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The calculation of internal temperatures— A demonstration experiment
Buihl. Sci. Vol. 2, pp. 191-196. Pergamon Press 1967. Printed in Great Britain
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[
U D C 697.001
The Calculation of Internal Temperatures A Demonstration Experiment R. W. M U N C E Y * T. S. H O L D E N +
The air and soL.air temperatures external to a concrete ho.v 5 /t square and 3 f i high were measured, and fi'om these data and a knowledge qf the thermal properties o/" the box the expected internal temperature was calculated, using the " matrix ' method of Muncey. In several configurations (e.g. windowless, ./brced ventilation, windows, and heated internally) the calculated values were compared with measured internal temperatures, Diurnal ranges Of internal temperature were o/ten 60 deg F and discrepancies h7 the comparison were generally q[ the order of 1 (leg F or h,ss; this error is sati,ffactori/y small and suggests that this method and others adopting comparable assumptions can reasonably be used in thermal calculations ./or buildings.
INTRODUCTION
On the other hand, to choose a small idealized structure and to enclose it in a room whose temperature conditions vary regularly will lead to criticism of the result as being unrealistic in practice. In such a case the experimental errors will not be zero, although with good equipment they may well be kept small. This paper describes a demonstration experiment chosen towards the idealized situation but with the model building exposed outdoors, and with choice of surface colour and weather designed generally to give as large a range of internal temperatures as practicable: obviously this case is a more difficult one in which to achieve agreement than one in which external (and consequently internal) conditions are nearly constant. Temperatures were recorded to the nearest } ' F from thermocouples using automatic potentiometric equipment arranged to produce a punched tape output[l].
T H E I N T E R N A L temperature of a building and the necessary heating or cooling load to condition it to an optimum temperature are frequently calculated. The basic assumptions are seldom listed explicitly, and the methods have generally derived from laws of heat transfer which may only approximate to the truth in the specific condition of interest. Far too few demonstrations have been reported confirming that the assumptions do in fact give acceptable accuracy. Any new method proposed for such calculations, even if they are based on a more precise mathematical treatment with fewer implied assumptions than are c o m m o n l y taken, must face the usual sceptical reception of such proposals, and should desirably be checked in practical situations. The difficulties facing the propounder of a new method in providing such a desirable demonstration are an inextricable mixture of possible theoretical errors and indefinable experimental inaccuracies. A demonstration on a large building is unlikely to lead to a convincing result because the spatial variability of temperature will give troubles of defining a mean, external conditions will vary over the surface area, and the habits of the occupants and the heat load provided by their activities will all tend to provide experimental errors far larger than could be tolerated in a satisfactory demonstration.
EXPERIMENTAL The basic structure was constructed o1" panels of concrete 2 in. thick using lightweight aggregate. These were assembled into a box-like structure 5 ft square and 3 ft high, the bottom of which was 3 fl above the ground. The external surface was painted black to give increased external temperatures: the ' sol-air " temperature of each surface was measured as that of a brass disk ½in. dia. and ~ in. thick, painted black, mounted with its outer fitce in the plane of the surface and supported on insulating expanded plastic 2 in. dia. and l in. thick. This configuration was devised for the measurement after it was found that thermocouples mounted on the top of a truncated pyramid gave results that were
* Division of Building Research, CS1RO, Melbourne, Australia. Present address, Division of Forest Products, Melbourne, + Division of Building Research, CSIRO, Melbmlrne, Australia. Present address, Division of Computing Research, Canberra. 191
192
R. W. Muncey and T. S. Holden
