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Analysis of a free flow solar collector
Solar Energy Vol. 35, No. 3, pp. 287-290, 1985
0038-092X/85 $3.00 + .00 © 1985 Pergamon Press Ltd.
Printed in the U.S.A.
TECHNICAL
NOTE
Analysis of a free flow solar collector M. VAXMANand M. SOKOLOV* Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel Aviv University, Ramat-Aviv 69978, Israel ( R e c e i v e d 24 F e b r u a r y 1984; a c c e p t e d in r e v i s e d f o r m 4 F e b r u a r y 1985)
mined by the inlet temperature, namely:
INTRODUCTION
The usage of solar energy, especially on a large scale, is very often inhibited by the collectors' cost. Thus, a simpler and less expensive collector is always a welcome addition to the field. One of the most simple collectors is probably the free flow flat plate collector, shown in Fig. 1. A fluid is pumped up to the top of the collector where it is allowed to fall freely on the inclined surface. On its way, the fluid absorbs the solar radiation directly and from the bottom plate. Since there is no pressure in the system and no need for thermal conducting elements, plastics seem to be a very suitable construction material. Some experiments have been done with a similar configuration in open channel[l] or plate free flow collectors[2, 3], but most of them lack a theoretical analysis which provides the designer with means of evaluation and directions for improvements. It is the purpose of this work to provide that analysis.
T=
T, at
x = 0.
(3)
{xF, "rv in eqns (1) and (2) are the film absorptance and transmittance, respectively, and should therefore satisfy: 0iF + "~F -~- De =
1,
(4)
where pF is the film reflectance. If K, the extinction coefficient of the fluid, is known, "re can be evaluated by: q'F =
exp( - K~).
(5)
This is justified for a thin film of fluid, within which K may be assumed to be constant. ~ is the film thickness, which depends on the mass flow rate per unit width, the plate inclination angle, and the fluid viscosity. It can be shown[4] that this dependence is given by:
ANALYSIS OF THE FREE FLOW COLLECTOR
rh = clC,
In this section, energy equations for the various collector's parts will be derived so that the efficiency can be evaluated. Throughout the derivation the following assumptions are made:
where
1. Velocity profile varies only perpendicularly to the plate. 2. A uniform film thickness throughout. 3. The temperature field is one-dimensional so variation in temperature occurs only in the flow direction. 4. The system is in a steady state. 5. Heat radiation losses from plate to ambient are negligible. 6. Edge effects are negligible. 7. Fluid vapor pressure is low, hence evaporation is negligible.
Cl = ( p 2 g s i n
dT
T) -
ut(T -
T~).
dT
C4-~
= H(T~
-
T) + t t B ( T p
-
To).
(7)
(8)
= C2 - C3T,
from which temperature distribution in the fluid film can be obtained, namely: T(x) = (Ti - c 2 / c 3 ) e x p ( - c 3 x / c 4 ) + c2/c3,
c2 = "rt[ctF + z ~ H c t p / ( H + HB)] + T.c3
(10)
c3 = (HBH + Hut + HBut)/(H + H s )
(11)
c4 = fncp,
(12)
and
(2)
H = k l L 0.834 [Lc]/3/p,] I/2 p r t / 3 t h 1/3 =
In these equations Tp and T are both functions of x. Boundary conditions for the set of equations is deter-
(9)
where
(1)
Thus, heat is transferred to the fluid film by direct absorptance of solar radiation, by convection from the plate, and heat is lost to the surroundings. A similar energy equation can be written for the plate: (~::I
a)/3~.
Equations (1) and (2) can be combined to yield:
The energy equation for the fluid film is given by:
f n c p - - ~ = c~FI~ + H ( T p -
(6)
csrh I/3,
(13)
from [5] (for uniform heat flux) and eqn (6). Efficiency of a collector is defined by:
* Author to whom correspondence should be addressed. 287
"q = thcp( Tout - Ti)/(IL ).
(14)
288
Technical Note
T~Thermal insulation Semi Ta Ut~~/~ fluidtransparent film Transparent-~~ ~ Tp covers
/'Y~ ~ H I ~!' I~ ' :Bol ck paint
Fig. 1. Schematic view of the free flow collector.
