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Performance prediction for a built-in, storage-type solar water heater
0360-544?/85 $3.00 t Pergamon Press
.oO
I Id
PERFORMANCE PREDICTION FOR A BUILT-IN, STORAGE-TYPE SOLAR WATER HEATER J. PARKASH Physics Department, Ramjas College, University of Delhi, Delhi-l
10007
and H. P. GARG and G. DATTA Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi- 1 IO016, India (Received 9 March 1983; receivedfix publication 1 February 1985) Abstract-We have investigated the performance of a solar water heater with collector and baffle plate for six continuous days during the summer and winter seasons. The following cases were studied: (i) no flow, (ii) constant water flow rates, (iii) intermittent flow to meet requirements of hot water. and (iv) intermittent draw, with water withdrawn for short time intervals at specific hours.
NOMENCLATURE specific heat of glass, 670.0 (J/kg”C) specific heat of plate, 420.0 (J/kg”C) specific heat of water, 4190.0 (J/kg”C) heat transfer coefficient from stagnant air to glass, 1.8 (W/m’ “C) heat transfer coefficient from plate to glass cover, 6.3 (W/m2 “C) heat transfer coefficient from the water column above the baffle plate to the one below it, 534.5 (W/m2 “C) heat transfer coefficient from edge of plate to ambient air I .3 (W/m2 “C) heat-transfer coefficient from the plate to the water, 257 (W/m* “C) thermal conductivity of the baffle plate, 0.04 (W/m* “C) thickness of the baffle plate, 0.025 (m) mass of the glass cover. 7.5 (kg) mass of water in the upper column, 25 (kg) mass of water in the lower column, 75 (kg) mass flow rate, (I/hr) fraction of the open area of the baffle plate for contact between the water columns above and below. enclosed air temperature (“C) ambient temperature (“C) temperature of water in the upper column (“C) temperature of water in the lower column (“C) heat-loss coefficient from the glass, 30 (W/m2 “C) heat-loss coefficient from the bottom of the heater heat-loss coefficient from the glass when it is covered by insulation, I .2 (W/m’ “C) absorptance of the glass cover, 0.06 absorptance of the plate. 0.9 transmittance of the glass, 0.94 temperature (“C) of the water in the upper column at the end of the day temperature (“C) of the water in the lower column at the end of the day temperature of water in the upper column at the beginning of the day (“C) temperature (“C) of water in the lower column at the beginning of the day INTRODUCTION
Since the supply and demand of solar energy is intermittent, it is imperative to store solar energy when it is available. Water is one of the best sensible storage media because it has high specific heat and is available everywhere. Water is also a useful heat transfer medium. Built-in. storage-type water heaters, with heat collection and storage in a single unit, have been extensively studied.lm5 We have shown’ that a system with a baffle plate of insulating material, located just below the absorbing plate, improves the performance of solar water heaters. In this paper, we discuss the performance of a built-in, storage-type water heater with baffle plate, with and without movable insulation cover, for six continuous days during the summer and winter seasons. The technique of finite difference analysis is used to estimate water temperatures. The analysis refers to the following input parameters: the solar radiation
1210
J.
PARKASH
et 01.
