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Nomographs for H2O-LiBr absorption-panel cooling systems
Energy Vol. 17, No. 11, pp. 1059-1064, 1992
0360-5442192 $5.00+ 0.00
Copyright@ 1992PergamonPressLtd
Printedin Great Britain.All rightsreserved
NOMOGRAPHS
FOR H20-LiBr ABSORPTION-PANEL COOLING SYSTEMS E. D. ROGDAKIS
Mechanical Engineering Department, National Technical University of Athens, Thermal Section, 42 Patission Street, Athens-106 82, Greece (Received 11 September 1991; received for publication 26 March 1992) Abstract-Panel cooling of buildings offers energy savings over conventional space-cooling systems. We present a procedure for calculating the performance of H,O-LiBr absorptionpanel cooling systems, in which the evaporator is the panel itself. Nomographs have been developed for this approach. Under the conditions examined, the H,O-LiBr absorption unit operates with a theoretical performance coefficient of about 90% and with a practically constant specific cooling capacity of 2394 kJ/kg H20. For common values of the parameters involved, the panel cooling power varies from 25 to 175 W/m* and the cooling water mass-flow rate through the panel is M-260 g/m’h. The thermal power needed to drive the system varies from 27 to 200 W/m’ and the associated temperatures from 70 to 100°C; thus, the system may be operated on solar energy.
INTRODUCTION
In panel cooling of buildings,’ the cooling element is the ceiling, which contains pipes through which coolant water flows (see Fig. 1). Panel-cooling systems offer energy savings over conventional space-cooling systems because (a) comfort is obtained with higher room temperatures owing to radiative heat exchange between the heads of people and the ceiling, (b) higher temperatures of the cooling water than normal are usable because of large cooling surfaces, and (c) the cool storage obtained within the structural elements reduces the peak loads. In the present study, we have considered panel cooling using HzO-LiBr absorption refrigerators. As is shown in Fig. 1, for small systems, the panel itself may be used as the evaporator of the absorption unit, thus reducing both construction costs and losses during operation. The purpose of this study is to provide an analysis of such systems and to develop nomographs allowing an immediate calculation of the main characteristics for various values of the parameters involved. The work is based on a method which simulates the operation of the HzO-LiBr unit. For the thermal behaviour of the panel, use is made of the analysis presented in Ref. 2, according to which the heat absorbed from a room per unit area of the panel QC(in W/m*) may be expressed as
where Fl
=
S hS -’ Do + (S - D,-,)F + nQht 1
F = tanh[m(S - D,)/%]/[m(S - &)/2],
m =
[h//w]“*.
(3) (4)
In the preceding equations, h (in W/m* “C) is the heat-transfer coefficient for the panel surface; T, and & (in “C) are the temperature of the room air and the mean temperature of the cooling water, respectively; S and w (in m) represent the pipe spacing and panel thickness, respectively (Fig. 1); Do and Di (in m) are the outside and inside pipe diameters, respectively; ht (in 1059
1060
E. D. ROGDAKIS
D--l Gen
Con
t ’
Fig. 1. Proposed
Heat flow from room
small panel cooling system working with an H,O-LiBr evaporator of which is the panel itself.
absorption-refrigerator,
the
W/m* “C) is the heat-transfer coefficient on the inside pipe surface, and k (in W/m “C) is the thermal conductivity of the panel.
OPERATION
OF
THE
H,O-LiBr
UNIT
Figure 2 shows an example of the HzO-LiBr absorption-refrigeration cycle calculated by using a method presented in previous publications.>5 The thermodynamic changes involved are the following: 1-2, heat exchange from the hot, strong absorbent to the weak absorbent; 2-3, generation of superheated steam; 3-4, cooling of superheated steam; 4-5, condensation of saturated steam; 5-6, subcooling of water; 6-7, evaporation; 7-8, superheating of steam; 8-1, absorption of steam by the strong absorbent which produces the weak absorbent. In the present simulation, the condensation temperature is fixed at T,,,=
r,=
T,=43.s”c>
P,,= 55 torr, P, = 6 torr. X,
z&b, = 59%,
Xs = 64%
100 90 80 c e
70-
? 3 6o %505 Q 40E I-” 30-
1
20 10 01
-1000
0
1000
Enthalpy Fig. 2. H,O-LiBr
absorption-refrigeration
2000
3000
(kJ/kg)
cycle in the enthalpy-temperature
plane
43.5
12.76
17.51
15
20
43.5
66.4
66.4
66.4
($1
‘s
50.5 55.5
53.7 58.7
56.7 61.7
59.7 64.7
43.5
43.5
9.18
‘VI
10
ph
66.4
abs,ll
6.52
=T
con
5
PL
T
(Torr) (%I
,&
Tf
52.7
53.3
53.6
53.9
(00'
93.2
82.0
70.0
79.5
86.3
100.6
75.9
qh 911
2580
2641
2696
2742
2394
2394
2394
2394
S=0.2m,Tr=240C
from 5 to 20°C.
