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A quick method of measuring thermal conductivity and thermal diffusivity of building fabrics
SfB Ab8 UDC
Build. Sci. Vol. 2, pp. 165-172. Pergamon Press 1967. Printed in Great Britain
]
697.001
A Quick Method of Measuring Thermal Conductivity and Thermal Diffusivity of Building Fabrics K. N. AGARWAL* V. V. VERMA*
A simple method has been developed for rapid determination of thermal conductivity and thermal diffusivity of building and insulating materials. The thermal conductivity has been measured in the steady state by introducing a heat flow meter in the twin sample arrangement whereas thermal diffusivity measurement has been done by recording the temperature history at the mid-point of a twin sample. One of the faces of the sample is in contact with a constant temperature source, while the temperature of the other face is maintained at the ambient level. Theoretical analysis has proved that the thermal response function is a delayed exponential function with rise time defined by the ratio d2/2D. Measurements of the thermal conductivity and thermal diffusivity of the standard sample (wall insulating board)from National Bureau of Standards, U.S.A. and other buildingfabrics have revealed that the method can be employed by the laboratories for testing building and insulating materials which are commonly used, in the temperature range below IO0°C with +_5 per cent accuracy and simple experimental set up.
INTRODUCTION MEASUREMENT of thermal conductivity by guarded hot plate is time consuming and requires more elaborate experimental set up. An indirect method of determining the thermal diffusivity is to measure specific heat per unit volume and thermal conductivity separately and make use of the simple relationship, D = K/C, where K is the thermal conductivity and C is the specific heat per unit volume. The building and insulation industry is in need of an apparatus that could quickly indicate the thermal conductivity values with an accuracy comparable to the hot plate and satisfying I.S.I.[1] and A.S.T.M.[2] standards. An apparatus has been developed for quick measurement of thermal conductivity using a heat flow meter. Various methods[3-6] have been suggested by different workers for measurement of thermal conductivity and thermal diffusivity in transient state. The method described in this paper enables measurement of thermal conductivity and diffusivity without any knowledge of either the heat transfer coefficient of the specimen surfaces or specific heat of the material. The proposed method determines thermal diffusivity by observing the rise time of the
0
~)
TWIN SLAB SPECIMEN
/
/ /i
1
HEAr q sou.Rcgl
I
/
t
/
/
/ I /" /
HEAT
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•
Fig, 1.
/
/
//// / / / / .
/
i.
/
A
L--HEAT FLOW METER Twin slab arrangement for the determination thermal conductivity and thermal diffusivity.
of
thermal response function at a point midway of twin sample arrangement, when one face is excited by a step function heat input while the other face is maintained at a constant ambient temperature.
* Central Building Research Institute, Roorkee, U.P., India.
165
K. N. Agarwal and V. V. Verma
166
The temperature of the hot and cold plate can be controlled from 20°C to 100°C with an accuracy of" _+0.1°C. The rise time has been taken as the time required, including the initial delay, for the response function to rise up to 63.2 per cent level of its final value. The thermal conductivity has been measured by introducing a heat-flow meter in the twin sample arrangement and measuring its output in the steady state. The accuracy of the instrument has been checked by using standard sample of wall insulating board, supplied by National Bureau of Standards. TAPER )
the heat flow across a twin sample arrangement when the temperature at the end faces are kept constant. If we define the response function as
F(t) =
-
~(0.
-
Oc)
where 0it and Oc are the temperatures of the end faces. Assumef(x) and 0,, to be equal to the constant ambient air temperature 0c. The solution of the equation (1) under the above boundary condition as given by Dass and Hossain[6] following Carslaw and Jaeger[7].