Table 1. Comparison between experimental [2] and theoretical performance of free flow collector
T~
To.t
T,,
34.1 35.2 44.7 50.2 54.9 41.7 41.6 32.2 31.9 31.3 29.8 28.9 28.2 26.8 26.3 49.5 48.4 50.9 50.5 51.9 35.3 35.3 35.3 20.1 25.3 26.6 28.4 31.4 34.7 36.8 27.8 43.4 22.6 19.9 19.9 21.8
44.4 46.2 54.7 60.1 63.5 55.2 55.0 46.7 45.7 44.2 41.5 39.8 38.7 36.1 35.2 57.4 57.2 59.8 60.5 61.7 48.6 48.1 47.8 37.0 41.8 43.3 46.5 40.8 44.6 47.9 43.9 55.3 35.3 39.5 39.3 41.7
7.0 7.0 8.0 9.0 9.0 11.5 12.5 13.5 14.0 14.5 14.0 14.0 14.0 14.0 14.0 17.0 18.0 18.5 19.0 19.0 22.0 22.0 23.0 4.0 4.0 4.0 5.0 - 1.0 - 1.0 - 1.0 0.0 0.0 3.0 7.0 9.0 10.0
1 0 0 ( ~ r - "qex )
m
I
V
{kg/h}
{w/m 2}
{m/sec}
nr
nex
459.6 458.3 452.3 448.5 446.1 452.0 452.1 458.0 458.6 459.7 461.6 462.8 463.6 465.4 466.0 450.4 450.6 448.7 448.3 447.4 456.6 456.9 457.1 281.6 279.5 278.8 277.5 280.0 278.3 ' 276.9 278.6 273.8 282.3 280.5 280.6 279.5
853.7 921.4 977.9 1006.3 1035.0 1091.3 1078.9 1046.9 1011.4 949.7 880.0 816.0 786.7 711.1 672.0 852.9 927.6 956.8 989.6 1009.1 1006.0 986.1 966.4 839.0 917.4 954.7 1012.3 800.7 870.6 917.0 957.8 1029.3 737.8 840.9 885.9 957.5
0. 0. 0. 0. 0. 0. 0. 0. 2. 4. 2. 3. 2. 2. 2. 1. 4. 4. 4. 4. 6. 4. 5. 8. 8. 8. 8. 6. 6. 6. 6. 6. 5. 5. 5. 5.
39.2 40.1 34.9 32.3 29.7 42.2 42.7 49.5 49.7 49.7 49.5 49.3 49.5 49.5 49.3 34.4 38.4 37.5 39.0 38.5 53.0 52.8 53.3 45.2 42.4 42.0 42.4 30.4 30.0 29.8 38.3 29.1 40.1 47.9 50.0 49.8
45.7 45.1 38.1 36.4 30.6 46.1 46.3 52.3 51.6 51.5 50.6 51.0 51.0 50.2 50.9 34.4 35.2 34.4 37.4 35.8 49.8 48.9 48.8 46.8 41.5 40.2 40.9 27.1 26.1 27.6 38.6 26.1 40.1 53.9 50.7 47.9
Vlex 14.2 -11.2 -8.6 -11.3 -2.7 -8.5 -7.8 -5.3 -3.7 -3.5 -2.2 -3.3 -3.1 - 1.3 -3.1 0.0 8.8 9.1 4.5 7.3 6.4 7.9 9.4 -3.3 2.2 4.5 3.6 12.1 14.8 7.8 -0.8 11.4 0.1 -11.2 -1.3 4.0 -
Technical Note
289
Now, Tout can be evaluated from eqn (9) and substituted the heat removal factor FR is given by into (14), to yield: mcPf l _ FR = Lc3 k exp ( -
c3L]
c'3L ~ ] thcp/j'
(18)
lq = Lc--'-~
c3(Ti ,; To)]. (15) and the equivalent solar absorptance of the collector is -
x
"r e~e+ H + t I B /
given by:
oteq = ~tF + "rF~l -- [1 -- cs~n]/3Ctp/(Csin '/3+ He)]}. (19) Incorporating, now, the dependence between the optical properties of the film and the mass flow rate by substituting eqns (4), (5), and (6) into (15), as well as H from The efficiency expression in eqn (I 6) can now be rewritten 03), the efficiency will be given by: in the conventional form, namely: rhcp
c3L ~ ]
(L-
"q = ~-~3( l - e x p ( - - ~ c c / j
~l = Fs[xc(~q - UL ~ c~Kn '/3 +
× exp(
K(m)'/'%] -c3 \Cl/ / J •
T.)].