92.8
90.6
88.8
87.3
28.1
63.2
98.3
133.4
42.3
95.0
147.8
200.6
m COP 4, (%I (W/m21 (g/m2h)
unit for evaporation temperatures
('C) (kJ/kgH20)(kJ/kgH20)
88.5
(OC)
h T gen,L Tgen,h
absorption-refrigeration
Tabs
Table1. Calculated characteristics of the H,O-LiBr
(Torr) (oC)
=T
r
E. D.
1062
ROGDAKIS
i.e. it is higher than the ambient temperature Tami,, thus ensuring heat rejection to the environment. The corresponding high pressure pi, of the cycle is calculated from the p-T relation of saturated water, i.e. ph = exp(32.4668 - [489.58/( T,,, + 273.15) + 3.77087]‘2}, where pi, is in torr and T,,, in “C. Calculations have been performed range
for various values of the evaporation
(6)
temperature
T,, = & = z-+= 5°C - 20°C.
in the
(7)
The low pressure p/ (in torr) of the cycle, corresponding to the values of T,, (in “C), is calculated from the p-T relation for saturated water [see Eq. (6)]. In order to ensure heat rejection from the absorber to the ambient, the lowest temperature in the absorber Tabs/ is taken to be higher than the ambient temperature and equal to the condensation temperature, i .e . T&,&= & = T,, = 43.5”C. The weak absorbent following equation:
Tabsl= A(X,)
where
and B(X,)
in terms of Tabs/ and T,, by solving the
mass fraction X, is calculated
AWJL
+ B(xw),
(8)
are polynomials of the third order with respect to X, (see Appendix). Tr =
24°C
(d) 175
25
225
185
cF 145 E
2
-E
105
65
25
1
I
I
I
I
I
25
55
65
115
145
175
c(
W/m”)
5
8
11
14
17
T, = (“C)
Fig. 3. Nomograph for the calculation of H,O-LiBr absorption-panel cooling systems for 24°C room temperature under conditions specified in the text.
20
Nomographs
The strong absorbent
for H,O-LiBr
absorption-panel
cooling
systems
1063
mass fraction X, is taken to be 5% greater than X,, i.e. x,=x,+5.
(9)
The highest temperature in the absorber Tabs,hand the lowest and highest temperatures generator are Tgen/ and Tgen,h, respectively and are calculated from the relations Tabs,h
=
B(X,),
(10)
Tgen~= T2 = A(Xw)Tc,,
+ WX,),
(11)
Tgen,h
+
(12)
=
K
=A(XdT,v
T3 =
+
in the
AVQL,,
stxs),
where the polynomials A(X) and B(X) are given in the Appendix. Taking into account that a part of the heat rejected along the cooling line 3-4 in Fig. 2 is used in preheating 1-2, the heat input qh (in kJ/kg H20) at the high-temperature level (generator) is calculated from3 q,, = h3 - h2 = 1.73T,,,,,
+ 2501.6 - x “;, s
w
h(L1,
X,)+x
1’u,
s
w
W&n,/, X,)7
(13)
where h(T, X) is the enthalpy function of the HzO-LiBr solution, which is given in terms of the temperature T and the mass fraction X in the Appendix. The cooling g/ (in kJ/kg H20) produced at the low-temperature level (evaporator) is3 q/= h, - h6 + [(h8 - h7) - (h5 - h6)] = h8 - h5 = 1.73Tabs/+ 2501.6 - 4. 199TC0,,
(14)
Tr = 20°C
(d)
(cl
(b)
225
la5 F
iz
“E
145
i%
-E
105
65
25 60
80
100
120
5
a
11
T, = 20°C
c(. W/m')
Fig. 4. As in Fig. 3 but for T, = 20°C.