NOZZLE
\
\ \ \ \
\ \ \\
", \ \ × , \ , t Y 6 ;
", \ \ \
"
F~e. 2. Design details of the plate. c~
THEORETICAL Unidirectional heat flow in solids is governed by the Fourier equation given below: dO _d20 d t = D~x-x2' (0 < K < 2d) (1) where, D = diffusivity. Let us take the initial boundary conditions as follows 0 =.f(~) when t = 0 0= 0cat'c=0 } 0 OH at K 2d t >= 0 where 0 is the temperature and t is the time. The equation under the boundary conditions represent
~z~-2-~(2n + 1) It=O
4d z where T = - - ~z D •
(2)
For large values of t equation (2) reduces to
F(t) g 1 - 4 exp ( - t / T ) g
,
,3,
It follows from equation (3) that the experimental
A Quick Method of Measuring Thermal Conductilfity and Thermal Diffusivity of Building Fabrics Thermal conductivity
time constant is related to the basic time constant as
The thermal conductivity can be calculated from the steady state heat flow equation
T e x p ~ 1.24T 1.24 × 4d 2
d2
nZD
2D
Hence T e x p - T
2.26 x S.u
(4)
= At = 0-19Texp
(5)
=
k(On- Oc1) (2d- K)
(6)
where S is the calibration constant of the heat flow meter in B.t.u./h. ft 2 per m.V at 80°F; dis thickness of the sample in cm; x is the heat flow-meter thickness in cm; K is thermal conductivity of the
From the response function [ 1 - F(t)]- a and T exp the values of D can be obtained by using equation
(4). HOT WATER THERMOS- 4-TAT65°C
L
~ RUBBER 1
;,
r
-~
; //
///////
_r---hi ~
r/////////~
P////////~/A ~
,.,/, / / / J I~ ' / / / / / / / / JL~ / / / / / / / l TAT
7
~oOc
RECORDER
P ANCE MATCHINt5
TUBIN6
I
--
J
~
tCOL D WATER
Fig. 3. Block diagram of the experimental set up. 1.00
D-----l-~-q ~----t----q :~_-0---~)---0---(
- -
#" O,70
II
O .J
/
h
I
/
/
I-hi "1-
/
050
!
t~.
o
0 BRICK TILE • DENSE CONCRETE t~ WINDOW OLASS
LU U Lid
0.2!
Y O.O( O
B
167
16
24 TIME
32 40 IN MINUTES
48
56
64
Fig. 4. Relation between the percent of heat flow and the time of testing for brick tile, dense concrete and window glass.
K. N. Agarwal and V. V. Verma
168 1.00
) i
0.75
/,I
o
---~-#(" t/ //
o. ~o o
tU
U or Ill II
0.0(
0
8
16
24
TIME
32
tN
40
48
56
6/,
MINUTES
Fig. 5. Relation between the percent of heat flow and the time of testing for thermocole, wall board and foam concrete.
,,"
./
i
LIJ t/) Z O Q.
60
120 TiME
Fig. 6.
t
180
24O
(see)
Experimental curves of response function for the determination of thermal diffusivity, Curve A, thermocole ; Curve B, Window glass; Curve C, Dense Concrete.
specimen Kcal/h deg cm and perature difference in deg C.
(On-Oc) is
the tem-
EXPERIMENTAL For the constant temperature source two aluminium plates of 2.5 cm thickness figure 2 have been designed and fabricated. The temperature of
the plates is controlled by two water thermostat giving a temperature control up to an accuracy of +_0.1°C. Copper-constantan thermocouples of 32 s.w.g, were used for the measurement of temperature using a microvolt recorder. Heat flow was measured by a heat-flow meter using an accurate potentiometer. The calibration of the heat flow
A Quick Method of Measuring Thermal Conductivity and Thermal Diffusivity of Building Fabrics meter was done by a guarded hot plate apparatus and corrected values of heat flow at each mean temperature was obtained from the calibration curve. The block diagram of the experimental setup is shown in figure 3. The whole apparatus was enclosed in an insulated chamber made of three laminated thermocole plywood panels to minimize heat losses by convection and radiation. 4
Thermal conductivity and thermal diffusivity For the measurement of thermal conductivity, when the temperatures of the heat source and heat sink become constant, test specimens were introduced and the heat flow meter readings were recorded at regular intervals of time. Experimental results obtained for the six samples are presented in figures 4 and 5. For thermal diffusivity measuref
/ / / / y
,••-
I
I
W Z O r~
~
t~ tv
I
O
150
~ ~(~MFOA CONCRETE • INSULATING BOARD O BRICKTILE 300 TIME t ( Sec)
~50
600
Fig. 7. Experimental curves of responsefunction for the determination of thermal diffusivity. Curve A, foam concrete; Curve B, insulating board; Curve C, brick tile.