(20)
Ha)
(TizI T,,)).
(16)
RESULTS AND DISCUSSION
From eqn (19), it can be seen that two major factors influence ~eq, the fluid absorptance and the mass flow For the free flow collector, the collector efficiency factor rate. The larger the mass flow rate becomes, so does the F' is unity since the heat is absorbed directly by the fluid film thickness and thus more energy can be absorbed, as film. Noting that the overall heat losses are given by: seen in eqn (5). The maximum obtainable absorptance is therefore given by: UL = Ut + lib = Ut +
1
I/H + 1~Ha --
C3,
(17)
c t e ~ = (xF
I "
(21)
Fr
.
°
f
/
f
/
/:
Fr u k / l O /
/
Fr T Cleq
/
\ \
IT, .z°'c
T,.2o'c
I
I
:: .8oo w/ l (To~_Ti V l O ~
0
•------
1
0.1
I (kg/sec.m)
Fig. 2. Efficiency and temperature dependence on mass flow rate.
0.2
290
Technical Note
Table 2. Data used in theoretical evaluation of the free flow collector Parameter
Cp HB
Value 1600 1 21
K k L
.14 4.9 7.3 1.1 45 ° .96
UT W ~t a W p OF T
10.5 × 914
10 - 3
.03 0.78
Dimension J/Kg°C W/m2°C m- t W/m°C m W/m2°C m --Kg/m sec Kg/m 3 ---
Source [2] assumed assumed [5] [2] [2] averaged [2] [2] assumed [2] [2] [2] [2]
which may be achieved for large K or rh. Thus, an obvious requirement of the fluid is to have high absorptance. This can be done by dyeing the fluid properly. Beard et al.[2] used silicone oil as the working fluid for experiments with a free flow collector. Comparison between their experimentally evaluated efficiency and the one evaluated by using eqn (16) is shown in Table 1. The values of parameters used in the theoretical efficiency evaluation are given in Table 2. Considering the fact that a large degree of uncertainty exists in the analytical determination of the various heat and radiation transfer coefficients, the agreement is quite good. The importance of the mass flow rate on such a system is shown in Fig. 2 for the system configuration reported in [2]. As expected, FR, the slope (FR, UL) and the intercept (Fg~tOteq) of the efficiency line increase with th. At the same time Tout-Ti decreases. Thus Fig. 2 is typical in providing information for design point selection of the free flow collector. NOMENCLATURE Cp cj c2 c3 c4 c5
Specific Defined Defined Defined Defined Defined
heat in eqn in eqn in eqn in eqn in eqn
(7) (9) (10) (ll) (12)
FR Heat removal factor H Heat transfer coefficient between the fluid and the plate HB The back side heat transfer coefficient I Solar heat flux K Extinction coefficient k Thermal conductivity of fluid L Collector length rh Mass flow rate per unit width T Fluid temperature T~ Ambient temperature Ti Fluid inlet temperature Tout Fluid outlet temperature Tp Plate temperature uL Collector losses heat transfer coefficient ut Top losses heat transfer coefficient w Collector width x coordinate in the fl0w direction Slope of the collector Oteq Equivalent absorptance of the collector aF Fluid absorptance ctp Plate absorptance 8 The fluid film thickness Collector efficiency tx Fluid dynamic viscosity pF Fluid film reflectance p Fluid density Transparent covers transmittance "rF Fluid film transmittance REFERENCES
1. J.T. Beard, F. A. Iachetta, L. U. Lillelebt, F. L. Huckstep, and W. B. May, Design and operation influences on thermal performance of "Solars", solar collector, J. Engng for Power 1110(4), 497-502 0978). 2. J. T. Beard, F. A. Iachetta, R. F. Messer, F. L. Huckstep, and W. B. May, Performance and analysis of an open fluid-film solar collector. Proc. 1977 Annual Meeting of the American Section of lSES 1 section l, 126-129 (Orlando F1 June 6, 1977). 3. Chungshiang Patrick Peng., Analysis of open inclined surface solar regenerators for absorption cooling applications-comprise between numerical and analytical models, Solar Energy 28(3), 265-268 0982). 4. D. Hershey, Transport Analysis, Plenum Press, New York, 112-113 (1973). 5. L. C. Thomas, Fundamentals of Heat Transfer, Prentice-Hall, Englewood Cliffs, N.J. (1980).
