1
REFERENCES
1. H. R. Hay and J. I. Yellot, International aspects of air conditioning with movable insolation. Solar Energy 12, 427-438 (1969). 2. W. B. Phillip, Thermal evaluation of a house using a movable insulation heating and cooling system. Solar Energy 18, 413 (1976).
Ra cos# < 1708 ~'1
1708 ~ 1708 < Ra cos# < 5900
Nu = 1 + 1.446 ( - R-~-;-C~J Nu = 0.229 (Ra cos#) 0"252 Nu = 0.157 (Ra cos#) °'285
5900 < Ra Cos# < 9.23 × 104 9.23 × 104 < Ra cos# < 106
where Nu and Ra are average Nusselt and Rayleigh numbers and # being the inclination ; zero in this particular case.
0960-1481/91 $3.00+.00 PergamonPressplc
TECHNICAL
NOTE
Theoretical and experimental analysis of a simply designed solar retrofitting heating and cooling system A. N. AYOOB and R. A. ATTALAGE Centre d'Energ6tique, Ecole Nationale Sup6rieure Des Mines de Paris, Rue Claude Daunesse, 06565 Valbonne, France
(Received 26 June 1990; accepted 31 January 1991) Abstraet--A new design of a solar heating and a passive cooling system was built and operated that uses a water pond as a day time collector in winter and as a night time radiator in summer. The system built incorporates the storage and water pond collector-radiator in a single unit. The heating or cooling effect is transferred to the building by means o f circulating air via ducts. A room size building was built to investigate experimentally the performance of the established heating and cooling system. An energy balance was established in order to obtain the governing equations which were utilised to model the system during its two modes of operation. The calculated and measured values of the water pond (thermal medium) temperature were compared. The system is compact and cheap and can be installed anywhere, especially in rural areas.
1. INTRODUCTION The manner in which heat is provided to the living space in buildings does not necessarily dictate the type o f solar heating and cooling system to be used, but convenience and economy may limit the options. The solar heating and cooling system can be divided into two main types. The first involves the heating of the fluid in a solar panel, its delivery to the storage and the heating medium used directly for heating via fan coil units in winter, or used to activise absorption chillers in summer. The second type, in limited experimental use, involves elimination of fluid circulation by combining the collector or radiator and the storage into a single unit located in or adjacent to the living space (roof pond system). This system uses a water pond with a movable cover as a roof in conventional buildings. The water is exposed to the atmosphere to loose heat through radiation and convection at night and covered at day time for summer cooling. The operation reverses for winter heating. This technique provides a year-round space conditioning with no or minimal use of fossil fuels. Hay and Yellot experimented on a room size building with a roof pond in Phoenix, Arizona and were able to maintain an indoor air temperature between 21 °C and 27°C throughout the year [1]. Another house with three bedrooms using roof pond system was built in Atascadero, California, the system supplied an indoor air temperature between 17°C and 26°C while the outdoor temperature varied from - 1 2 ° C to 43°C [2]. A year long experimental and theoretical study on a building with a roof pond system at Brisbane, Australia showed that it can supply an indoor temperature 18°C-26°C during the whole year. The average ambient temperature varied from 6°C to 37°C [3]. Another experimental summer cooling results for a test structure with roof pond system in Baghdad showed an indoor temperature between 25°C and 27°C when the ambient temperature varied between 35°C and 45°C [4].
In this study a retrofitting solar heating and radiative cooling is described and assessed. It is a combined collectorradiator and storage energy system in a single unit. Unlike a roof pond system this design can be installed at any place in the building. 2. THE DESIGN O F THE SYSTEM A practical air conditioning system utilising radiative cooling in summer and collecting solar radiation in winter has been designed and constructed to air-condition a test room. The collector-radiator and the thermal storage medium are combined in a single unit, Fig. 1. The unit consists of (2 x 1 × 0.2 m) galvanized iron black painted pond which contains a polyethylene bag designed to contain 200 liters of waters as the thermal medium. The buldglng of the base and the sides of the pond under the pressure of the water bag are reduced by using angle iron plates bolted on the sides of the frame. It is drawn as asides, that the water and the water polyethylene bag can absorb the solar radiation in the day time during the heating season, or to radiate to the night sky during the cooling season. The stored heat is conducted to or extracted from the base of the pond which acts as a heat exchanger with the circulated air between the system and the test room. The circulated air is forced via a 5 cm deep passage in the system by means of a small powered fan. A movable insulation cover is provided and located in a place over the structure to prevent night time losses or day time energy absorption during the heating and cooling seasons. The structure rests on settled earth which serves as the floor o f the building. 3. E X P E R I M E N T A L TESTS RESULTS Under actual conditions of sun shine and air velocity, performance of the retrofitting heating and cooling system was 513
514
Technical Note 8 Air streom passo~e 7 Heat e~chonger 6 Supports
. -G.I
.
