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A comparison of thermal requirements of buildings
Energy and Buildings, 1 ( 1 9 7 7 ) 1 5 9 - 1 6 5 © Elsevier S e q u o i a S.A., L a u s a n n e - - P r i n t e d in t h e N e t h e r l a n d s
159
A Comparison of Thermal Requirements of Buildings STEPHEN JAEGER
Department of Civil Engineering, University of Texas at Austin, Austin, Texas (U.S.A.) FRANCISCO ARUMI
Department of Architecture and Planning, University of Texas at Austin, Austin, Texas (U.S.A.)
In the U.S.A., thermal requirements for buildings have the form o f resistance, R for U values; in European countries, the weight or mass of the building shell is included as part o f the thermal requirement for a building. In this study, these European thermal requirements, which vary substantially, are numerically tested and compared. The comparison is the ratio o f heat transmitted during a day by a wall which incorporates the thermal requirements to a wall which has no mass and only thermal resistance. The comparison shows a wide discrepancy in the thermal response of the requirements for different countries. For the purpose o f comparison, the pysical properties o f the thermal requirements are normalized to groups which are part of the solution to the differential equation of heat transfer. Also compared are Givoni's recommended requirements which, in relation to other requirements, show good consistency.
Unlike the U.S.A., some European countries specify both thermal resistance and thermal capacity* for wall systems. Austria, West Germany, and Scandinavia have building codes that include thermal capacity in some form. This may be a resistance capacity p r o d u c t or weight per unit areas of wall. The requirements of different countries vary in structure, b u t have t w o characteristics in c o m m o n : different climatic zones of the country have individual requirements and a reduced thermal resistance is allowed for high thermal capacity of walls. * T h e r m a l c a p a c i t y is used t o r e f e r t o t h e p r o d u c t o f d e n s i t y , specific h e a t , a n d weight.
The European thermal requirements are cast into equivalent wall forms where the dynamic heat transfer through the wall is calculated by a complex solution of the different equations. Needless to say, some assumptions are necessary and these can be found in the Appendix. The total heat transfer for a day through these equivalent walls is then compared to the heat transfer through an imaginary wall; a wall w i t h o u t thermal mass and only a minimum thermal resistance. The results of the c o m p u t e r analysis of the heat transfer are found in the t w o plots where an easy comparison of the effectiveness of the requirements is made. The thermal requirements of the European countries are extracted from Givoni's b o o k , [1]. Givoni suggests some thermal requirements, which are tested for performance in this study along with the European requirements. These requirements are converted to the English engineering system of measurements and with assumptions converted to " g a m m a " and " G " valuesT. The maximum possible heat transmission occurs when the internal resistance of the wall and the mass of the wall are zero; the only inhibitor to heat transmission is the inside film resistance. The condition is referred to herein as the "standard wall". For
T"Gamma"=l
P ~ V 2k
Xl
w h e r e p = d e n s i t y o f t h e m a t e r i a l , c = specified h e a t o f t h e m a t e r i a l , ~0 = f r e q u e n c y o f t h e o u t s i d e t e m p e r a t u r e cycle, h = t h e r m a l c o n d u c t i v i t y o f m a t e r i a l , I = t h i c k n e s s o f m a t e r i a l ; a n d " G " ~ h/hl, w h e r e k = t h e r m a l c o n d u c t i v i t y o f t h e m a t e r i a l , h -- i n t e r n a l film c o e f f i c i e n t o f t h e wall, l = t h i c k n e s s o f t h e wall.
160 TABLE 1 Test conditions and total heat transmission used in the comparisons Hot temperature conditions
Cold temperature conditions
Yearly temperature conditions
Daily temperature range Film coefficient Comfort zone Mean outside surface temperature
16.67 0.20 18.33 - 26.67
16.67 0.20 18.33 - 26.67
16.67 °C 0.20 kcal/m2/h °C 18.33 - 26.67 °C
29.28
12.11
Total heat transmission
42,967 kcal/m2/month
68,596 kcal/m2/month
average daily degrees (C) temperature [ 5 ], 508,003 kcal/mZ/year
an actual wall, it is necessary to calculate its inside surface temperature to determine performance, considering heat transfer only when the temperature is outside the c o m f o r t zone. For the standard wall, the inside surface temperature is the same as the outside surface temperature since there is no internal resistance. Maximum possible heat transmissions, calculated for the two extremes and the entire year, are given in Table 1.