0.030
E
0o 0.025
f
U ,,.e
FU
0.020
Q Z 0
x
"" O.015 W -r" I,-
O.O1(O
2.5
5.0 THICKNESS
169
IN
10.0 cm$
Fig. 8. Variationof thermal conductivity with thickness.
K.N. Agarwaland V. V. Verma
170
/HEAT FLOW METER 60
l
"x
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•
PRACTICAL CURVE
O
THEORETICALCURVE !
55
o~ LU e~
50
t.
)
l,,u r',,
-
t,o
O. I,O '-r
F-
u
z,5
3
0 THICKNESS
fN cm$
Fig. 9, Experimental and theoretical temperature distribution curves in the steady state.
Table 1. Measured values of thermal conductivity of building fabrics I I
I1
Specimen No. and name of the material 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Wall insulating board Thermocole Foam concrete Bartex Insulation Board Soft Board Astrolith Board Mineral Wool Slab Dense concrete Brick tile Window glass
Illll
II
II
I I
I
Density (kg/m 3)
Mean temp. (°C)
Thermal conductivity by the appatatus (Kcal/h degcm)
Thermal conductivity by the hot plate (Kcal/h deg cm)
342,0 22,0 704.0 329-6 249'0 674.0 192.0 2280.0 1820.0 2350.0
42.5 44"3 41.2 59.5 35.0 52.0 41-0 43.8 40.4 59-5
0.046 0.026 0' 123 0.055 0.044 0.093 0.043 1.440 0.672 0.760
0,047 0,027 0"128 0,058 0.041 -0.046 1-360 0.697 0.701
.
.
.
.
.
.
.
•
i i
Table 2. Experimental values of Texp and thermal diffusivity of building fabrics ii
ill|
Specimen No. and name of the material I. 2, 3. 4. 5. 6.
Wall insulating board Thermocole Foam concrete Dense concrete Brick tile Window glass
.i
Sample thickness (cm)
Rise time Texp (s)
1.25 1-24 1"50 1"23 2'50 0-40
471 92 429 201 550 147
ii
j,i
ii
Thermal conductivity Thermal diffusivity Thermal capacity (Kcal/h deg era) (Dx 10- 3 m2/h) (Kcal/m 3) 0-046 0.026 0-123 1.440 0.672 0.760
4"08 19"24 8.03 9"63 13'07 14.12
11-10 1.43 15-4 152-10 51-20 54.90
A Quick Method of Measuring Thermal Conductivity and Thermal Diffusivity of Building Fabrics ments, thermocouples were fixed at the middle point and temperatures were recorded by a recorder. The thermal response curve are shown in figures 6 and 7. Experiments were conducted with six different thicknesses of thermocole to obtain the range of optimum thickness. The optimum range of thickness will also depend upon the value of thermal conductivity of the material to be tested. The variation of the thermal conductivity of thermocole with thickness is shown in figure 8. Experiments were also performed to measure temperature at different points along the thickness of the thermocole in the steady state to examine the effect of the thickness of the sample on the temperature distribution. The temperature distribution obtained from the experiment and calculated from the theory in the steady state are shown in figure 9. The range of optimum thickness for board type of insulating materials like thermocole, wall insulating board, and other wood fiber boards are approximately 4 cm. It has been noted from the .temperature distribution curve that during the steady state, the temperature distribution in the heat flow meter region is different because of thickness of the heat flow meter.
Comparison with the standard results Measured values of conductivity of ten samples ranging from window glass to thermocole are presented in Table 1. Table 2 gives the measured values of T exp for six samples from which the values of diffusivity has been calculated using equation (4). The validity and accuracy of the
1. 2. 3. 4. 5. 6. 7.