5 Air Fan
. --
.
4 3 2 I
Air Ducts InsuLotion Cover of poor (movobte) Wooden frame !Item
G.I styropor Wood Wood Mot.
/•//•
,,~
reflector sheet
Fig. 1. Design drawing of the system.
established. Thermocouples points were inserted at various locations in the system. An electronic thermometer was used to record the data. Solar radiation was recorded by an electronic solar meter.
3.1. Heating mode The heating has been tested over the winter season for the evaluation of the thermal performance. The pond was exposed to solar radiation between sunrise and sunset to collect and absorb solar heating which was utilized for charging the circulated air after sunset. Samples of the results are presented in Fig. 2: Ambient and water temperatures, inlet and outlet circulated air temperatures were recorded. It car~ be seen that the water temperature in the polyethylene bag reached 36°C after few hours in a normal sunny day in winter in Baghdad where the test was carried out. This temperature is quite adequate for obtaining warm circulated air for the building.
3.2. Cooling mode Cooling performance of the system was observed in summer system. Figure 3 shows the results during two consecutive days in July. The pond of the system was exposed to the ambient after sunset and covered before sunrise every day. The water depth in the polyethylene bag was kept constant during the period of experimentation. It is clear from this figure that at a rate of 0.18 m 3 s -n of circulating air, the difference between the outlet and inlet system temperatures arranged between 0.5°C and 2.5°C throughout the day, and the test room temperature is always maintained between 27°C and 32°C.
4. ANALYSIS An analysis was carried out for the two principle operating modes, heating and cooling. In order to develop energy bal-
40-~ u m
30-
/
/\
20 - * t ° l I ~
8.0
SoLar r 0 d i o t . i o n
, Wo r
\Exit m "I.__
?,.~
16.0
/
l~
inLetqNb+*'°~..e"
24.0
8.0 T i m e (hr)
~lmls,,.
~
"o-o" ....
16.0
"~'t.+*.
24.0
8.0
Fig. 2. Measured thermal characteristics of the system in the heating mode for two consecutive days.
Technical Note
:50Fl /
•.•. ll"
\
",.
/
o
/
""
3oL..+..-..+.,:,.,'++~ +++ + 4,.+,+ .i..i. ~
]
ll.•.•l i / hl.it I ! ll"
i-i'w'w' Xm Ambient
,ok;
l~.t.#.#.t.#.• .l.i.l t.i
~- et~[i~#'~
7 l l . • ,. •.ill
k InLet
kllll~
d
X e-,'t~*'+~. % • . % = ,; ~r . ~ ~ +,+ .÷ .
~ "r-'T'-I-
~'i-i'i
~
515
. ~ . I . i . t , . i . i , # .e.i.i.#., I
4vi.##,i'i'i'~""
Water pond
-i-o-i-
"-,-",,--r
"i'i'i'i'i#
/ io/
l
I
I
I
I
I
80
16.0
24.0
8.0
16.0
24.0
8,0
Time (hr) Fig. 3. Measured thermal characteristics of the system in the cooling mode for two consecutive days.
ance equations of the water pond, the following assumptions have been made. (i) the system is horizontally installed in such a way that it sees only the sky ; (ii) the bulk mean temperature of water, and that of the polyethylene cover and of the G1 sheet at the bottom are the same at any particular instant after a period of continuous operation ; (iii) the heat capacity of those other than water is neglected ; (iv) side insulation is perfect ; (v) the net radiant heat exchange between the two GI sheets in the passage is neglected compared to other types of heat exchange ; (vi) the water pond is not stratified. In addition, the sky is considered as a blackbody at some equivalent temperature. In fact the atmosphere is not at a uniform temperature and it radiates only in certain wavelength bands (i.e. it is essentially transparent in 8-14 /~m band and has radiating bands covering much of the infrared spectrum). In order to evaluate the equivalent sky temperature the following relationship, proposed by Clark and Berdahl, was used in the analysis [5]. Tsky = f°'25(T~ +273)
(ii) Between sunrise and sunset. in the passage, mrCpf dTr L 2 dx
For the circulating air
hb(T, - Tr)
(3a)
this results, Tw - Tf
~ -- hbL2x]
(3b)
for the water pond, dTw fL, ( M C p ) w ~ - = -- =o h u ( T w - Tr)L2 d x
(4a)
using (3b), dTw dt
mfCpr (Tw-Tri) (MCp),
exp
- 1
(4b)
LmrCprJ
the solution of this equation for a time interval of 0 to t yields T~ = Tn0 + (Two - Tn0) exp (Qt)
(4c)
where mrCw {exp~-hbA'~
Q = (MCp)w
(1)
11.