0038-092X/85 $3.00 + .00 © 1985 Pergamon Press Ltd.
Printed in the U.S.A.
TECHNICAL
NOTE
Analysis of a free flow solar collector M. VAXMANand M. SOKOLOV* Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel Aviv University, Ramat-Aviv 69978, Israel ( R e c e i v e d 24 F e b r u a r y 1984; a c c e p t e d in r e v i s e d f o r m 4 F e b r u a r y 1985)
mined by the inlet temperature, namely:
INTRODUCTION
The usage of solar energy, especially on a large scale, is very often inhibited by the collectors' cost. Thus, a simpler and less expensive collector is always a welcome addition to the field. One of the most simple collectors is probably the free flow flat plate collector, shown in Fig. 1. A fluid is pumped up to the top of the collector where it is allowed to fall freely on the inclined surface. On its way, the fluid absorbs the solar radiation directly and from the bottom plate. Since there is no pressure in the system and no need for thermal conducting elements, plastics seem to be a very suitable construction material. Some experiments have been done with a similar configuration in open channel[l] or plate free flow collectors[2, 3], but most of them lack a theoretical analysis which provides the designer with means of evaluation and directions for improvements. It is the purpose of this work to provide that analysis.
T=
T, at
x = 0.
(3)
{xF, "rv in eqns (1) and (2) are the film absorptance and transmittance, respectively, and should therefore satisfy: 0iF + "~F -~- De =
1,
(4)
where pF is the film reflectance. If K, the extinction coefficient of the fluid, is known, "re can be evaluated by: q'F =
exp( - K~).
(5)
This is justified for a thin film of fluid, within which K may be assumed to be constant. ~ is the film thickness, which depends on the mass flow rate per unit width, the plate inclination angle, and the fluid viscosity. It can be shown[4] that this dependence is given by:
ANALYSIS OF THE FREE FLOW COLLECTOR
rh = clC,
In this section, energy equations for the various collector's parts will be derived so that the efficiency can be evaluated. Throughout the derivation the following assumptions are made:
where
1. Velocity profile varies only perpendicularly to the plate. 2. A uniform film thickness throughout. 3. The temperature field is one-dimensional so variation in temperature occurs only in the flow direction. 4. The system is in a steady state. 5. Heat radiation losses from plate to ambient are negligible. 6. Edge effects are negligible. 7. Fluid vapor pressure is low, hence evaporation is negligible.
Cl = ( p 2 g s i n
dT
T) -
ut(T -
T~).
dT
C4-~
= H(T~
-
T) + t t B ( T p
-
To).
(7)
(8)
= C2 - C3T,
from which temperature distribution in the fluid film can be obtained, namely: T(x) = (Ti - c 2 / c 3 ) e x p ( - c 3 x / c 4 ) + c2/c3,
c2 = "rt[ctF + z ~ H c t p / ( H + HB)] + T.c3
(10)
c3 = (HBH + Hut + HBut)/(H + H s )
(11)
c4 = fncp,
(12)
and
(2)
H = k l L 0.834 [Lc]/3/p,] I/2 p r t / 3 t h 1/3 =
In these equations Tp and T are both functions of x. Boundary conditions for the set of equations is deter-
(9)
where
(1)
Thus, heat is transferred to the fluid film by direct absorptance of solar radiation, by convection from the plate, and heat is lost to the surroundings. A similar energy equation can be written for the plate: (~::I
a)/3~.
Equations (1) and (2) can be combined to yield:
The energy equation for the fluid film is given by:
f n c p - - ~ = c~FI~ + H ( T p -
(6)
csrh I/3,
(13)
from [5] (for uniform heat flux) and eqn (6). Efficiency of a collector is defined by:
* Author to whom correspondence should be addressed. 287
"q = thcp( Tout - Ti)/(IL ).
(14)
288
Technical Note
T~Thermal insulation Semi Ta Ut~~/~ fluidtransparent film Transparent-~~ ~ Tp covers
/'Y~ ~ H I ~!' I~ ' :Bol ck paint
Fig. 1. Schematic view of the free flow collector.