WEST GERMANY
The design o u t d o o r temperature is used in West Germany as the criteria for thermal requirements of walls. These requirements (Table 2) include the thermal resistance of the walls and weight per area. TABLE 2
the specific heat of the material is assumed to be 0.11 kcal/kg °C (0.2 Btu/lb. °F). This conversion of thermal resistance and weight per unit area is found in Appendix A. The specific heat assumed is the average value of most construction materials (0.11 kcal/kg °C). This assumption is reasonable in light of the statem e n t by Mackey and Wright [3] : There is not a wide range in the gravimetric specific heats o f non-metallic solids; solids o f mineral origin have gravimetric specific heats between 0.08 and 0.14 kcal/kg °C (0.15 and 0.25 Btu/lb °F), while the specific heat o f dry solids o f vegetable origin are commonly between 0.17 and 0.22 kcal/kg °C (0.3 and 0.4 Btu/lb °F) at temperature important in this study. The thermal requirements for the o u t d o o r design temperature o f - - 1 2 °C (10.4 °F} are converted to " g a m m a " and " G " and listed in Table 3.
West Germany's thermal resistance requirements for buildings (m 2 °C h/kcal) [6] Weight (kg/m 2)
Outdoor design temperature
TABLE 3
--12 °C
--15 °C
--18 °C
20 50 100
1.30 1.00 0.70
1.85 1.40 0.95
2.60 2.00 1.30
(4)
150
0.55
O.65
O.9O
West Germany's thermal requirements normalized to "gamma" and " V " Outdoor design temperature, --12 °C Inside surface film coefficient, 0.2 kcal/m 2 h °C Specific heat, 0.11 kcal/kg °C
(5) (6)
200 300
0.50 0.45
0.60 0.55
0.75 0.65
(1) (2) (3)
Weight (kg/m 2)
Resistance "Gamma . . . . (m 2 h °C/kcal)
20 50 100 150 200 300
1.30 1.00 0.70 0.55 0.50 0.45
G"
(Thermal resistance of walls alone)
With the thermal resistance and weight per unit area, part of this information is converted into " g a m m a " and " G " values where
(1) (2) (3) (4) (5) (6)
0.825 1.143 1.354 1.470 1.618 1.882
0.095 0.124 0.193 0.226 0.248 0.257
161 AUSTRIA
The Austrian thermal requirements specify resistance and thermal time constant (resistance-capacity product) but do not allow a range of values as do West Germany's requirements. These requirements are based on the average minimum outdoor design temperature. In Table 4 are thermal resistance and thermal time constants for three design minimum temperatures (--9, --12, --15 °C).
TABLE4 Austrianthermalrequirementsforbuildin~ Design m i n i m u m temperature
Required resistance (m 2 h °C/kcal) Thermal time constant (h)
--9°C
--12°C
--15°C
0.41
0.49
0.57
19
21
23
(1)
(2)
(3)
The guidelines for these requirements are the maintenance of the indoor temperature at 20 °C and the prevention of surface condensation. The conversion of these requirements (Table 5) is accomplished assuming that the wall is homogeneous (see Appendix B).
FRANCE
The thermal requirements for French buildings are very detailed with subdivisions for a roof or a wall, climatic zones, quality of heating system, and the weight of the wall (Table 6). Assuming the specific heat of the material of the wall is 0.11 kcal/kg °C (0.2 Btu/lb °F) and the walls are homogeneous, the "gamma" and "G" values of six walls are calculated (Table 8). These walls conform to the thermal requirements of Table 7 and are for a facade wall on the Atlantic coast with average heating quality (see Appendix A for the method of conversion).
TABLE 5 Austrian thermal requirements normalized to "gamma" and " G " Inside surface film coefficient = 0.2 kcal/m 2 h °C
(1) (2) (3)
Outdoor design temperature (°C)
Required resistance (m 2 h °C/kcal)
Thermal time constant (h)
"Gamma"
"G"
--9 --12 --15
0.41 0.49 0.57
19.0 21.0 23.0
1.58 1.66 1.74
0.303 0.254 0.218
TABLE 6 French subdivisions of thermal requirements for buildings Components
Climatic zone
Heating quality
Roof Gable Facade wall
High mountain Average inland Atlantic coast Mediterranean coast
Superior Average Inferior
Weight of wall >600 450-600 350-450 250-350 150-250 75-150 <75
A typical set of requirements in France for a facade wall on the Atlantic coast with an average heating system is in Table 5.
162
TABLE 7 Typical French thermal requirements for buildings Component : Facade wall Climatic zone: Atlantic coast Heating quality: Average Weight
Thermal resistance
kg/m 2 (1) (2) (3) (4) (5) (6) (7)
lb/ft 2
<75 75-150 150 - 250 250 - 350 350 - 450 450-600 >600
<15.3 15.3- 31 31 51 51 72 72 92 92 -123 >123
m 2 h °C/kcal
ft 2 h °F/Btu
0.83 0.67 0.59 0.59 0.56 0.56 0.53
4.05 3.27 2.88 2.88 2.73 2.73 2.44
TABLE 8
TABLE 9
French thermal requirements normalized to "gamma" and "G" Component: Facade wall Climatic zone: Atlantic coast Heating quality : Average
Givoni's recommended thermal resistance of walls of buildings (see Appendix B for conversion) Outdoor design temperature = --10 °C
(1) (2) (3) (4) (5) (6)
Weight (kg/m 2)
Thermal resistance (m 2 h °C/kca])
"Gamma . . . .