in the plane of the absorbing plate and the ambient air temperature Delhi, at half-hourly intervals. DESIGN
OF
THE
measured at IIT, New
HEATER
The solar water heater is shown schematically in Fig. 1. It consists of a rectangular, galvanised iron sheet tank of 12.5 cm depth and 1 m* exposed surface area. The top surface of the tank is the absorber plate and is coated with black paint. The bottom and the sides of the tank are insulated with a 5 cm thick layer of fiberglass insulation. A glass cover, 3 mm thick, is placed over the black surface of the tank with an air gap of 2.5 cm. A baffle plate of 1 m2 surface area, 2.5 cm thickness and of good quality thermocol is fixed 2.5 cm below and parallel to the absorbing plate inside the tank, which contains 100 liters of water. Two holes in the baffle plate maintain contact between the water above and below. A sheet of 5 cm thick, good quality thermocol covers the glazing from 4:30 p.m. to 7:00 a.m. (offsunshine hours). Hot water is drawn from the outlet pipe located at the top above the baffle plate by opening a gate valve at the inlet pipe located at the bottom of the heater. The heater is inclined at 45” from the vertical and faces south to collect the maximum solar insolation at Delhi (28”N). MATHEMATICAL
FORMULATION
In order to predict the performance of the system, we have developed a transient model, which takes into consideration environmental conditions and heat capacities of various components of the heater. Heat balance equations for each collector node are written. The nodal temperatures are assumed to be uniform across any section of the heater. Changes in axial conduction have been neglected. (i) Energy balance in the absence of heat withdrawal The energy balance equation at the glass cover, absorber plate and for water above and below the baffle plate are, respectively:
hfgcg(atgiat) = 0$(f) + h,(t, - t&?)+ h& - tg) - U,(t* - ta) ~pCp(dtpl~t) = vS(t) M,t,(dt,/at)
- [h&p -
tA)
+
h2(tp
-
tg)
+
h,(t, - tl )I
= h,(t, - tl) - hj(tl - t2)R - k/d(t, - t2)(1 - R)
hf2tw(at2iat) = h&, -
t2)R
+
k/d(t, - &)(l - R) - Uz(t2 - t,),
(I) (2) (3) (4)
where tA
=
(tp
+
(5)
t,)/2
(ii) Energy balance with night insulation The glass plate is covered by an insulating cover during off-sunshine hours to reduce heat losses from water above baffle plate. The energy-balance equations at the glass plate and the absorber plate then become
Mgcgwgiat) = h&A - t3) + h&p - t&.)- U,(tg - ta)
(6)
~pcp@t~lat) = h&A - 4,) + h&. - tp) + hdt, - tp,),
(7)
while Eqs. (3) and (4) for water above and below the baffle plate remain unchanged. NIGHT GLASS
INSULMON COVER
ABSORBER WATER INSULATION BAFFLE
Fig.
PLATE
I. The design of the solar water heater.
COVER
Performance prediction for a solar water heater
6
16
6
1.3
1st DAV
_
T,t
WITH
_---
T,2
WITHOUT
-
AMBIENT
6
2nd
16
WV
3rd
6
INSULATION
TEMPERATURE
1.3
DAY
121 I
INSULATION
6
41h
16
DAY
6
5th
l@
DAY
6
6th
DAY
HOURS
Fig. 2. Effect of night insulation for no flow condition in summer
Energy balance with heat withdrawal For the mode when hot water is withdrawn from above the baffle flow rate by letting in cold water at ambient temperature at the bottom (1) and (2) again represent the energy balances at the glass cover and respectively. However, the energy balance equations above and below spectively, are modified to (iii)
h,&,
-
~1)
-
I@,
-
&JR
+
h61ul
-
f2)
-
plate at a constant of the heater, Eqs. the absorber plate, the baffle plate, re-
M,C,,@,l~0
=
MC’,,@,
-
22),
M2C,(at,/&)
= [hjR + hh(1 - R)J(t, - t2) - U2(12- to) - MC,,,(t2 - r,)
(8)
(9)
where h6 = K/l. The average efficiency of the heater is defined by
S(t) dt,
(10)
where Q is the sum of the heat stored in the collector and the heat withdrawn during a 24hour interval. For cases (i) and (ii) Q
=
Bf2G;
-
t20)
+
M,(f’,
-
MI(~‘,
-
t,o)lG
(11)
and for case (iii) Q
=
[M2(t;
-
~20)
+
~,o)lC,
+ MG s
(22
-
to)
6th
DAV
Integration in Eq. (12) refers to the water-flow period only. --
1 st DAY
2nd
T,t
WITH
T,2
WITHOUT
-
N
SOLAR
-
AMBIENT
DAV
3rd
INSULATION INSULATION
INSOLATION
DAV
TEMPERATURE
4 th DAY
5th
DAY
HOURS
Fig. 3. Effect of night insulation for no flow condition in winter.
dl
(12)
J. PARKASH et al.
1212 FLOW _.-.- -
-
-
I I 18
YES
SUMMER
40
10
YES
WINTER
10
”
NO
WINTER
40
‘1
NO
SUMMER
10
IJ
NO
6
SUMMER
40
‘I
WINTER
IO
J)
WINTER
40
,I
L
I I
I
II 6
1 51 DAY
INSULATION
10 I/hr
----
I
RATE
SUMMER
10 2nd
NO
AT
BETWEEN OTHER
9
&
21 HOURS
HOURS
NO
I I 18
OAV
FLOW
FLOW
YES YES
I I2 6
I
CONSTANT
I I* 6
I
3rd
I 18
DAY
L
4 th
1
I 18 6
I
1 18
‘FLOW NO FLOW
I I 6
I
II
1
1.3
5 th OAV
OAV
6th
OAV
HOURS
Fig. 4. Constant flow of water between 9:00 a.m. and 9:00 p.m.