14
17
20
1064
E. D. ROGDAKIS
and the coefficient of performance
is COP = qdqh.
Table 1 shows the characteristics to 20°C.
(15)
of the absorption-refrigeration
DEVELOPMENT
OF
unit for T,, ranging from 5
NOMOGRAPHS
Figure 3 shows a nomograph connecting characteristics of the cooling panel to characteristics of the H,O-LiBr absorption-refrigeration unit. The parameters for the panel are T, = 24”C, h = 9.7 W/m’“C, 0, =O.O2m, Q = O.O18m, k = 1.4 W/m”C; also w = O.O4m, and hf= 3100 W/m’“C, while the HzO-LiBr unit operates under the conditions described in the previous section. Figure 3(a) has been plotted by the use of Eqs. (l)-(4) and shows the cooling power of the panel Qc (in W/m2) in terms of the cooling-fluid temperature T,= T,, (in “C) with the tube spacing S (in m) as a parameter. As is shown in Table 1, the specific cooling capacity of the H,O-LiBr unit is practically constant at q/= 2394 kJ/kg. Therefore, for each value of the tube spacing S, the refrigerant mass-flow rate ti can be expressed in terms of Tf only, i.e. ti = Q,(T,)/q,
for S = constant.
(16)
Figure 3(b) shows ti (in g/m2h) in terms of Tf with S as a parameter
according to Eq. (16).
T, = 28°C
(a)
(4 zoo
COP = 100%
\
170
140
110
80
50
lb)
(cl 225 -
185 -
145 -
65 -
25 50
I
I
I
I
I
80
110
140
170
200
5
I
I
I
I
I
8
11
14
17
20
cih P/m21
T,("C)
Fig. 5. As in Fig. 3 but for T, = 28°C.
1065
Nomographs for H,O-LiBr absorption-panel cooling systems The thermal
power
4,, (in W/m”) required
4h(+
to drive the HzO-LiBr
unit is
&) = ~qll(Tf),
(17)
where the specific heat input at the high-temperature level q,,(T,) is a function of 1). Figure 3(c) shows the & - ri? relation with Tf as a parameter according to Eq. Figure 3(d) shows the panel-cooling power Qc (in W/m’) in terms of the thermal W/m*) required to drive the unit, with the coefficient of performance COP as a the relation
Tf (see Table (17). power & (in parameter in
& = (COP)&
(18)
An example of the use of the nomograph is given by the dotted lines in Fig. 3. If the required cooling power is gc = 95 W/m* with a tube spacing S = 0.20 m, then the remaining characteristics of the system will be as follows: Tr = lOS”C, ti = 142.9 g/m*h, Q,, = 107 W/m*, and COP = 89%. Similar nomographs for T, = 20 and 28°C have also been developed and are given in Figs. 4 and 5, respectively.
REFERENCES 1. R. W. Shoemaker, Radiant Heating, McGraw-Hill, New York, NY (1954). 2. K. A. Antonopoulos, Znt. J. Heat Mass Transfer, in press (1992). 3. D. A, Kouremenos, K. A. Antonopoulos, and E. D. Rogdakis, Heat Recovery Systems CHP 9, 189 (1989). 4. D. A. Kouremenos,
5. D. A. Kouremenos,
K. A. Antonopoulos, and E. D. Rogdakis, Sol. Wind Technol. 7, 111 (1990). E. D. Rogdakis, and K. A. Antonopoulos, Energy-The International Journal 14,
893 (1989).