112.20 200.00 302.44 400.00 521.95 609.76
0.67 0.59 0.59 0.56 0.56 0.50
1.40 1.78 2.16 2.42 2.77 2.83
Weight
G"
0.19 0.21 0.21 0.22 0.22 0.25
RECOMMENDED THERMAL REQUIREMENTS BY GIVONI T h e t h e r m a l r e q u i r e m e n t s for walls recomm e n d e d b y G i v o n i [ 4 ] are c o n v e r t e d t o E n g l i s h u n i t s a n d l i s t e d i n T a b l e 9.
(1) (2) (3) (4) (5) (6) (7) (8)
Thermal resistance
kg/m 2
lb/ft 2
m 2 h °C/kcal
ft 2 h °F/Btu
20.0 50.0 100.0 200.0 300.0 500.0 700.0 900.0
4.1 10.2 20.5 40.9 61.4 102.3 143.2 184.2
1.29 1.27 1.25 1.20 1.15 1.05 0.95 0.85
6.30 6.20 6.10 5.86 5.61 5.13 4.64 4.15
These values are reduced by 0.2 to obtain the resistance of walls, without considering the surface resistance.
TABLE 10 Givoni's recommended thermal resistance for walls normalized to " g a m m a " and " G "
PERFORMANCE OF THERMAL REQUIREMENTS FOR WALLS The thermal requirements of European countries and Givoni's recommended thermal r e q u i r e m e n t s are c a s t i n t e r m s o f " g a m m a " and "G" values {Table 10), with the hot temperature and cold temperature performance of these requirements determined. The mean o u t d o o r air t e m p e r a t u r e , t h e d a i l y t e m p e r a ture range, the comfort zone, and the inside c o e f f i c i e n t are a s s u m e d t o b e as f o l l o w s :
Weight
(1) (2) (3) (4) (5) (6) (7) (8)
(kg/m 2)
Thermal " G a m m a " "G" resistance (m 2 h °C/kcal)
0.84 2.09 4.19 8.37 12.56 20.93 29.30 37.69
1.29 1.27 1.25 1.20 1.15 1.05 0.95 0.85
0.82 1.20 1.81 2.51 3.01 3.71 4.18 4.48
0.096 0.098 0.099 0.103 0.108 0.118 0.131 0.146
163
M e a n air t e m p e r a t u r e Daily t e m p e r a t u r e range Comfort zone Inside surface film coefficient Temperature ratio
Hot temperature
Cold temperature
29.28
12.1 °C
16.7 18,3 - 26.7
16.7 °C 18.3 - 26.7 °C
0,20 0.75
0.20 k c a l / m 2 h °C 0.32
In Fig. 1, the performance of thermal requirements for hot temperature conditions are displayed. The thermal requirements of West Germany, Austria, and France, in addition to the recommended thermal requirements of Givoni, are translated into performance on this graph. Givoni's recommended thermal requirements perform the best of the group, while those of Austria have the worst performance. While the performance* of the first two values of the West German thermal requirements is approximately 10%, the performance of the last four values is 15 20%. The German requirements allow an excessive reduction in thermal resistance requirements for heavy weight walls and, as a result, the performance for the heavy walls is substandard. The Austrian thermal requirements have a 21% performance for the first value but improve for the second and third values to 15%. These requirements are for three different outdoor design temperatures (--9, --12, --15 °C) and it is expected that the performance improves as the design temperature condition is lowered. The French thermal requirements and Givoni's recommended requirements show consistency of performance, indicating the trade-off between thermal capacity and thermal resistance is well balanced for these thermal requirements. In Fig. 1, the "gamma" and " G " values of the thermal requirements are tested under the cold temperature conditions also. The results for this condition are very similar to the results for the hot temperature conditions, with the West German requirements * P e r f o r m a n c e is t h e f r a c t i o n o f m a x i m u m possible h e a t transfer.
showing inconsistency and poor performance and the thermal requirements of Givoni consistent and well performing. The European thermal requirements for building walls are superior to those of the United States because they account for the effect of thermal capacity while the American thermal requirements specify only the resistance. The calculation of performance for the European requirements is accomplished by
t
Plot Temperoture
Conditions
ACTS. W.Oer.
, ~
@/vont~
0 1.
~ ,
~ .
GAMMA
Cold Temperature
:~ .
~ .