too low (average internal temperature notably higher than average external sol-air) and that thermocouples without the brass disk for a thermal capacity followed the fluctuations of solar radiation too rapidly and consequent sampling errors led to incorrect results in conditions of light cloud. The variations introduced in this basic arrangement were: I. Forced ventilation at the rate of 6 air changes/h. 2. Internal electrical heating of 2800 &u/h for a period of 6 h in every 24. 3. Windows 24 in. x 10 in. in all faces. 4. An internal ‘ load ’ consisting of 60 clay bricks arranged in a number of single brick ‘ piers ‘. The mean internal temperature was derived from These were fifteen individual thermocouples. located at five points in plan (one at the centre and the others 12 in. from each corner) and at three heights (1 in., 18 in., and 35 in. from the floor). The temperature gradient was found in early experiments to be non-linear in the vertical direction, and the average temperature was derived by assuming a quadratic distribution of the form T = az’ + bz + c where z is the distance (in.) from
the bottom of the box. The mean value of the continuous function T over the vertical height of the box is then Ta = 1/36;6 Tdz = 432a+ 18b+c
[Ic
= [432 18 I] z
0
The coefficients a, b, c can then be found in terms of the measured temperatures TI, T2, T, corresponding to distances (z) of 1, 18, 35 in. [ 3 I=[
$
:i
1
j’
[ ;;
The average internal temperatures were compared with those calculated from the external conditions and the thermal properties of the structure by the matrix method[2]. Whilst it is probable that these properties, particularly the film resistances, were not strictly constant from one lest to the next, the calculations were all carried out with the following assumed properties: External air film resistance
0.15ft2 hdegF
internal air film resistance
0.4 ft” h deg F Btu- ’
Concrete thermal conductivity (as measured)
5.7 Btu in. ft- ’ h- ’ deg F- ’
Concrete heat capacity for 2 in. thickness
3.9 Btu deg F - ’ ft - L
Glass thermal conductance
100 Btu ft- i h-- ’ deg F- ’
Glass thermal capacity
0.6 Btu deg F- ’ f’t _ z!
Btu-’
Internal air mass in lb water equivalent 1.18 Ventilation rate
zero or 350 ft3 h-‘.
Solar radiation transmitted by the windows was calculated from observed values of solar intensity, using the known angles of incidence of the direct solar beam to calculate the reflected component. RESULTS The diurnal range of internal temperatuce was frequently 60 deg F and the discrepancies between measured and calculated temperatures were generally of the order of 1 deg F. Typical curves for various combinations of heating and ventilation are are shown in figures 1 to 6.
1,
whence
CONCLUSIONS = O-187?-,+0.6261; +0*187T,, where Ta is the derived temperature T1 is the temperature near the bottom of the box, TZ is the temperature box, and T3 is the temperature
at the middle of the near the top of the box.
External air temperature was measured standard Stevenson screen situated nearby.
in a
For the case of internal heating the external conditions used were relatively constant over 48 h, and for all other cases two days with clear skies and light to moderate winds were taken since these conditions led to the largest range of internal temperatures.
The temperatures measured inside a concrete box structure were found to agree very well with the corresponding temperatures calculated from the observed external conditions using the matrix method. The discrepancies which do occur may be caused by both experimental error and deficiencies in the theory, but in any case are unlikely to be of any practical significance. The ratio of these discrepancies to the diurnal range-of the order of 1 in 50-is small enough to justify use of the method in more complicated cases, especially as the available externat data in such instances are likely to be less precise than in the present study. Ackoowklgement-The measurements were made by J. A. E. Hutchinson, whose assistance is greatly appreciated.
The Calculation oJ'Internal Temperatures--A Demonstration Experiment
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The Calculation oJ" Internal T e m p e r a t u r e s - - A Demonstration Ex'periment tUO
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Internal (calculated and obser~,ed) and external oh" temperatures--internal piers.
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f'Sf. 6. Internal (calculated and observed) and external air temperatures-internal heating; no l~entilation; internal piers (combination of conditions in Figs. 3 and 5).
MIDN
195
196
R. W. Muncey and T. S. Holden REFERENCES 1. T. S. HOLDI~N,J. scient. Instrum. 37, 269 (1960). 2. R. W. MUNCEY, Aust. J. appl. Sci. 4, 189 (1953).