APPENDIX The polynomials A(X) and B(X) used in Eqs. (10) and (12)-(14) 0.16976X - 3. 133362X21O-3 - 1.9766X310-‘,
are A(X) = -2.0075 +
B(X) = 124.94 - 7.71649X + 0.1522858X2 - 7.95O9X31O-4. The enthalpy h(T, X) of the H20/LiBr solution used in Eq. (15) is given in terms of the temperature T (in “C) and the mass fraction X (%) by the relation h(T, X) = E,(X) + TE,(X) + T2E2(X), where E,(X) = -2024.18588321+
163.2976010204X - 4.88126853177X2
+ 6.30250843X310-* - 2.9135O364X41O-4, E,(X) = 18.2816227619 - 1.169094163968X + 3.24785671X210-* -4.O339O218X31O-4 + 1.85192774X41O-6, E*(X) = -0.0370056321+
2.88756514X1O-3 - 8. 13O75689X21O-5
+ 9.91O97142X31O-7 - 4.44381O71X41O-9. NOMENCLATURE A(X),
B(X) = Third-order
polynomials given in the Appendix COP = Coefficient of performance DO, Di = Outside and inside pipe diameters (m), respectively
J%(X), E,(X), = Fourth-order polynomials given in the Appendix Ez(X) F, fi = Dimensionless coefficients given by Eqs. (3) and (2), respectively
E. D. ROGDAKIS
1066
h, h, = Heat-transfer coefficients (W/m’ “C) of the panel surface and of the inside pipe surface, respectively hi = Specific enthalpy at state i &J/kg HzO) h( T, X) = Specific enthalpy function
@J/kg H,O) k = Thermal conductivity
of the panel (W/m “C) ti = Refrigerant mass-flow rate through the panel (kg H,O/m’s or g H,O/m’h) m = Variable (m-‘) given in Eq. (4) p/, ph = Low and high pressure (torr) respectively q/, qh = Heat inputs (kJ/kg H,O) at the low- and hightemperature levels, respectively Qc= Specific cooling capacity of the panel (W/m’)
g,, = Specific thermal power required to drive the system (W/m’) S = Pipe spacing of the panel (m) Krnb = Ambient temperature (“C) T,,, Ten= Condensation and evaporation temperatures (“C), respectively Tf = Cooling-fluid temperature through the panel, which is equal to T,, (“C) T, = Room-air temperature (“C) Tat&> Tabs.,,= Lowest and highest temperatures in the absorber (“C) Tgen/p Tgen.h= Lowest and highest temperatues in the generator (“C) w = Panel thickness (m) X,, X, = Weak and strong absorbent mass fractions (% , 100 X kg LiBr/kg mixture)
0360-5442192 $5.00+ 0.00
Copyright@ 1992PergamonPressLtd
Printedin Great Britain.All rightsreserved
NOMOGRAPHS
FOR H20-LiBr ABSORPTION-PANEL COOLING SYSTEMS E. D. ROGDAKIS
Mechanical Engineering Department, National Technical University of Athens, Thermal Section, 42 Patission Street, Athens-106 82, Greece (Received 11 September 1991; received for publication 26 March 1992) Abstract-Panel cooling of buildings offers energy savings over conventional space-cooling systems. We present a procedure for calculating the performance of H,O-LiBr absorptionpanel cooling systems, in which the evaporator is the panel itself. Nomographs have been developed for this approach. Under the conditions examined, the H,O-LiBr absorption unit operates with a theoretical performance coefficient of about 90% and with a practically constant specific cooling capacity of 2394 kJ/kg H20. For common values of the parameters involved, the panel cooling power varies from 25 to 175 W/m* and the cooling water mass-flow rate through the panel is M-260 g/m’h. The thermal power needed to drive the system varies from 27 to 200 W/m’ and the associated temperatures from 70 to 100°C; thus, the system may be operated on solar energy.
INTRODUCTION
In panel cooling of buildings,’ the cooling element is the ceiling, which contains pipes through which coolant water flows (see Fig. 1). Panel-cooling systems offer energy savings over conventional space-cooling systems because (a) comfort is obtained with higher room temperatures owing to radiative heat exchange between the heads of people and the ceiling, (b) higher temperatures of the cooling water than normal are usable because of large cooling surfaces, and (c) the cool storage obtained within the structural elements reduces the peak loads. In the present study, we have considered panel cooling using HzO-LiBr absorption refrigerators. As is shown in Fig. 1, for small systems, the panel itself may be used as the evaporator of the absorption unit, thus reducing both construction costs and losses during operation. The purpose of this study is to provide an analysis of such systems and to develop nomographs allowing an immediate calculation of the main characteristics for various values of the parameters involved. The work is based on a method which simulates the operation of the HzO-LiBr unit. For the thermal behaviour of the panel, use is made of the analysis presented in Ref. 2, according to which the heat absorbed from a room per unit area of the panel QC(in W/m*) may be expressed as
where Fl
=
S hS -’ Do + (S - D,-,)F + nQht 1
F = tanh[m(S - D,)/%]/[m(S - &)/2],
m =
[h//w]“*.