NUMERICAL
CALCULATIONS
The simultaneous energy balance differential equations are converted into algebraic equations by replacing derivatives by difference terms of the ratios. The resulting algebraic equations are solved numerically with initial conditions that all of the various components of the collector are at ambient temperature. We found that the results of the calculations do not change significantly when the time intervals are reduced below 5 sec. The calculations were performed for six continuous clear days, both for winter and summer. RESULTS
AND
DISCUSSIONS
The results of numerical computations are shown in Figs. 2 to 6. Figures 2 and 3 illustrate the differences in water temperature with and without night insulation for no flow conditions in summer and winter, respectively. The water temperature is about 60°C in summer and about 50°C in winter during the morning hours. Figure 4 shows water temperatures for FLOW
RATE
INSULATION
----
WINTER
40
I/hr
NO
----
WINTER
10
)t
NO
-
SbMMER
40
I,
NO
-
SUMMER
10
I,
NO
-
WINTER
40
1,
YES
-Mt-
WINTER
10
1,
-.-
SUMMER
40
J!
YES YES
-.-
SUMMER
10
1,
WATER
YES
WITHORAWN 9 13 -
11 16
18 -
20
BETWEEN
60 z
50
Y 3 t
40
%
30
g
20
k t3
10
W FLOW
0 6
I2
18 1 st DAY
24
6
12
18
2 nd
DAV
24
6
12 3rd
1.9
24
6
DAY
12
18 4th
24
6
DAY
HOURS
Fig. 5. Intermittent flow of water.
12
18 5th
24 DAY
6
12
18
6 th DAY
24
6
Performance prediction for a solar water heater WATER
WITHDRAWN
NIGHT
INSULATION
251
at
11,13,15
&
17
1213
HOURS
PRESENT
” L
ii
60
? 2
40
$
20
9
FLOW NO FLOW
0 F
6
18
6
1 st DAV
18 ‘2nd
6 DAY
18 3rd
6 OAV
16
6
4 th DAY
18 5th
6 DAV
18 6th
6 DAY
HOURS
Fig. 6. Intermittent flow of water for 5 min intervals.
as well as summer, with and without night insulation, for the case when hot water is withdrawn from the heater at constant flow rates of 10 l./hr and 40 l./hr between 9:00 a.m. and 9:00 p.m. It is clear from Fig. 4 that the night insulation does not enhance water temperatures when hot water is withdrawn at 40 l./hr; however, for withdrawal of 10 l./hr, the enhancement of water temperature is marginal. Figure 5 is a similar plot of water temperatures for the case when hot water is withdrawn intermittently between 9:00 and 11:OOa.m., 1:OOand 5:00 p.m. and 6:00-8:OO p.m. at flow rates of 40 l./hr and 10 l./hr. In Fig. 6, we have plotted water temperatures when 25 liters of water are withdrawn in 5 minutes, four times a day (at 11:OOa.m., l:OO, 3:00, and 5:00 p.m.). From Fig. 6, we see that the withdrawal of hot water at 11:OOa.m. is not recommended on the first day, since the water temperature is only slightly higher than the ambient temperature. winter
CONCLUSION
The following conclusions may be drawn from our studies: (i) sufficient hot water can be obtained with a built-in, storage-type water heater for day-time use at high efficiency; (ii) for the summer months, the heater can be used with continuous flow throughout the day: (iii) for the winter months, it is preferable to use the heater with intermittent flow/draw conditions; (iv) the use of an insulation cover at night does not improve the performance significantly during continuous or intermittent flow conditions, especially for higher flow rates. REFERENCES
I. J. Prakash, H. P. Garg and G. Datta, Energy 8, 38 I (1983). 2. H. P. Garg, Treatise on Solar Energy, Vol. I: Fundamental of Solar Energy, John Wiley and Sons, Chichester. England (1982). 3. M. S. Sodha, P. K. Bansal and S. C. Kaushik, ht. J. Energy Res. 6,95 (1980). 4. H. P. Garg, Solar Energy 17, 167 (1975). 5. H. P. Garg and U. Rani, Solar Energy 29,467 (1982).