Les temp6ratures de Fair et de solair fl I'ext6rieur d'un caisson en b6ton avec la base carr6e de 1.524 m de cot6 et d'une hauteur de 91.44 cm ont ~t6 mesur6es. Se basant sur les notions obtenues ainsi que--sur la connaissance des propriet~s thermiques de caisson, la temp&ature int~rieure ~t pr6voir 6tait calcut6e, se servant de la m6thode de matrice de Muncey. Tenant diff6rents modes de construction (par exernple sans fen~tres, ventilation forc6e, avec le fen~tres, chauff6s fl 1 mteneure) les valeurs calcu!ee. 6taient eompar6es avec les temp&atures m6sur6es ~ l'int6rieur. Les degr6s-jours de la temp6rature int&ieure souvent 6taient 15.56°C et les 6carts compar6s s'averaient g~n&alement comme 6tant de l'ordre de ~ 0.55°C; l'erreur aussi insignifiant permets d'attmettre que cette m~thode, ainsi que les autres, assurant les suppositions com, parables peuvent &re raisonablement appliqu6es pour les calculs thermiques dans les bfitiments. Die Luft und Boden-Luft Temperaturen auBerhalb eines Betonkastens mit der quadratischer Base von 1.524 m Seite und 91.44 cm hoch wurden gemessen und an Hand dieser Werte und der Kenntnis der Wfirmeeigenschaften des Kastens wurde die erwartete lnnertemperatur berechnet unter Verwendung der ' Matrix '-Methode yon Muncey. In mehreren Anordnungsweisen (z.B. fensterlos, DruckRiftung, Fenster, innen geheizt) wurden die berechneten Werte mit der gemessenen Innentemperaturen verglichen. Die tageszeitlichen Temperaturgfinge der Innentemperatur betrugen oft 15-56°C und die Abweichungen beim Vergleichen beliefen sich allgemein auf ~ 0, 55 'C; dieser Fehler ist zufriedenstellend gering und lfigt annehmen, dab diese Methode und andere, die vergleichbare Annahmen zulassen, zweekmfiBig in Wfirmeberechnungen fiir Gebfiude verwendent werden k~Snnen.
SfB Ab8
[
U D C 697.001
The Calculation of Internal Temperatures A Demonstration Experiment R. W. M U N C E Y * T. S. H O L D E N +
The air and soL.air temperatures external to a concrete ho.v 5 /t square and 3 f i high were measured, and fi'om these data and a knowledge qf the thermal properties o/" the box the expected internal temperature was calculated, using the " matrix ' method of Muncey. In several configurations (e.g. windowless, ./brced ventilation, windows, and heated internally) the calculated values were compared with measured internal temperatures, Diurnal ranges Of internal temperature were o/ten 60 deg F and discrepancies h7 the comparison were generally q[ the order of 1 (leg F or h,ss; this error is sati,ffactori/y small and suggests that this method and others adopting comparable assumptions can reasonably be used in thermal calculations ./or buildings.
INTRODUCTION
On the other hand, to choose a small idealized structure and to enclose it in a room whose temperature conditions vary regularly will lead to criticism of the result as being unrealistic in practice. In such a case the experimental errors will not be zero, although with good equipment they may well be kept small. This paper describes a demonstration experiment chosen towards the idealized situation but with the model building exposed outdoors, and with choice of surface colour and weather designed generally to give as large a range of internal temperatures as practicable: obviously this case is a more difficult one in which to achieve agreement than one in which external (and consequently internal) conditions are nearly constant. Temperatures were recorded to the nearest } ' F from thermocouples using automatic potentiometric equipment arranged to produce a punched tape output[l].
T H E I N T E R N A L temperature of a building and the necessary heating or cooling load to condition it to an optimum temperature are frequently calculated. The basic assumptions are seldom listed explicitly, and the methods have generally derived from laws of heat transfer which may only approximate to the truth in the specific condition of interest. Far too few demonstrations have been reported confirming that the assumptions do in fact give acceptable accuracy. Any new method proposed for such calculations, even if they are based on a more precise mathematical treatment with fewer implied assumptions than are c o m m o n l y taken, must face the usual sceptical reception of such proposals, and should desirably be checked in practical situations. The difficulties facing the propounder of a new method in providing such a desirable demonstration are an inextricable mixture of possible theoretical errors and indefinable experimental inaccuracies. A demonstration on a large building is unlikely to lead to a convincing result because the spatial variability of temperature will give troubles of defining a mean, external conditions will vary over the surface area, and the habits of the occupants and the heat load provided by their activities will all tend to provide experimental errors far larger than could be tolerated in a satisfactory demonstration.