Table 1. Comparison between experimental [2] and theoretical performance of free flow collector
T~
To.t
T,,
34.1 35.2 44.7 50.2 54.9 41.7 41.6 32.2 31.9 31.3 29.8 28.9 28.2 26.8 26.3 49.5 48.4 50.9 50.5 51.9 35.3 35.3 35.3 20.1 25.3 26.6 28.4 31.4 34.7 36.8 27.8 43.4 22.6 19.9 19.9 21.8
44.4 46.2 54.7 60.1 63.5 55.2 55.0 46.7 45.7 44.2 41.5 39.8 38.7 36.1 35.2 57.4 57.2 59.8 60.5 61.7 48.6 48.1 47.8 37.0 41.8 43.3 46.5 40.8 44.6 47.9 43.9 55.3 35.3 39.5 39.3 41.7
7.0 7.0 8.0 9.0 9.0 11.5 12.5 13.5 14.0 14.5 14.0 14.0 14.0 14.0 14.0 17.0 18.0 18.5 19.0 19.0 22.0 22.0 23.0 4.0 4.0 4.0 5.0 - 1.0 - 1.0 - 1.0 0.0 0.0 3.0 7.0 9.0 10.0
1 0 0 ( ~ r - "qex )
m
I
V
{kg/h}
{w/m 2}
{m/sec}
nr
nex
459.6 458.3 452.3 448.5 446.1 452.0 452.1 458.0 458.6 459.7 461.6 462.8 463.6 465.4 466.0 450.4 450.6 448.7 448.3 447.4 456.6 456.9 457.1 281.6 279.5 278.8 277.5 280.0 278.3 ' 276.9 278.6 273.8 282.3 280.5 280.6 279.5
853.7 921.4 977.9 1006.3 1035.0 1091.3 1078.9 1046.9 1011.4 949.7 880.0 816.0 786.7 711.1 672.0 852.9 927.6 956.8 989.6 1009.1 1006.0 986.1 966.4 839.0 917.4 954.7 1012.3 800.7 870.6 917.0 957.8 1029.3 737.8 840.9 885.9 957.5
0. 0. 0. 0. 0. 0. 0. 0. 2. 4. 2. 3. 2. 2. 2. 1. 4. 4. 4. 4. 6. 4. 5. 8. 8. 8. 8. 6. 6. 6. 6. 6. 5. 5. 5. 5.
39.2 40.1 34.9 32.3 29.7 42.2 42.7 49.5 49.7 49.7 49.5 49.3 49.5 49.5 49.3 34.4 38.4 37.5 39.0 38.5 53.0 52.8 53.3 45.2 42.4 42.0 42.4 30.4 30.0 29.8 38.3 29.1 40.1 47.9 50.0 49.8
45.7 45.1 38.1 36.4 30.6 46.1 46.3 52.3 51.6 51.5 50.6 51.0 51.0 50.2 50.9 34.4 35.2 34.4 37.4 35.8 49.8 48.9 48.8 46.8 41.5 40.2 40.9 27.1 26.1 27.6 38.6 26.1 40.1 53.9 50.7 47.9
Vlex 14.2 -11.2 -8.6 -11.3 -2.7 -8.5 -7.8 -5.3 -3.7 -3.5 -2.2 -3.3 -3.1 - 1.3 -3.1 0.0 8.8 9.1 4.5 7.3 6.4 7.9 9.4 -3.3 2.2 4.5 3.6 12.1 14.8 7.8 -0.8 11.4 0.1 -11.2 -1.3 4.0 -
Technical Note
289
Now, Tout can be evaluated from eqn (9) and substituted the heat removal factor FR is given by into (14), to yield: mcPf l _ FR = Lc3 k exp ( -
c3L]
c'3L ~ ] thcp/j'
(18)
lq = Lc--'-~
c3(Ti ,; To)]. (15) and the equivalent solar absorptance of the collector is -
x
"r e~e+ H + t I B /
given by:
oteq = ~tF + "rF~l -- [1 -- cs~n]/3Ctp/(Csin '/3+ He)]}. (19) Incorporating, now, the dependence between the optical properties of the film and the mass flow rate by substituting eqns (4), (5), and (6) into (15), as well as H from The efficiency expression in eqn (I 6) can now be rewritten 03), the efficiency will be given by: in the conventional form, namely: rhcp
c3L ~ ]
(L-
"q = ~-~3( l - e x p ( - - ~ c c / j
~l = Fs[xc(~q - UL ~ c~Kn '/3 +
× exp(
K(m)'/'%] -c3 \Cl/ / J •
T.)].