(3) (4)
In the preceding equations, h (in W/m* “C) is the heat-transfer coefficient for the panel surface; T, and & (in “C) are the temperature of the room air and the mean temperature of the cooling water, respectively; S and w (in m) represent the pipe spacing and panel thickness, respectively (Fig. 1); Do and Di (in m) are the outside and inside pipe diameters, respectively; ht (in 1059
1060
E. D. ROGDAKIS
D--l Gen
Con
t ’
Fig. 1. Proposed
Heat flow from room
small panel cooling system working with an H,O-LiBr evaporator of which is the panel itself.
absorption-refrigerator,
the
W/m* “C) is the heat-transfer coefficient on the inside pipe surface, and k (in W/m “C) is the thermal conductivity of the panel.
OPERATION
OF
THE
H,O-LiBr
UNIT
Figure 2 shows an example of the HzO-LiBr absorption-refrigeration cycle calculated by using a method presented in previous publications.>5 The thermodynamic changes involved are the following: 1-2, heat exchange from the hot, strong absorbent to the weak absorbent; 2-3, generation of superheated steam; 3-4, cooling of superheated steam; 4-5, condensation of saturated steam; 5-6, subcooling of water; 6-7, evaporation; 7-8, superheating of steam; 8-1, absorption of steam by the strong absorbent which produces the weak absorbent. In the present simulation, the condensation temperature is fixed at T,,,=
r,=
T,=43.s”c>
P,,= 55 torr, P, = 6 torr. X,
z&b, = 59%,
Xs = 64%
100 90 80 c e
70-
? 3 6o %505 Q 40E I-” 30-
1
20 10 01
-1000
0
1000
Enthalpy Fig. 2. H,O-LiBr
absorption-refrigeration
2000
3000
(kJ/kg)
cycle in the enthalpy-temperature
plane
43.5
12.76
17.51
15
20
43.5
66.4
66.4
66.4
($1
‘s
50.5 55.5
53.7 58.7
56.7 61.7
59.7 64.7
43.5
43.5
9.18
‘VI
10
ph
66.4
abs,ll
6.52
=T
con
5
PL
T
(Torr) (%I
,&
Tf
52.7
53.3
53.6
53.9
(00'
93.2
82.0
70.0
79.5
86.3
100.6
75.9
qh 911
2580
2641
2696
2742
2394
2394
2394
2394
S=0.2m,Tr=240C
from 5 to 20°C.
92.8
90.6
88.8
87.3
28.1
63.2
98.3
133.4
42.3
95.0
147.8
200.6
m COP 4, (%I (W/m21 (g/m2h)
unit for evaporation temperatures
('C) (kJ/kgH20)(kJ/kgH20)
88.5
(OC)
h T gen,L Tgen,h
absorption-refrigeration
Tabs
Table1. Calculated characteristics of the H,O-LiBr
(Torr) (oC)
=T
r
E. D.
1062
ROGDAKIS
i.e. it is higher than the ambient temperature Tami,, thus ensuring heat rejection to the environment. The corresponding high pressure pi, of the cycle is calculated from the p-T relation of saturated water, i.e. ph = exp(32.4668 - [489.58/( T,,, + 273.15) + 3.77087]‘2}, where pi, is in torr and T,,, in “C. Calculations have been performed range
for various values of the evaporation
(6)
temperature
T,, = & = z-+= 5°C - 20°C.
in the
(7)
The low pressure p/ (in torr) of the cycle, corresponding to the values of T,, (in “C), is calculated from the p-T relation for saturated water [see Eq. (6)]. In order to ensure heat rejection from the absorber to the ambient, the lowest temperature in the absorber Tabs/ is taken to be higher than the ambient temperature and equal to the condensation temperature, i .e . T&,&= & = T,, = 43.5”C. The weak absorbent following equation:
Tabsl= A(X,)
where
and B(X,)
in terms of Tabs/ and T,, by solving the
mass fraction X, is calculated
AWJL
+ B(xw),
(8)
are polynomials of the third order with respect to X, (see Appendix). Tr =
24°C
(d) 175
25
225
185
cF 145 E
2
-E
105
65
25
1
I
I
I
I
I
25
55
65
115
145
175
c(
W/m”)
5
8
11
14
17
T, = (“C)
Fig. 3. Nomograph for the calculation of H,O-LiBr absorption-panel cooling systems for 24°C room temperature under conditions specified in the text.