~ndltlo~$
Olvonl*s
GAMMA Fig. 1. P e r f o r m a n c e o f t h e r m a l r e q u i r e m e n t f o r walls vs. g a m m a . Daily t e m p e r a t u r e r a n g e = 1 6 . 6 7 °C; c o m f o r t z o n e -- 18.33 - 26.67 °C. (a) H o t t e m p e r a t u r e c o n d i t i o n s ; ( b ) cold t e m p e r a t u r e c o n d i t i o n s .
the transformation of the requirements into "gamma" and "G" values with the assumption for homogeneous walls and specific heat. The level of calculated performance is not consistent for the requirements, indicating an exact criteria is not used to establish the requirements. The recommended thermal requirements of Givoni, which account for thermal resistance and thermal capacity, are more consistent than the European requirements, even though that author bases these requirements on experience alone. A systematic classification of architectural walls according to their conductance and thermal inertia, (G and gamma values) can be found in ref. [11]. The equivalent walls and
164 the trade o f f between c o n d u c t a n c e and thermal inertia for their energy p e r f o r m a n c e can be found in refs. [11] and [ 1 2 ] . CONCLUSION In Europe, thermal mass is included in the building codes with a variety of forms, and it has been shown, t hat the thermal performance of walls based on the E ur ope a n building codes is inconsistent, In the future, thermal mass will m os t likely be included in the energy conservation requirements o f American building codes. An alternative approach to the classification of thermal perf o r m a n c e o f wall sections is the d e t e r m i n a t i o n o f " g a m m a " and " G " (or conduct ance) . T he identification o f " g a m m a " and " G " or o f wall sections together with the climatic factors is a rational approach for accounting for the e f f ect o f thermal mass and has been very useful in this study. Numerical simulations m a y be used, as in this study, and building envelopes components may be tested and c o m p a r e d against each o t h e r or an established norm. T he results o f this study, while based on a n u m b e r of assumptions, show an application o f this rational approach in the comparison o f European building codes. ACKNOWLEDGEMENT The authors wish to acknowledge the aid of Richard Dodge, Associate Professor, University o f Texas.
7 B. Givoni, Man, Climate and Architecture, Elsevier, New York, 1969. 8 B. H. Jennings, Environmental Engineering, International Textbook Co., Scranton, 1970. 9 F. Kreith, Principles of Heat Transfer, International Textbook Co., Scranton, 1966. 10 C. O. Mackey and L. T. Wright, Homogeneous walls and roofs, ASHVE Trans., 50 (1944) 203. 11 F. N. Arumi, Energy Performance Guidelines, City of Austin, Texas Building Inspection Department, 1976. 12 F. N. Arumi, Operating cost of external walls: a dynamic analysis, Proc. Int. Symp. Lower Cost Housing Problems, May 1976.
APPENDIX A
Conversion o f the resistance a n d w e i g h t p e r unit area to " g a m m a " and " G " e q u a t i o n s
Thermal resistance = R -
l
k
(A1)
assuming h o m o g e n e o u s wall, where l is the thickness of the wall in ft, k is the thermal conductivity of the wall in Btu/h ft 2 °F. Weight per area = Wa = p × l
(A2)
where p is the density of the wall material in lb/ft s.
•/pco9
" g a m m a " = 7 = V 2k
Xl
(A3)
where c is the specific heat o f the wall material in Bt u/ h °F, ¢0 is the f r e q u e n c y of the t e m p e r a t u r e change in h-1. "V" -
k
(A4)
hl
REFERENCES 1 B. Givoni, Man, Climate and Architecture, Elsevier, New York, 1969. 2 B. Givoni, Man, Climate and Architecture, Elsevier, New York, 1969, p. 296. 3 C. O. Maekey and L. T. Wright, Periodic heat flow-composite walls and roofs, ASHVE Trans.,
52 (1946) 283. 4 B. Givoni, Man, Climate and Architecture, Elsevier, New York, (1969), p. 301. 5 F. N. Arumi, Computer program DEROB, unpublished computer program for determining the energy interaction in buildings, School of Architecture and Planning, The University of Texas at Austin, 1975. 6 American Society of Heating, Refrigerating and Air-conditioning, A S H R A E Handbook of Fundamentals, ASHRAE, New York, 1974.
where h is the film coefficient and equals 1.65 Bt u/ h ft 2 °F. Conversion factors
Coefficient of heat transfer: 1.0 kcal/m 2 h °C = 0.205 B t u / f t 2 h °F
(A5)
Weight per area: 1 kg/m 2 = 4.89 l b / f t 2
(A6)
Substitutions
Substituting eqn. (A1) into eqn. (A4) l " G " = - - × 0.606 k
(A7)
165
Squaring eqn. (A3) and substituting eqns. (A2) and (A1) into it:
~2 =
Wa Xc X 6o X R
(A8)
2
V
× R
Xl
k (A9)
~G
~' ~
(B3)
(B4)
__
lh Substitutions Substituting eqn. (B2) into eqn. (84)
APPENDIX B
C o n v e r s i o n o f t h e r m a l resistance and t h e r m a l t i m e c o n s t a n t " g a m m a " and " G "
Thermal time co ns t a nt = T T C -
(B2)
" g a m m a " = ~/= 1 ~
where w = 2 × n / 2 4 , c = 0.2 Btu/lb °F T h e r e f o r e " g a m m a " = 0.162 ~
l k
Resistance = R -
12pc k
(81)
1 " G " = -- )< 0.606 R
(B5)
Substituting eqn. (B1) into eqn. (B3)
"Gamma"= V
?i--
(B6)
159
A Comparison of Thermal Requirements of Buildings STEPHEN JAEGER
Department of Civil Engineering, University of Texas at Austin, Austin, Texas (U.S.A.) FRANCISCO ARUMI
Department of Architecture and Planning, University of Texas at Austin, Austin, Texas (U.S.A.)