.oO
I Id
PERFORMANCE PREDICTION FOR A BUILT-IN, STORAGE-TYPE SOLAR WATER HEATER J. PARKASH Physics Department, Ramjas College, University of Delhi, Delhi-l
10007
and H. P. GARG and G. DATTA Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi- 1 IO016, India (Received 9 March 1983; receivedfix publication 1 February 1985) Abstract-We have investigated the performance of a solar water heater with collector and baffle plate for six continuous days during the summer and winter seasons. The following cases were studied: (i) no flow, (ii) constant water flow rates, (iii) intermittent flow to meet requirements of hot water. and (iv) intermittent draw, with water withdrawn for short time intervals at specific hours.
NOMENCLATURE specific heat of glass, 670.0 (J/kg”C) specific heat of plate, 420.0 (J/kg”C) specific heat of water, 4190.0 (J/kg”C) heat transfer coefficient from stagnant air to glass, 1.8 (W/m’ “C) heat transfer coefficient from plate to glass cover, 6.3 (W/m2 “C) heat transfer coefficient from the water column above the baffle plate to the one below it, 534.5 (W/m2 “C) heat transfer coefficient from edge of plate to ambient air I .3 (W/m2 “C) heat-transfer coefficient from the plate to the water, 257 (W/m* “C) thermal conductivity of the baffle plate, 0.04 (W/m* “C) thickness of the baffle plate, 0.025 (m) mass of the glass cover. 7.5 (kg) mass of water in the upper column, 25 (kg) mass of water in the lower column, 75 (kg) mass flow rate, (I/hr) fraction of the open area of the baffle plate for contact between the water columns above and below. enclosed air temperature (“C) ambient temperature (“C) temperature of water in the upper column (“C) temperature of water in the lower column (“C) heat-loss coefficient from the glass, 30 (W/m2 “C) heat-loss coefficient from the bottom of the heater heat-loss coefficient from the glass when it is covered by insulation, I .2 (W/m’ “C) absorptance of the glass cover, 0.06 absorptance of the plate. 0.9 transmittance of the glass, 0.94 temperature (“C) of the water in the upper column at the end of the day temperature (“C) of the water in the lower column at the end of the day temperature of water in the upper column at the beginning of the day (“C) temperature (“C) of water in the lower column at the beginning of the day INTRODUCTION
Since the supply and demand of solar energy is intermittent, it is imperative to store solar energy when it is available. Water is one of the best sensible storage media because it has high specific heat and is available everywhere. Water is also a useful heat transfer medium. Built-in. storage-type water heaters, with heat collection and storage in a single unit, have been extensively studied.lm5 We have shown’ that a system with a baffle plate of insulating material, located just below the absorbing plate, improves the performance of solar water heaters. In this paper, we discuss the performance of a built-in, storage-type water heater with baffle plate, with and without movable insulation cover, for six continuous days during the summer and winter seasons. The technique of finite difference analysis is used to estimate water temperatures. The analysis refers to the following input parameters: the solar radiation
1210
J.
PARKASH
et 01.