20
Nomographs
The strong absorbent
for H,O-LiBr
absorption-panel
cooling
systems
1063
mass fraction X, is taken to be 5% greater than X,, i.e. x,=x,+5.
(9)
The highest temperature in the absorber Tabs,hand the lowest and highest temperatures generator are Tgen/ and Tgen,h, respectively and are calculated from the relations Tabs,h
=
B(X,),
(10)
Tgen~= T2 = A(Xw)Tc,,
+ WX,),
(11)
Tgen,h
+
(12)
=
K
=A(XdT,v
T3 =
+
in the
AVQL,,
stxs),
where the polynomials A(X) and B(X) are given in the Appendix. Taking into account that a part of the heat rejected along the cooling line 3-4 in Fig. 2 is used in preheating 1-2, the heat input qh (in kJ/kg H20) at the high-temperature level (generator) is calculated from3 q,, = h3 - h2 = 1.73T,,,,,
+ 2501.6 - x “;, s
w
h(L1,
X,)+x
1’u,
s
w
W&n,/, X,)7
(13)
where h(T, X) is the enthalpy function of the HzO-LiBr solution, which is given in terms of the temperature T and the mass fraction X in the Appendix. The cooling g/ (in kJ/kg H20) produced at the low-temperature level (evaporator) is3 q/= h, - h6 + [(h8 - h7) - (h5 - h6)] = h8 - h5 = 1.73Tabs/+ 2501.6 - 4. 199TC0,,
(14)
Tr = 20°C
(d)
(cl
(b)
225
la5 F
iz
“E
145
i%
-E
105
65
25 60
80
100
120
5
a
11
T, = 20°C
c(. W/m')
Fig. 4. As in Fig. 3 but for T, = 20°C.
14
17
20
1064
E. D. ROGDAKIS
and the coefficient of performance
is COP = qdqh.
Table 1 shows the characteristics to 20°C.
(15)
of the absorption-refrigeration
DEVELOPMENT
OF
unit for T,, ranging from 5
NOMOGRAPHS
Figure 3 shows a nomograph connecting characteristics of the cooling panel to characteristics of the H,O-LiBr absorption-refrigeration unit. The parameters for the panel are T, = 24”C, h = 9.7 W/m’“C, 0, =O.O2m, Q = O.O18m, k = 1.4 W/m”C; also w = O.O4m, and hf= 3100 W/m’“C, while the HzO-LiBr unit operates under the conditions described in the previous section. Figure 3(a) has been plotted by the use of Eqs. (l)-(4) and shows the cooling power of the panel Qc (in W/m2) in terms of the cooling-fluid temperature T,= T,, (in “C) with the tube spacing S (in m) as a parameter. As is shown in Table 1, the specific cooling capacity of the H,O-LiBr unit is practically constant at q/= 2394 kJ/kg. Therefore, for each value of the tube spacing S, the refrigerant mass-flow rate ti can be expressed in terms of Tf only, i.e. ti = Q,(T,)/q,
for S = constant.
(16)
Figure 3(b) shows ti (in g/m2h) in terms of Tf with S as a parameter
according to Eq. (16).
T, = 28°C
(a)
(4 zoo
COP = 100%
\
170
140
110
80
50
lb)
(cl 225 -
185 -
145 -
65 -
25 50
I
I
I
I
I
80
110
140
170
200
5
I
I
I
I
I
8
11
14
17
20
cih P/m21
T,("C)
Fig. 5. As in Fig. 3 but for T, = 28°C.