In the U.S.A., thermal requirements for buildings have the form o f resistance, R for U values; in European countries, the weight or mass of the building shell is included as part o f the thermal requirement for a building. In this study, these European thermal requirements, which vary substantially, are numerically tested and compared. The comparison is the ratio o f heat transmitted during a day by a wall which incorporates the thermal requirements to a wall which has no mass and only thermal resistance. The comparison shows a wide discrepancy in the thermal response of the requirements for different countries. For the purpose o f comparison, the pysical properties o f the thermal requirements are normalized to groups which are part of the solution to the differential equation of heat transfer. Also compared are Givoni's recommended requirements which, in relation to other requirements, show good consistency.
Unlike the U.S.A., some European countries specify both thermal resistance and thermal capacity* for wall systems. Austria, West Germany, and Scandinavia have building codes that include thermal capacity in some form. This may be a resistance capacity p r o d u c t or weight per unit areas of wall. The requirements of different countries vary in structure, b u t have t w o characteristics in c o m m o n : different climatic zones of the country have individual requirements and a reduced thermal resistance is allowed for high thermal capacity of walls. * T h e r m a l c a p a c i t y is used t o r e f e r t o t h e p r o d u c t o f d e n s i t y , specific h e a t , a n d weight.
The European thermal requirements are cast into equivalent wall forms where the dynamic heat transfer through the wall is calculated by a complex solution of the different equations. Needless to say, some assumptions are necessary and these can be found in the Appendix. The total heat transfer for a day through these equivalent walls is then compared to the heat transfer through an imaginary wall; a wall w i t h o u t thermal mass and only a minimum thermal resistance. The results of the c o m p u t e r analysis of the heat transfer are found in the t w o plots where an easy comparison of the effectiveness of the requirements is made. The thermal requirements of the European countries are extracted from Givoni's b o o k , [1]. Givoni suggests some thermal requirements, which are tested for performance in this study along with the European requirements. These requirements are converted to the English engineering system of measurements and with assumptions converted to " g a m m a " and " G " valuesT. The maximum possible heat transmission occurs when the internal resistance of the wall and the mass of the wall are zero; the only inhibitor to heat transmission is the inside film resistance. The condition is referred to herein as the "standard wall". For
T"Gamma"=l
P ~ V 2k
Xl
w h e r e p = d e n s i t y o f t h e m a t e r i a l , c = specified h e a t o f t h e m a t e r i a l , ~0 = f r e q u e n c y o f t h e o u t s i d e t e m p e r a t u r e cycle, h = t h e r m a l c o n d u c t i v i t y o f m a t e r i a l , I = t h i c k n e s s o f m a t e r i a l ; a n d " G " ~ h/hl, w h e r e k = t h e r m a l c o n d u c t i v i t y o f t h e m a t e r i a l , h -- i n t e r n a l film c o e f f i c i e n t o f t h e wall, l = t h i c k n e s s o f t h e wall.
160 TABLE 1 Test conditions and total heat transmission used in the comparisons Hot temperature conditions
Cold temperature conditions
Yearly temperature conditions
Daily temperature range Film coefficient Comfort zone Mean outside surface temperature
16.67 0.20 18.33 - 26.67
16.67 0.20 18.33 - 26.67
16.67 °C 0.20 kcal/m2/h °C 18.33 - 26.67 °C
29.28
12.11
Total heat transmission
42,967 kcal/m2/month
68,596 kcal/m2/month
average daily degrees (C) temperature [ 5 ], 508,003 kcal/mZ/year
an actual wall, it is necessary to calculate its inside surface temperature to determine performance, considering heat transfer only when the temperature is outside the c o m f o r t zone. For the standard wall, the inside surface temperature is the same as the outside surface temperature since there is no internal resistance. Maximum possible heat transmissions, calculated for the two extremes and the entire year, are given in Table 1.
WEST GERMANY
The design o u t d o o r temperature is used in West Germany as the criteria for thermal requirements of walls. These requirements (Table 2) include the thermal resistance of the walls and weight per area. TABLE 2
the specific heat of the material is assumed to be 0.11 kcal/kg °C (0.2 Btu/lb. °F). This conversion of thermal resistance and weight per unit area is found in Appendix A. The specific heat assumed is the average value of most construction materials (0.11 kcal/kg °C). This assumption is reasonable in light of the statem e n t by Mackey and Wright [3] : There is not a wide range in the gravimetric specific heats o f non-metallic solids; solids o f mineral origin have gravimetric specific heats between 0.08 and 0.14 kcal/kg °C (0.15 and 0.25 Btu/lb °F), while the specific heat o f dry solids o f vegetable origin are commonly between 0.17 and 0.22 kcal/kg °C (0.3 and 0.4 Btu/lb °F) at temperature important in this study. The thermal requirements for the o u t d o o r design temperature o f - - 1 2 °C (10.4 °F} are converted to " g a m m a " and " G " and listed in Table 3.