in the plane of the absorbing plate and the ambient air temperature Delhi, at half-hourly intervals. DESIGN
OF
THE
measured at IIT, New
HEATER
The solar water heater is shown schematically in Fig. 1. It consists of a rectangular, galvanised iron sheet tank of 12.5 cm depth and 1 m* exposed surface area. The top surface of the tank is the absorber plate and is coated with black paint. The bottom and the sides of the tank are insulated with a 5 cm thick layer of fiberglass insulation. A glass cover, 3 mm thick, is placed over the black surface of the tank with an air gap of 2.5 cm. A baffle plate of 1 m2 surface area, 2.5 cm thickness and of good quality thermocol is fixed 2.5 cm below and parallel to the absorbing plate inside the tank, which contains 100 liters of water. Two holes in the baffle plate maintain contact between the water above and below. A sheet of 5 cm thick, good quality thermocol covers the glazing from 4:30 p.m. to 7:00 a.m. (offsunshine hours). Hot water is drawn from the outlet pipe located at the top above the baffle plate by opening a gate valve at the inlet pipe located at the bottom of the heater. The heater is inclined at 45” from the vertical and faces south to collect the maximum solar insolation at Delhi (28”N). MATHEMATICAL
FORMULATION
In order to predict the performance of the system, we have developed a transient model, which takes into consideration environmental conditions and heat capacities of various components of the heater. Heat balance equations for each collector node are written. The nodal temperatures are assumed to be uniform across any section of the heater. Changes in axial conduction have been neglected. (i) Energy balance in the absence of heat withdrawal The energy balance equation at the glass cover, absorber plate and for water above and below the baffle plate are, respectively:
hfgcg(atgiat) = 0$(f) + h,(t, - t&?)+ h& - tg) - U,(t* - ta) ~pCp(dtpl~t) = vS(t) M,t,(dt,/at)
- [h&p -
tA)
+
h2(tp
-
tg)
+
h,(t, - tl )I
= h,(t, - tl) - hj(tl - t2)R - k/d(t, - t2)(1 - R)
hf2tw(at2iat) = h&, -
t2)R
+
k/d(t, - &)(l - R) - Uz(t2 - t,),
(I) (2) (3) (4)
where tA
=
(tp
+
(5)
t,)/2
(ii) Energy balance with night insulation The glass plate is covered by an insulating cover during off-sunshine hours to reduce heat losses from water above baffle plate. The energy-balance equations at the glass plate and the absorber plate then become
Mgcgwgiat) = h&A - t3) + h&p - t&.)- U,(tg - ta)
(6)
~pcp@t~lat) = h&A - 4,) + h&. - tp) + hdt, - tp,),
(7)
while Eqs. (3) and (4) for water above and below the baffle plate remain unchanged. NIGHT GLASS
INSULMON COVER
ABSORBER WATER INSULATION BAFFLE
Fig.
PLATE
I. The design of the solar water heater.
COVER
Performance prediction for a solar water heater
6
16
6
1.3
1st DAV
_
T,t
WITH
_---
T,2
WITHOUT
-
AMBIENT
6
2nd
16
WV
3rd
6
INSULATION
TEMPERATURE
1.3
DAY
121 I
INSULATION
6
41h
16
DAY
6
5th
l@
DAY
6
6th
DAY
HOURS
Fig. 2. Effect of night insulation for no flow condition in summer
Energy balance with heat withdrawal For the mode when hot water is withdrawn from above the baffle flow rate by letting in cold water at ambient temperature at the bottom (1) and (2) again represent the energy balances at the glass cover and respectively. However, the energy balance equations above and below spectively, are modified to (iii)
h,&,
-
~1)
-
I@,
-
&JR
+
h61ul
-
f2)
-
plate at a constant of the heater, Eqs. the absorber plate, the baffle plate, re-
M,C,,@,l~0
=
MC’,,@,
-
22),
M2C,(at,/&)
= [hjR + hh(1 - R)J(t, - t2) - U2(12- to) - MC,,,(t2 - r,)
(8)
(9)
where h6 = K/l. The average efficiency of the heater is defined by
S(t) dt,
(10)
where Q is the sum of the heat stored in the collector and the heat withdrawn during a 24hour interval. For cases (i) and (ii) Q
=
Bf2G;
-
t20)
+
M,(f’,
-
MI(~‘,
-
t,o)lG
(11)
and for case (iii) Q
=
[M2(t;
-
~20)
+
~,o)lC,
+ MG s
(22
-
to)
6th
DAV
Integration in Eq. (12) refers to the water-flow period only. --
1 st DAY
2nd
T,t
WITH
T,2
WITHOUT
-
N
SOLAR
-
AMBIENT
DAV
3rd
INSULATION INSULATION
INSOLATION
DAV
TEMPERATURE
4 th DAY
5th
DAY
HOURS
Fig. 3. Effect of night insulation for no flow condition in winter.
dl
(12)
J. PARKASH et al.
1212 FLOW _.-.- -
-
-
I I 18
YES
SUMMER
40
10
YES
WINTER
10
”
NO
WINTER
40
‘1
NO
SUMMER
10
IJ
NO
6
SUMMER
40
‘I
WINTER
IO
J)
WINTER
40
,I
L
I I
I
II 6
1 51 DAY
INSULATION
10 I/hr
----
I
RATE
SUMMER
10 2nd
NO
AT
BETWEEN OTHER
9
&
21 HOURS
HOURS
NO
I I 18
OAV
FLOW
FLOW
YES YES
I I2 6
I
CONSTANT
I I* 6
I
3rd
I 18
DAY
L
4 th
1
I 18 6
I
1 18
‘FLOW NO FLOW
I I 6
I
II
1
1.3
5 th OAV
OAV
6th
OAV
HOURS
Fig. 4. Constant flow of water between 9:00 a.m. and 9:00 p.m.