EXPERIMENTAL The basic structure was constructed o1" panels of concrete 2 in. thick using lightweight aggregate. These were assembled into a box-like structure 5 ft square and 3 ft high, the bottom of which was 3 fl above the ground. The external surface was painted black to give increased external temperatures: the ' sol-air " temperature of each surface was measured as that of a brass disk ½in. dia. and ~ in. thick, painted black, mounted with its outer fitce in the plane of the surface and supported on insulating expanded plastic 2 in. dia. and l in. thick. This configuration was devised for the measurement after it was found that thermocouples mounted on the top of a truncated pyramid gave results that were
* Division of Building Research, CS1RO, Melbourne, Australia. Present address, Division of Forest Products, Melbourne, + Division of Building Research, CSIRO, Melbmlrne, Australia. Present address, Division of Computing Research, Canberra. 191
192
R. W. Muncey and T. S. Holden
too low (average internal temperature notably higher than average external sol-air) and that thermocouples without the brass disk for a thermal capacity followed the fluctuations of solar radiation too rapidly and consequent sampling errors led to incorrect results in conditions of light cloud. The variations introduced in this basic arrangement were: I. Forced ventilation at the rate of 6 air changes/h. 2. Internal electrical heating of 2800 &u/h for a period of 6 h in every 24. 3. Windows 24 in. x 10 in. in all faces. 4. An internal ‘ load ’ consisting of 60 clay bricks arranged in a number of single brick ‘ piers ‘. The mean internal temperature was derived from These were fifteen individual thermocouples. located at five points in plan (one at the centre and the others 12 in. from each corner) and at three heights (1 in., 18 in., and 35 in. from the floor). The temperature gradient was found in early experiments to be non-linear in the vertical direction, and the average temperature was derived by assuming a quadratic distribution of the form T = az’ + bz + c where z is the distance (in.) from
the bottom of the box. The mean value of the continuous function T over the vertical height of the box is then Ta = 1/36;6 Tdz = 432a+ 18b+c
[Ic
= [432 18 I] z
0
The coefficients a, b, c can then be found in terms of the measured temperatures TI, T2, T, corresponding to distances (z) of 1, 18, 35 in. [ 3 I=[
$
:i
1
j’
[ ;;
The average internal temperatures were compared with those calculated from the external conditions and the thermal properties of the structure by the matrix method[2]. Whilst it is probable that these properties, particularly the film resistances, were not strictly constant from one lest to the next, the calculations were all carried out with the following assumed properties: External air film resistance
0.15ft2 hdegF
internal air film resistance
0.4 ft” h deg F Btu- ’
Concrete thermal conductivity (as measured)
5.7 Btu in. ft- ’ h- ’ deg F- ’
Concrete heat capacity for 2 in. thickness
3.9 Btu deg F - ’ ft - L
Glass thermal conductance
100 Btu ft- i h-- ’ deg F- ’
Glass thermal capacity
0.6 Btu deg F- ’ f’t _ z!
Btu-’
Internal air mass in lb water equivalent 1.18 Ventilation rate
zero or 350 ft3 h-‘.
Solar radiation transmitted by the windows was calculated from observed values of solar intensity, using the known angles of incidence of the direct solar beam to calculate the reflected component. RESULTS The diurnal range of internal temperatuce was frequently 60 deg F and the discrepancies between measured and calculated temperatures were generally of the order of 1 deg F. Typical curves for various combinations of heating and ventilation are are shown in figures 1 to 6.
1,
whence
CONCLUSIONS = O-187?-,+0.6261; +0*187T,, where Ta is the derived temperature T1 is the temperature near the bottom of the box, TZ is the temperature box, and T3 is the temperature
at the middle of the near the top of the box.