171
method can be examined from the value obtained for standard sample of wall insulating board. It may be observed that the values of these board type insulating materials, are in close agreement with the values obtained by the standard hot plate method but for the building material like dense concrete and window glass the values are some what higher than those by the hot plate. The accuracy of the method is within _ 5 per cent. This agreement is expected due to comparable contact resistance. Figures 4 and 5 illustrate, that the maximum time of testing for thermocole is 60 min whereas for window glass it is only 25 min. This shows that in most of the cases time of testing will not be more than one hour. As expected, there will be small variation of temperature in the test area. However, average values of T exp were found to give a close agreement between the measured values of diffusivity of the standard sample. In certain cases it was noticed that the thermal response curves (figures 6 and 7) were not linear. It can be due to variation of the temperature of the thermostats and fluctuations in the supply voltage. It can finally be concluded from the various experimental results that the method can be used for the rapid determination of the thermal properties of building fabrics, without the use of complicated electronic controls. Acknowledgements--Theauthors are thankful to Shri N. K. D. Choudhury for his encouragement and suggestions. They are also thankful to Shri B. C. Raychaudhuri for initiating the work and Shri M. P. Carg for his assistance in setting up the apparatus. The paper is published with the permission of the Director, Central Building Research Institute, Roorkee.
REFERENCES Book of A.S.T.M. Standards, part III, pp. 1084-1092. A.S.T.M. Bulletin, Publication on thermal conductivity (1957). M. CUTTLERand G. T. CI-IENEY,J. appl. Phys. 34, 1902 (1965). T.Z. HARMATTY,J. appL Phys. 35, 1190 (1964). B. K. SAXENA,Ind. J. Tech. 2, 27 (1964). M.B. DASS and M. A. HOSSAIN,Br. J. appl. Phys. 17, 87 (1966). H.S. CARLAWand J. C. JAEGAR,Conduction of Heat in Solids, 2nd Edn. pp. 99-102 (1959).
Une m6thode simple a 6t6 6tablie ayant pour but une prompte d6t6rmination de la conductivit6 thermique et de la diffusivit6 thermique des mat6riaux de construction et de l'isolation. La conductivit6 thermique a 6t6 mesur6e dans son 6tat ferme h l'aide d'un calorim6tre, intercal6 dans un ensemble faisant l'6chantillon double, tandis que le mesurage de la diffusivit6 thermique a 6t6 fait moyennant l'enregistrement de la suite des temp6ratures lues dans le point du milieu de l'6chantillon double. Par un c6t6, cet 6chantillon 6rant en contact direct avec la source de la temp6rature constante pendant que la temp6rature de l'autre c6t6 eut 6t6 maintenue sur le niveau d'ambiance. L'analyse th6orique a montr6 que la fonction de la r6ponse thermique n'est q'une fonction exponentielle retard6e, avec le temps de mont6e exprim6 par le rapport. Les mesurage de la conductivit6 thermique et de la diffusivit6 thermique d'un 6chantillon d'usage courant (planche isolatrice des tours) provenant de National Bureau of Standards U.S.A. (Bureau National de l'Unification des Etats Unis d'Am6rique), ainsi que d'autres mat6riaux de construction prouvaient que la m6thode puisse ~tre suivie par les laboratoires s'occupant d'essayage des mat6riaux de construction et d'isolation, de l'usage courant, dans le diapason des temp6ratures au dessous de 100°C, avec une pr6cision de lecture + 5 %, et, se servant d'un simple dispositif exp6rimental. Eine einfache Methode zur schnellen Bestimming der W~irmeleit--und der W~rmediffusionsf/ihigkeit von Bau--und Isolationsstoffen wurde ausgearbeitet. Die W/irme-
172
K. N. Agarwal and V. V. Verma
leitf~ihigkeit wurde im gleichbleibendem Zustand gemessen mittels Einfiihrung eines W~irmeflul3meters in Doppelprobesanordnung, w~ihrend die Messung der Diffusionsf~ihigkeit durch Registrierung des Temperaturzustandes im Mittelpunkt des Doppelprobestiickes erfolgte. Eine der Seitenfl~iche des Probestiickes ist im Kontakt mit einer konstanten Temperaturquelle, w~ihrend die andere Seitenfl~iche auf dem umgebenden Temperaturniveau gehalten ist. Eine theoretische Analyse bewies, dab die thermische Empfindlichkeitsfunktion eine verz/3gerte Exponentialfunktion ist, yon einer Steigzeit, die durch das Verh~iltnis bestimmt ist. Messungen der W/irmeleitf~ihigkeit und der W~irmediffusionsf/ihigkeit eines Standardmusters (Wandisolationsplatte) des National Bureau of Standards, U.S.A. (Landesbtiro der Industrienormen, Vereinigte Staaten von Amerika) und andere Baustoffe haben gezeigt, dal3 die Methode angewandt werden kann in kaboratorien ftir Prtifung von Bau--und Isolationsstoffe fiir den allgemeinen Gebrauch, in einem Temperaturbereich unter 100°C mit einer ~o, mit Anwendung einer einfachen Prtifungsvorrichtung. Toleranz von + 5 °/ _