West Germany's thermal resistance requirements for buildings (m 2 °C h/kcal) [6] Weight (kg/m 2)
Outdoor design temperature
TABLE 3
--12 °C
--15 °C
--18 °C
20 50 100
1.30 1.00 0.70
1.85 1.40 0.95
2.60 2.00 1.30
(4)
150
0.55
O.65
O.9O
West Germany's thermal requirements normalized to "gamma" and " V " Outdoor design temperature, --12 °C Inside surface film coefficient, 0.2 kcal/m 2 h °C Specific heat, 0.11 kcal/kg °C
(5) (6)
200 300
0.50 0.45
0.60 0.55
0.75 0.65
(1) (2) (3)
Weight (kg/m 2)
Resistance "Gamma . . . . (m 2 h °C/kcal)
20 50 100 150 200 300
1.30 1.00 0.70 0.55 0.50 0.45
G"
(Thermal resistance of walls alone)
With the thermal resistance and weight per unit area, part of this information is converted into " g a m m a " and " G " values where
(1) (2) (3) (4) (5) (6)
0.825 1.143 1.354 1.470 1.618 1.882
0.095 0.124 0.193 0.226 0.248 0.257
161 AUSTRIA
The Austrian thermal requirements specify resistance and thermal time constant (resistance-capacity product) but do not allow a range of values as do West Germany's requirements. These requirements are based on the average minimum outdoor design temperature. In Table 4 are thermal resistance and thermal time constants for three design minimum temperatures (--9, --12, --15 °C).
TABLE4 Austrianthermalrequirementsforbuildin~ Design m i n i m u m temperature
Required resistance (m 2 h °C/kcal) Thermal time constant (h)
--9°C
--12°C
--15°C
0.41
0.49
0.57
19
21
23
(1)
(2)
(3)
The guidelines for these requirements are the maintenance of the indoor temperature at 20 °C and the prevention of surface condensation. The conversion of these requirements (Table 5) is accomplished assuming that the wall is homogeneous (see Appendix B).
FRANCE
The thermal requirements for French buildings are very detailed with subdivisions for a roof or a wall, climatic zones, quality of heating system, and the weight of the wall (Table 6). Assuming the specific heat of the material of the wall is 0.11 kcal/kg °C (0.2 Btu/lb °F) and the walls are homogeneous, the "gamma" and "G" values of six walls are calculated (Table 8). These walls conform to the thermal requirements of Table 7 and are for a facade wall on the Atlantic coast with average heating quality (see Appendix A for the method of conversion).
TABLE 5 Austrian thermal requirements normalized to "gamma" and " G " Inside surface film coefficient = 0.2 kcal/m 2 h °C
(1) (2) (3)
Outdoor design temperature (°C)
Required resistance (m 2 h °C/kcal)
Thermal time constant (h)
"Gamma"
"G"
--9 --12 --15
0.41 0.49 0.57
19.0 21.0 23.0
1.58 1.66 1.74
0.303 0.254 0.218
TABLE 6 French subdivisions of thermal requirements for buildings Components
Climatic zone
Heating quality
Roof Gable Facade wall
High mountain Average inland Atlantic coast Mediterranean coast
Superior Average Inferior
Weight of wall >600 450-600 350-450 250-350 150-250 75-150 <75
A typical set of requirements in France for a facade wall on the Atlantic coast with an average heating system is in Table 5.
162
TABLE 7 Typical French thermal requirements for buildings Component : Facade wall Climatic zone: Atlantic coast Heating quality: Average Weight
Thermal resistance
kg/m 2 (1) (2) (3) (4) (5) (6) (7)
lb/ft 2
<75 75-150 150 - 250 250 - 350 350 - 450 450-600 >600
<15.3 15.3- 31 31 51 51 72 72 92 92 -123 >123
m 2 h °C/kcal
ft 2 h °F/Btu
0.83 0.67 0.59 0.59 0.56 0.56 0.53
4.05 3.27 2.88 2.88 2.73 2.73 2.44
TABLE 8
TABLE 9
French thermal requirements normalized to "gamma" and "G" Component: Facade wall Climatic zone: Atlantic coast Heating quality : Average
Givoni's recommended thermal resistance of walls of buildings (see Appendix B for conversion) Outdoor design temperature = --10 °C
(1) (2) (3) (4) (5) (6)
Weight (kg/m 2)
Thermal resistance (m 2 h °C/kca])
"Gamma . . . .