(20)
Ha)
(TizI T,,)).
(16)
RESULTS AND DISCUSSION
From eqn (19), it can be seen that two major factors influence ~eq, the fluid absorptance and the mass flow For the free flow collector, the collector efficiency factor rate. The larger the mass flow rate becomes, so does the F' is unity since the heat is absorbed directly by the fluid film thickness and thus more energy can be absorbed, as film. Noting that the overall heat losses are given by: seen in eqn (5). The maximum obtainable absorptance is therefore given by: UL = Ut + lib = Ut +
1
I/H + 1~Ha --
C3,
(17)
c t e ~ = (xF
I "
(21)
Fr
.
°
f
/
f
/
/:
Fr u k / l O /
/
Fr T Cleq
/
\ \
IT, .z°'c
T,.2o'c
I
I
:: .8oo w/ l (To~_Ti V l O ~
0
•------
1
0.1
I (kg/sec.m)
Fig. 2. Efficiency and temperature dependence on mass flow rate.
0.2
290
Technical Note
Table 2. Data used in theoretical evaluation of the free flow collector Parameter
Cp HB
Value 1600 1 21
K k L
.14 4.9 7.3 1.1 45 ° .96
UT W ~t a W p OF T
10.5 × 914
10 - 3
.03 0.78
Dimension J/Kg°C W/m2°C m- t W/m°C m W/m2°C m --Kg/m sec Kg/m 3 ---
Source [2] assumed assumed [5] [2] [2] averaged [2] [2] assumed [2] [2] [2] [2]
which may be achieved for large K or rh. Thus, an obvious requirement of the fluid is to have high absorptance. This can be done by dyeing the fluid properly. Beard et al.[2] used silicone oil as the working fluid for experiments with a free flow collector. Comparison between their experimentally evaluated efficiency and the one evaluated by using eqn (16) is shown in Table 1. The values of parameters used in the theoretical efficiency evaluation are given in Table 2. Considering the fact that a large degree of uncertainty exists in the analytical determination of the various heat and radiation transfer coefficients, the agreement is quite good. The importance of the mass flow rate on such a system is shown in Fig. 2 for the system configuration reported in [2]. As expected, FR, the slope (FR, UL) and the intercept (Fg~tOteq) of the efficiency line increase with th. At the same time Tout-Ti decreases. Thus Fig. 2 is typical in providing information for design point selection of the free flow collector. NOMENCLATURE Cp cj c2 c3 c4 c5
Specific Defined Defined Defined Defined Defined
heat in eqn in eqn in eqn in eqn in eqn
(7) (9) (10) (ll) (12)
FR Heat removal factor H Heat transfer coefficient between the fluid and the plate HB The back side heat transfer coefficient I Solar heat flux K Extinction coefficient k Thermal conductivity of fluid L Collector length rh Mass flow rate per unit width T Fluid temperature T~ Ambient temperature Ti Fluid inlet temperature Tout Fluid outlet temperature Tp Plate temperature uL Collector losses heat transfer coefficient ut Top losses heat transfer coefficient w Collector width x coordinate in the fl0w direction Slope of the collector Oteq Equivalent absorptance of the collector aF Fluid absorptance ctp Plate absorptance 8 The fluid film thickness Collector efficiency tx Fluid dynamic viscosity pF Fluid film reflectance p Fluid density Transparent covers transmittance "rF Fluid film transmittance REFERENCES
1. J.T. Beard, F. A. Iachetta, L. U. Lillelebt, F. L. Huckstep, and W. B. May, Design and operation influences on thermal performance of "Solars", solar collector, J. Engng for Power 1110(4), 497-502 0978). 2. J. T. Beard, F. A. Iachetta, R. F. Messer, F. L. Huckstep, and W. B. May, Performance and analysis of an open fluid-film solar collector. Proc. 1977 Annual Meeting of the American Section of lSES 1 section l, 126-129 (Orlando F1 June 6, 1977). 3. Chungshiang Patrick Peng., Analysis of open inclined surface solar regenerators for absorption cooling applications-comprise between numerical and analytical models, Solar Energy 28(3), 265-268 0982). 4. D. Hershey, Transport Analysis, Plenum Press, New York, 112-113 (1973). 5. L. C. Thomas, Fundamentals of Heat Transfer, Prentice-Hall, Englewood Cliffs, N.J. (1980).