Build. Sci. Vol. 2, pp. 165-172. Pergamon Press 1967. Printed in Great Britain
]
697.001
A Quick Method of Measuring Thermal Conductivity and Thermal Diffusivity of Building Fabrics K. N. AGARWAL* V. V. VERMA*
A simple method has been developed for rapid determination of thermal conductivity and thermal diffusivity of building and insulating materials. The thermal conductivity has been measured in the steady state by introducing a heat flow meter in the twin sample arrangement whereas thermal diffusivity measurement has been done by recording the temperature history at the mid-point of a twin sample. One of the faces of the sample is in contact with a constant temperature source, while the temperature of the other face is maintained at the ambient level. Theoretical analysis has proved that the thermal response function is a delayed exponential function with rise time defined by the ratio d2/2D. Measurements of the thermal conductivity and thermal diffusivity of the standard sample (wall insulating board)from National Bureau of Standards, U.S.A. and other buildingfabrics have revealed that the method can be employed by the laboratories for testing building and insulating materials which are commonly used, in the temperature range below IO0°C with +_5 per cent accuracy and simple experimental set up.
INTRODUCTION MEASUREMENT of thermal conductivity by guarded hot plate is time consuming and requires more elaborate experimental set up. An indirect method of determining the thermal diffusivity is to measure specific heat per unit volume and thermal conductivity separately and make use of the simple relationship, D = K/C, where K is the thermal conductivity and C is the specific heat per unit volume. The building and insulation industry is in need of an apparatus that could quickly indicate the thermal conductivity values with an accuracy comparable to the hot plate and satisfying I.S.I.[1] and A.S.T.M.[2] standards. An apparatus has been developed for quick measurement of thermal conductivity using a heat flow meter. Various methods[3-6] have been suggested by different workers for measurement of thermal conductivity and thermal diffusivity in transient state. The method described in this paper enables measurement of thermal conductivity and diffusivity without any knowledge of either the heat transfer coefficient of the specimen surfaces or specific heat of the material. The proposed method determines thermal diffusivity by observing the rise time of the
0
~)
TWIN SLAB SPECIMEN
/
/ /i
1
HEAr q sou.Rcgl
I
/
t
/
/
/ I /" /
HEAT
/ / / / i ,
•
Fig, 1.
/
/
//// / / / / .
/
i.
/
A
L--HEAT FLOW METER Twin slab arrangement for the determination thermal conductivity and thermal diffusivity.
of
thermal response function at a point midway of twin sample arrangement, when one face is excited by a step function heat input while the other face is maintained at a constant ambient temperature.
* Central Building Research Institute, Roorkee, U.P., India.
165
K. N. Agarwal and V. V. Verma
166
The temperature of the hot and cold plate can be controlled from 20°C to 100°C with an accuracy of" _+0.1°C. The rise time has been taken as the time required, including the initial delay, for the response function to rise up to 63.2 per cent level of its final value. The thermal conductivity has been measured by introducing a heat-flow meter in the twin sample arrangement and measuring its output in the steady state. The accuracy of the instrument has been checked by using standard sample of wall insulating board, supplied by National Bureau of Standards. TAPER )
the heat flow across a twin sample arrangement when the temperature at the end faces are kept constant. If we define the response function as
F(t) =
-
~(0.
-
Oc)
where 0it and Oc are the temperatures of the end faces. Assumef(x) and 0,, to be equal to the constant ambient air temperature 0c. The solution of the equation (1) under the above boundary condition as given by Dass and Hossain[6] following Carslaw and Jaeger[7].