[mrCof j -
(b) Heating mode (i) Between sunrise and sunset. For the circulating air in the passage,
where f = 0.77+0.045 Tdp. (a) Cooling mode (i) Between sunset and sunrise. For the water pond,
mrCpf dTr dx - hb(T'~- Tr)
(5a)
T w - Tr _ exp ~-hbL,X~_ - _
(5b)
L,
this results, +eaA{(Tw + 273)'-(T~ky)'}
the solution of this equation for a time interval of 0 to t yields, Tw = T~0 + (Two - T~0) exp
(--Pot)
(2)
where A
[/
Lt.,+
hb'~ .
{(T~ + 273) ' -- (T~ky0)'}-] ( ~ - - T:0) J"
Tw--Tn
( mrCpfJ
for the water pond, dT~ (MCv),~ ~ = hlA -- htA(Tw - 7".) - etrA {(Tw + 273) 4
-- (Tsky)4} -
hb(Tw-Tf)L2dx =0
(6a)
516
Technical Note 40 -
*...3O P
25 E2o
--D-- measured - e - cotcuLat.ed
Heat.in(] mode I0 8.0
I
I
I
I
I
I
16.0
24.0
8.0
160
24.0
8.0
Time (Hrs)
Fig. 4. Comparison of measured and calculated values of the water pond temperatures in the heating mode for two consecutive days.
40 -
CooLing mode
55 *-.--50
~
25
20
15 _
-0-- Measured - e - caLcuLated
io 8.0
[
I
I
-I
I
I
16.0
24.0
8.0
16.0
24.0
8.0
Time
(Hrs)
Fig. 5. Comparison of measured and calculated values o f the water pond temperature in the cooling mode for two consecutive days.
dt
A [
(ii) Between sunset and sunrise. For the circulating air in the passage, as derived in (i) o f the heating mode,
(MCp)w Iq--ht(T*--T~)--ea{(T*+273)4
T , - Tf
-- hbA
Tw - Tn
the solution of this equation for a time interval of 0 to t yields 7". = Ta0 + (Two- Tao) exp (Rot)
Ro =
(7)
for the water pond,
dT,
fL~ =ohb(Tw-Tr)L2dx
(8a)
d~ = mfCpf(Tw- Tr,) exp (mrCpr j - 1
(8b)
(MCp), ~
= --
(6c)
l (Two 1"=o) ht-~o {(Two + 273) 4 - (T,~yo)4} (Two -- T~o)
~ (r~o-r~,____~f
~-hbL~x~ exp ( mrCp-------~j
the solution of this equation for a time interval of 0 to t yields,
Tw = Tr,o+ (Two-- Trio)exp (St)
f--hbA]
mfcpf(r.o_r.o) ~eXP~m---7~r;-1}]
where
(8c)
517
Technical Note
(MCp)w
(rnrCprJ
different air mass flow rates circulated through the system during the heating mode. The calculated thermal system effÉciencywhich is defined as the amount of heat taken by the circulating air over absorbed solar heat by the water pond at its heating mode at different mass flow rates are shown in Fig. 6. The coefficient of performance (C.O.P.) of the system in the cooling mode was determined from the total cooling provided by the system over the maximum potential of the water pond to absorb heat from the circulating air are presented in Fig. 7.
"
In developing the energy balance equations it was implicitly assumed that the system operates in a 'quasi-steady state' manner i.e. the conditions remain steady during one time step at the end of which they change abruptly and remain steady during the second time step. This is the reason for which 8Tr/Sxis replaced by dTddx in the energy balance. 5. NUMERICAL RESULTS AND DISCUSSION The water pond temperature Tw was modelled on an hourly basis for the two modes of operation, using hourly values of solar insolation, ambient and inlet air temperatures. As the system was assumed to behave in a quasi-steady state manner the calculated value of Tw at the end of a particular hour was taken as the initial for the succeeding hour. In order to model the water pond temperature the following parameters e = 0.9 and ~t = 0.85, were used in addition to the empirical correlations given in the Appendix to calculate the necessary heat transfer coefficients. Calculated and measured water pond temperature values are shown in Figs 4 and 5 for the two modes, from which it is seen that they are in good agreement. Figure 6 shows the calculated exit air temperature with that of the measured for
6. CONCLUSION The designed solar heating and radiative cooling system is an attractive way of heating and cooling in the rural areas. The system built incorporates the storage volume and the collector-radiator in a single unit. The important features of the system are : It is easy to use and operate. The system is free from welding, soldering joints, bends etc. It has a low cost and easy to fabricate. The efficiency of the system is quite good for the intended purposes. It is easy to install anywhere around the building.