112.20 200.00 302.44 400.00 521.95 609.76
0.67 0.59 0.59 0.56 0.56 0.50
1.40 1.78 2.16 2.42 2.77 2.83
Weight
G"
0.19 0.21 0.21 0.22 0.22 0.25
RECOMMENDED THERMAL REQUIREMENTS BY GIVONI T h e t h e r m a l r e q u i r e m e n t s for walls recomm e n d e d b y G i v o n i [ 4 ] are c o n v e r t e d t o E n g l i s h u n i t s a n d l i s t e d i n T a b l e 9.
(1) (2) (3) (4) (5) (6) (7) (8)
Thermal resistance
kg/m 2
lb/ft 2
m 2 h °C/kcal
ft 2 h °F/Btu
20.0 50.0 100.0 200.0 300.0 500.0 700.0 900.0
4.1 10.2 20.5 40.9 61.4 102.3 143.2 184.2
1.29 1.27 1.25 1.20 1.15 1.05 0.95 0.85
6.30 6.20 6.10 5.86 5.61 5.13 4.64 4.15
These values are reduced by 0.2 to obtain the resistance of walls, without considering the surface resistance.
TABLE 10 Givoni's recommended thermal resistance for walls normalized to " g a m m a " and " G "
PERFORMANCE OF THERMAL REQUIREMENTS FOR WALLS The thermal requirements of European countries and Givoni's recommended thermal r e q u i r e m e n t s are c a s t i n t e r m s o f " g a m m a " and "G" values {Table 10), with the hot temperature and cold temperature performance of these requirements determined. The mean o u t d o o r air t e m p e r a t u r e , t h e d a i l y t e m p e r a ture range, the comfort zone, and the inside c o e f f i c i e n t are a s s u m e d t o b e as f o l l o w s :
Weight
(1) (2) (3) (4) (5) (6) (7) (8)
(kg/m 2)
Thermal " G a m m a " "G" resistance (m 2 h °C/kcal)
0.84 2.09 4.19 8.37 12.56 20.93 29.30 37.69
1.29 1.27 1.25 1.20 1.15 1.05 0.95 0.85
0.82 1.20 1.81 2.51 3.01 3.71 4.18 4.48
0.096 0.098 0.099 0.103 0.108 0.118 0.131 0.146
163
M e a n air t e m p e r a t u r e Daily t e m p e r a t u r e range Comfort zone Inside surface film coefficient Temperature ratio
Hot temperature
Cold temperature
29.28
12.1 °C
16.7 18,3 - 26.7
16.7 °C 18.3 - 26.7 °C
0,20 0.75
0.20 k c a l / m 2 h °C 0.32
In Fig. 1, the performance of thermal requirements for hot temperature conditions are displayed. The thermal requirements of West Germany, Austria, and France, in addition to the recommended thermal requirements of Givoni, are translated into performance on this graph. Givoni's recommended thermal requirements perform the best of the group, while those of Austria have the worst performance. While the performance* of the first two values of the West German thermal requirements is approximately 10%, the performance of the last four values is 15 20%. The German requirements allow an excessive reduction in thermal resistance requirements for heavy weight walls and, as a result, the performance for the heavy walls is substandard. The Austrian thermal requirements have a 21% performance for the first value but improve for the second and third values to 15%. These requirements are for three different outdoor design temperatures (--9, --12, --15 °C) and it is expected that the performance improves as the design temperature condition is lowered. The French thermal requirements and Givoni's recommended requirements show consistency of performance, indicating the trade-off between thermal capacity and thermal resistance is well balanced for these thermal requirements. In Fig. 1, the "gamma" and " G " values of the thermal requirements are tested under the cold temperature conditions also. The results for this condition are very similar to the results for the hot temperature conditions, with the West German requirements * P e r f o r m a n c e is t h e f r a c t i o n o f m a x i m u m possible h e a t transfer.
showing inconsistency and poor performance and the thermal requirements of Givoni consistent and well performing. The European thermal requirements for building walls are superior to those of the United States because they account for the effect of thermal capacity while the American thermal requirements specify only the resistance. The calculation of performance for the European requirements is accomplished by
t
Plot Temperoture
Conditions
ACTS. W.Oer.
, ~
@/vont~
0 1.
~ ,
~ .
GAMMA
Cold Temperature
:~ .
~ .