NUMERICAL
CALCULATIONS
The simultaneous energy balance differential equations are converted into algebraic equations by replacing derivatives by difference terms of the ratios. The resulting algebraic equations are solved numerically with initial conditions that all of the various components of the collector are at ambient temperature. We found that the results of the calculations do not change significantly when the time intervals are reduced below 5 sec. The calculations were performed for six continuous clear days, both for winter and summer. RESULTS
AND
DISCUSSIONS
The results of numerical computations are shown in Figs. 2 to 6. Figures 2 and 3 illustrate the differences in water temperature with and without night insulation for no flow conditions in summer and winter, respectively. The water temperature is about 60°C in summer and about 50°C in winter during the morning hours. Figure 4 shows water temperatures for FLOW
RATE
INSULATION
----
WINTER
40
I/hr
NO
----
WINTER
10
)t
NO
-
SbMMER
40
I,
NO
-
SUMMER
10
I,
NO
-
WINTER
40
1,
YES
-Mt-
WINTER
10
1,
-.-
SUMMER
40
J!
YES YES
-.-
SUMMER
10
1,
WATER
YES
WITHORAWN 9 13 -
11 16
18 -
20
BETWEEN
60 z
50
Y 3 t
40
%
30
g
20
k t3
10
W FLOW
0 6
I2
18 1 st DAY
24
6
12
18
2 nd
DAV
24
6
12 3rd
1.9
24
6
DAY
12
18 4th
24
6
DAY
HOURS
Fig. 5. Intermittent flow of water.
12
18 5th
24 DAY
6
12
18
6 th DAY
24
6
Performance prediction for a solar water heater WATER
WITHDRAWN
NIGHT
INSULATION
251
at
11,13,15
&
17
1213
HOURS
PRESENT
” L
ii
60
? 2
40
$
20
9
FLOW NO FLOW
0 F
6
18
6
1 st DAV
18 ‘2nd
6 DAY
18 3rd
6 OAV
16
6
4 th DAY
18 5th
6 DAV
18 6th
6 DAY
HOURS
Fig. 6. Intermittent flow of water for 5 min intervals.
as well as summer, with and without night insulation, for the case when hot water is withdrawn from the heater at constant flow rates of 10 l./hr and 40 l./hr between 9:00 a.m. and 9:00 p.m. It is clear from Fig. 4 that the night insulation does not enhance water temperatures when hot water is withdrawn at 40 l./hr; however, for withdrawal of 10 l./hr, the enhancement of water temperature is marginal. Figure 5 is a similar plot of water temperatures for the case when hot water is withdrawn intermittently between 9:00 and 11:OOa.m., 1:OOand 5:00 p.m. and 6:00-8:OO p.m. at flow rates of 40 l./hr and 10 l./hr. In Fig. 6, we have plotted water temperatures when 25 liters of water are withdrawn in 5 minutes, four times a day (at 11:OOa.m., l:OO, 3:00, and 5:00 p.m.). From Fig. 6, we see that the withdrawal of hot water at 11:OOa.m. is not recommended on the first day, since the water temperature is only slightly higher than the ambient temperature. winter
CONCLUSION
The following conclusions may be drawn from our studies: (i) sufficient hot water can be obtained with a built-in, storage-type water heater for day-time use at high efficiency; (ii) for the summer months, the heater can be used with continuous flow throughout the day: (iii) for the winter months, it is preferable to use the heater with intermittent flow/draw conditions; (iv) the use of an insulation cover at night does not improve the performance significantly during continuous or intermittent flow conditions, especially for higher flow rates. REFERENCES
I. J. Prakash, H. P. Garg and G. Datta, Energy 8, 38 I (1983). 2. H. P. Garg, Treatise on Solar Energy, Vol. I: Fundamental of Solar Energy, John Wiley and Sons, Chichester. England (1982). 3. M. S. Sodha, P. K. Bansal and S. C. Kaushik, ht. J. Energy Res. 6,95 (1980). 4. H. P. Garg, Solar Energy 17, 167 (1975). 5. H. P. Garg and U. Rani, Solar Energy 29,467 (1982).