External air temperature was measured standard Stevenson screen situated nearby.
in a
For the case of internal heating the external conditions used were relatively constant over 48 h, and for all other cases two days with clear skies and light to moderate winds were taken since these conditions led to the largest range of internal temperatures.
The temperatures measured inside a concrete box structure were found to agree very well with the corresponding temperatures calculated from the observed external conditions using the matrix method. The discrepancies which do occur may be caused by both experimental error and deficiencies in the theory, but in any case are unlikely to be of any practical significance. The ratio of these discrepancies to the diurnal range-of the order of 1 in 50-is small enough to justify use of the method in more complicated cases, especially as the available externat data in such instances are likely to be less precise than in the present study. Ackoowklgement-The measurements were made by J. A. E. Hutchinson, whose assistance is greatly appreciated.
The Calculation oJ'Internal Temperatures--A Demonstration Experiment
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TEMPERATURE
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The Calculation oJ" Internal T e m p e r a t u r e s - - A Demonstration Ex'periment tUO
~-
90~
CALCULATED . q ' / ~ .
OBSERVED
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28 vii 64
29 Vii 64 I
Fig. 5.
Internal (calculated and obser~,ed) and external oh" temperatures--internal piers.
lOOp
9Ok
CALCULATED
' ,1
OBSERVED
!1
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CALCULATED
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OBSERVED~,~' '-~
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f'Sf. 6. Internal (calculated and observed) and external air temperatures-internal heating; no l~entilation; internal piers (combination of conditions in Figs. 3 and 5).
MIDN
195
196
R. W. Muncey and T. S. Holden REFERENCES 1. T. S. HOLDI~N,J. scient. Instrum. 37, 269 (1960). 2. R. W. MUNCEY, Aust. J. appl. Sci. 4, 189 (1953).
Les temp6ratures de Fair et de solair fl I'ext6rieur d'un caisson en b6ton avec la base carr6e de 1.524 m de cot6 et d'une hauteur de 91.44 cm ont ~t6 mesur6es. Se basant sur les notions obtenues ainsi que--sur la connaissance des propriet~s thermiques de caisson, la temp&ature int~rieure ~t pr6voir 6tait calcut6e, se servant de la m6thode de matrice de Muncey. Tenant diff6rents modes de construction (par exernple sans fen~tres, ventilation forc6e, avec le fen~tres, chauff6s fl 1 mteneure) les valeurs calcu!ee. 6taient eompar6es avec les temp&atures m6sur6es ~ l'int6rieur. Les degr6s-jours de la temp6rature int&ieure souvent 6taient 15.56°C et les 6carts compar6s s'averaient g~n&alement comme 6tant de l'ordre de ~ 0.55°C; l'erreur aussi insignifiant permets d'attmettre que cette m~thode, ainsi que les autres, assurant les suppositions com, parables peuvent &re raisonablement appliqu6es pour les calculs thermiques dans les bfitiments. Die Luft und Boden-Luft Temperaturen auBerhalb eines Betonkastens mit der quadratischer Base von 1.524 m Seite und 91.44 cm hoch wurden gemessen und an Hand dieser Werte und der Kenntnis der Wfirmeeigenschaften des Kastens wurde die erwartete lnnertemperatur berechnet unter Verwendung der ' Matrix '-Methode yon Muncey. In mehreren Anordnungsweisen (z.B. fensterlos, DruckRiftung, Fenster, innen geheizt) wurden die berechneten Werte mit der gemessenen Innentemperaturen verglichen. Die tageszeitlichen Temperaturgfinge der Innentemperatur betrugen oft 15-56°C und die Abweichungen beim Vergleichen beliefen sich allgemein auf ~ 0, 55 'C; dieser Fehler ist zufriedenstellend gering und lfigt annehmen, dab diese Methode und andere, die vergleichbare Annahmen zulassen, zweekmfiBig in Wfirmeberechnungen fiir Gebfiude verwendent werden k~Snnen.