1065
Nomographs for H,O-LiBr absorption-panel cooling systems The thermal
power
4,, (in W/m”) required
4h(+
to drive the HzO-LiBr
unit is
&) = ~qll(Tf),
(17)
where the specific heat input at the high-temperature level q,,(T,) is a function of 1). Figure 3(c) shows the & - ri? relation with Tf as a parameter according to Eq. Figure 3(d) shows the panel-cooling power Qc (in W/m’) in terms of the thermal W/m*) required to drive the unit, with the coefficient of performance COP as a the relation
Tf (see Table (17). power & (in parameter in
& = (COP)&
(18)
An example of the use of the nomograph is given by the dotted lines in Fig. 3. If the required cooling power is gc = 95 W/m* with a tube spacing S = 0.20 m, then the remaining characteristics of the system will be as follows: Tr = lOS”C, ti = 142.9 g/m*h, Q,, = 107 W/m*, and COP = 89%. Similar nomographs for T, = 20 and 28°C have also been developed and are given in Figs. 4 and 5, respectively.
REFERENCES 1. R. W. Shoemaker, Radiant Heating, McGraw-Hill, New York, NY (1954). 2. K. A. Antonopoulos, Znt. J. Heat Mass Transfer, in press (1992). 3. D. A, Kouremenos, K. A. Antonopoulos, and E. D. Rogdakis, Heat Recovery Systems CHP 9, 189 (1989). 4. D. A. Kouremenos,
5. D. A. Kouremenos,
K. A. Antonopoulos, and E. D. Rogdakis, Sol. Wind Technol. 7, 111 (1990). E. D. Rogdakis, and K. A. Antonopoulos, Energy-The International Journal 14,
893 (1989).
APPENDIX The polynomials A(X) and B(X) used in Eqs. (10) and (12)-(14) 0.16976X - 3. 133362X21O-3 - 1.9766X310-‘,
are A(X) = -2.0075 +
B(X) = 124.94 - 7.71649X + 0.1522858X2 - 7.95O9X31O-4. The enthalpy h(T, X) of the H20/LiBr solution used in Eq. (15) is given in terms of the temperature T (in “C) and the mass fraction X (%) by the relation h(T, X) = E,(X) + TE,(X) + T2E2(X), where E,(X) = -2024.18588321+
163.2976010204X - 4.88126853177X2
+ 6.30250843X310-* - 2.9135O364X41O-4, E,(X) = 18.2816227619 - 1.169094163968X + 3.24785671X210-* -4.O339O218X31O-4 + 1.85192774X41O-6, E*(X) = -0.0370056321+
2.88756514X1O-3 - 8. 13O75689X21O-5
+ 9.91O97142X31O-7 - 4.44381O71X41O-9. NOMENCLATURE A(X),
B(X) = Third-order
polynomials given in the Appendix COP = Coefficient of performance DO, Di = Outside and inside pipe diameters (m), respectively
J%(X), E,(X), = Fourth-order polynomials given in the Appendix Ez(X) F, fi = Dimensionless coefficients given by Eqs. (3) and (2), respectively
E. D. ROGDAKIS
1066
h, h, = Heat-transfer coefficients (W/m’ “C) of the panel surface and of the inside pipe surface, respectively hi = Specific enthalpy at state i &J/kg HzO) h( T, X) = Specific enthalpy function
@J/kg H,O) k = Thermal conductivity
of the panel (W/m “C) ti = Refrigerant mass-flow rate through the panel (kg H,O/m’s or g H,O/m’h) m = Variable (m-‘) given in Eq. (4) p/, ph = Low and high pressure (torr) respectively q/, qh = Heat inputs (kJ/kg H,O) at the low- and hightemperature levels, respectively Qc= Specific cooling capacity of the panel (W/m’)
g,, = Specific thermal power required to drive the system (W/m’) S = Pipe spacing of the panel (m) Krnb = Ambient temperature (“C) T,,, Ten= Condensation and evaporation temperatures (“C), respectively Tf = Cooling-fluid temperature through the panel, which is equal to T,, (“C) T, = Room-air temperature (“C) Tat&> Tabs.,,= Lowest and highest temperatures in the absorber (“C) Tgen/p Tgen.h= Lowest and highest temperatues in the generator (“C) w = Panel thickness (m) X,, X, = Weak and strong absorbent mass fractions (% , 100 X kg LiBr/kg mixture)