25
40 --O- meosured
,£
--55
•- ~ - - c a l c u l a t e d T e m p e r o t u re
~2o
__2obJ
Efficiency
W
- - 15
0,6
I
o.,8
I
020 Air flow
I
I
022 ra{e
I
o.24
°26
o12~°
(M3/S)
Fig. 6. Measured and calculated exit air temperatures and efficiency at different air flow rates.
b.O - -
~. Q5 U
Qo '8
i
I
Io
IZ
I
I
I
I
14
16
le
2o
Time (hr)
Fig. 7. The coefficient of performance of the system.
518
Technical Note
The low powered circulated air fan can be easily operated by solar cells if the rural area is without electricity. The theoretical model established could be utilized to characterize the heating and cooling performance of the system. NOMENCLATURE Ta ambient temperature (°C) Tw bulk mean temperature of the water pond (°C) Tf temperature of the circulating air at a distance x from the passage inlet (°C) Ta inlet temperature of air to the passage (°C) Tsky equivalent blackbody sky temperature (K) Tap ambient dew point temperature (°C) /h convective heat transfer coefficient of the top surface of the water pond (Win-2 K-t) hb convective heat transfer coefficient of the bottom surface of the water pond (Wm- 2K - ~) (MCp)w heat capacity of the water pond (JK -~) m r mass flow rate of air through the passage (kgs-~) Cpr specific heat of air circulating through the passage (Jkg-I K -I ) A area of the water pond perpendicular to the heat transfer (m 2) L~, L2 length and breadth of the water pond (m) 1 hourly global irradiance on a horizontal plane (Wh m -2) e emmisivity of the water pond for long wave radiation ~/ mean optical efficiency of the water pond for short wave radiation tr Stephan-Boltzman constant (Win-2 K-4).
Subscripts 0
initial value for a particular time interval for the parameter concerned.
3. I. Ahmad, The roof pool and its influence on the internal thermal environment, Ph.D. Thesis submitted to the University of Queensland, Australia (1977). 4. I. Ahmad and A. N. Ayoob, Summer performance a roof pond system in hot and arid climates, Energy Xconference, Canada, 1982. 5. D. O. Hall and J. Morton, Solar WorldForum Vol. 3, pp. 1789--1791, Pergamon Press (1982). 6. J. A. Duffle and W. Beckman, Solar Engineering of Thermal Processes, Wiley Interscience publication (1980). 7. S. P. Sukhatme, Solar Energy, Tata McGraw Hill (1984). APPENDIX The convective heat transfer coefficient of the top surface of the water pond was given by [6] h t = 2.8+3.0V where V is the wind velocity in m s-~ and h t in Wm -2 K -~ . The evaluation of the convective heat transfer coefficient of the bottom surface of the water pond was done using one of the following expressions. --for the case in which there was a forced circulation of air in the passage, assuming a fully developed turbulent flow with one side heated and the other side insulated, the relationship between the average Nusselt number (Nu) and Reynolds number (Re) was given by [6]. Nu = 0.0158 Re °'8 for which the hydraulic diameter d, is given by
do
4 x flow area wetted perimeter
--for the case in which there was no circulation of air in the passage the heat transfer coefficient between inclined parallel surfaces was given by [7]. Nu = 1
REFERENCES
1. H. R. Hay and J. I. Yellot, International aspects of air conditioning with movable insolation. Solar Energy 12, 427-438 (1969). 2. W. B. Phillip, Thermal evaluation of a house using a movable insulation heating and cooling system. Solar Energy 18, 413 (1976).
Ra cos# < 1708 ~'1
1708 ~ 1708 < Ra cos# < 5900
Nu = 1 + 1.446 ( - R-~-;-C~J Nu = 0.229 (Ra cos#) 0"252 Nu = 0.157 (Ra cos#) °'285
5900 < Ra Cos# < 9.23 × 104 9.23 × 104 < Ra cos# < 106
where Nu and Ra are average Nusselt and Rayleigh numbers and # being the inclination ; zero in this particular case.