~ndltlo~$
Olvonl*s
GAMMA Fig. 1. P e r f o r m a n c e o f t h e r m a l r e q u i r e m e n t f o r walls vs. g a m m a . Daily t e m p e r a t u r e r a n g e = 1 6 . 6 7 °C; c o m f o r t z o n e -- 18.33 - 26.67 °C. (a) H o t t e m p e r a t u r e c o n d i t i o n s ; ( b ) cold t e m p e r a t u r e c o n d i t i o n s .
the transformation of the requirements into "gamma" and "G" values with the assumption for homogeneous walls and specific heat. The level of calculated performance is not consistent for the requirements, indicating an exact criteria is not used to establish the requirements. The recommended thermal requirements of Givoni, which account for thermal resistance and thermal capacity, are more consistent than the European requirements, even though that author bases these requirements on experience alone. A systematic classification of architectural walls according to their conductance and thermal inertia, (G and gamma values) can be found in ref. [11]. The equivalent walls and
164 the trade o f f between c o n d u c t a n c e and thermal inertia for their energy p e r f o r m a n c e can be found in refs. [11] and [ 1 2 ] . CONCLUSION In Europe, thermal mass is included in the building codes with a variety of forms, and it has been shown, t hat the thermal performance of walls based on the E ur ope a n building codes is inconsistent, In the future, thermal mass will m os t likely be included in the energy conservation requirements o f American building codes. An alternative approach to the classification of thermal perf o r m a n c e o f wall sections is the d e t e r m i n a t i o n o f " g a m m a " and " G " (or conduct ance) . T he identification o f " g a m m a " and " G " or o f wall sections together with the climatic factors is a rational approach for accounting for the e f f ect o f thermal mass and has been very useful in this study. Numerical simulations m a y be used, as in this study, and building envelopes components may be tested and c o m p a r e d against each o t h e r or an established norm. T he results o f this study, while based on a n u m b e r of assumptions, show an application o f this rational approach in the comparison o f European building codes. ACKNOWLEDGEMENT The authors wish to acknowledge the aid of Richard Dodge, Associate Professor, University o f Texas.
7 B. Givoni, Man, Climate and Architecture, Elsevier, New York, 1969. 8 B. H. Jennings, Environmental Engineering, International Textbook Co., Scranton, 1970. 9 F. Kreith, Principles of Heat Transfer, International Textbook Co., Scranton, 1966. 10 C. O. Mackey and L. T. Wright, Homogeneous walls and roofs, ASHVE Trans., 50 (1944) 203. 11 F. N. Arumi, Energy Performance Guidelines, City of Austin, Texas Building Inspection Department, 1976. 12 F. N. Arumi, Operating cost of external walls: a dynamic analysis, Proc. Int. Symp. Lower Cost Housing Problems, May 1976.
APPENDIX A
Conversion o f the resistance a n d w e i g h t p e r unit area to " g a m m a " and " G " e q u a t i o n s
Thermal resistance = R -
l
k
(A1)
assuming h o m o g e n e o u s wall, where l is the thickness of the wall in ft, k is the thermal conductivity of the wall in Btu/h ft 2 °F. Weight per area = Wa = p × l
(A2)
where p is the density of the wall material in lb/ft s.
•/pco9
" g a m m a " = 7 = V 2k
Xl
(A3)
where c is the specific heat o f the wall material in Bt u/ h °F, ¢0 is the f r e q u e n c y of the t e m p e r a t u r e change in h-1. "V" -
k
(A4)
hl
REFERENCES 1 B. Givoni, Man, Climate and Architecture, Elsevier, New York, 1969. 2 B. Givoni, Man, Climate and Architecture, Elsevier, New York, 1969, p. 296. 3 C. O. Maekey and L. T. Wright, Periodic heat flow-composite walls and roofs, ASHVE Trans.,
52 (1946) 283. 4 B. Givoni, Man, Climate and Architecture, Elsevier, New York, (1969), p. 301. 5 F. N. Arumi, Computer program DEROB, unpublished computer program for determining the energy interaction in buildings, School of Architecture and Planning, The University of Texas at Austin, 1975. 6 American Society of Heating, Refrigerating and Air-conditioning, A S H R A E Handbook of Fundamentals, ASHRAE, New York, 1974.
where h is the film coefficient and equals 1.65 Bt u/ h ft 2 °F. Conversion factors
Coefficient of heat transfer: 1.0 kcal/m 2 h °C = 0.205 B t u / f t 2 h °F
(A5)
Weight per area: 1 kg/m 2 = 4.89 l b / f t 2
(A6)
Substitutions
Substituting eqn. (A1) into eqn. (A4) l " G " = - - × 0.606 k
(A7)
165
Squaring eqn. (A3) and substituting eqns. (A2) and (A1) into it:
~2 =
Wa Xc X 6o X R
(A8)
2
V
× R
Xl
k (A9)
~G
~' ~
(B3)
(B4)
__
lh Substitutions Substituting eqn. (B2) into eqn. (84)
APPENDIX B
C o n v e r s i o n o f t h e r m a l resistance and t h e r m a l t i m e c o n s t a n t " g a m m a " and " G "
Thermal time co ns t a nt = T T C -
(B2)
" g a m m a " = ~/= 1 ~
where w = 2 × n / 2 4 , c = 0.2 Btu/lb °F T h e r e f o r e " g a m m a " = 0.162 ~
l k
Resistance = R -
12pc k
(81)
1 " G " = -- )< 0.606 R
(B5)
Substituting eqn. (B1) into eqn. (B3)
"Gamma"= V
?i--
(B6)