NOZZLE
\
\ \ \ \
\ \ \\
", \ \ × , \ , t Y 6 ;
", \ \ \
"
F~e. 2. Design details of the plate. c~
THEORETICAL Unidirectional heat flow in solids is governed by the Fourier equation given below: dO _d20 d t = D~x-x2' (0 < K < 2d) (1) where, D = diffusivity. Let us take the initial boundary conditions as follows 0 =.f(~) when t = 0 0= 0cat'c=0 } 0 OH at K 2d t >= 0 where 0 is the temperature and t is the time. The equation under the boundary conditions represent
~z~-2-~(2n + 1) It=O
4d z where T = - - ~z D •
(2)
For large values of t equation (2) reduces to
F(t) g 1 - 4 exp ( - t / T ) g
,
,3,
It follows from equation (3) that the experimental
A Quick Method of Measuring Thermal Conductilfity and Thermal Diffusivity of Building Fabrics Thermal conductivity
time constant is related to the basic time constant as
The thermal conductivity can be calculated from the steady state heat flow equation
T e x p ~ 1.24T 1.24 × 4d 2
d2
nZD
2D
Hence T e x p - T
2.26 x S.u
(4)
= At = 0-19Texp
(5)
=
k(On- Oc1) (2d- K)
(6)
where S is the calibration constant of the heat flow meter in B.t.u./h. ft 2 per m.V at 80°F; dis thickness of the sample in cm; x is the heat flow-meter thickness in cm; K is thermal conductivity of the
From the response function [ 1 - F(t)]- a and T exp the values of D can be obtained by using equation
(4). HOT WATER THERMOS- 4-TAT65°C
L
~ RUBBER 1
;,
r
-~
; //
///////
_r---hi ~
r/////////~
P////////~/A ~
,.,/, / / / J I~ ' / / / / / / / / JL~ / / / / / / / l TAT
7
~oOc
RECORDER
P ANCE MATCHINt5
TUBIN6
I
--
J
~
tCOL D WATER
Fig. 3. Block diagram of the experimental set up. 1.00
D-----l-~-q ~----t----q :~_-0---~)---0---(
- -
#" O,70
II
O .J
/
h
I
/
/
I-hi "1-
/
050
!
t~.
o
0 BRICK TILE • DENSE CONCRETE t~ WINDOW OLASS
LU U Lid
0.2!
Y O.O( O
B
167
16
24 TIME
32 40 IN MINUTES
48
56
64
Fig. 4. Relation between the percent of heat flow and the time of testing for brick tile, dense concrete and window glass.
K. N. Agarwal and V. V. Verma
168 1.00
) i
0.75
/,I
o
---~-#(" t/ //
o. ~o o
tU
U or Ill II
0.0(
0
8
16
24
TIME
32
tN
40
48
56
6/,
MINUTES
Fig. 5. Relation between the percent of heat flow and the time of testing for thermocole, wall board and foam concrete.
,,"
./
i
LIJ t/) Z O Q.
60
120 TiME
Fig. 6.
t
180
24O
(see)
Experimental curves of response function for the determination of thermal diffusivity, Curve A, thermocole ; Curve B, Window glass; Curve C, Dense Concrete.
specimen Kcal/h deg cm and perature difference in deg C.
(On-Oc) is
the tem-
EXPERIMENTAL For the constant temperature source two aluminium plates of 2.5 cm thickness figure 2 have been designed and fabricated. The temperature of
the plates is controlled by two water thermostat giving a temperature control up to an accuracy of +_0.1°C. Copper-constantan thermocouples of 32 s.w.g, were used for the measurement of temperature using a microvolt recorder. Heat flow was measured by a heat-flow meter using an accurate potentiometer. The calibration of the heat flow
A Quick Method of Measuring Thermal Conductivity and Thermal Diffusivity of Building Fabrics meter was done by a guarded hot plate apparatus and corrected values of heat flow at each mean temperature was obtained from the calibration curve. The block diagram of the experimental setup is shown in figure 3. The whole apparatus was enclosed in an insulated chamber made of three laminated thermocole plywood panels to minimize heat losses by convection and radiation. 4
Thermal conductivity and thermal diffusivity For the measurement of thermal conductivity, when the temperatures of the heat source and heat sink become constant, test specimens were introduced and the heat flow meter readings were recorded at regular intervals of time. Experimental results obtained for the six samples are presented in figures 4 and 5. For thermal diffusivity measuref
/ / / / y
,••-
I
I
W Z O r~
~
t~ tv
I
O
150
~ ~(~MFOA CONCRETE • INSULATING BOARD O BRICKTILE 300 TIME t ( Sec)
~50
600
Fig. 7. Experimental curves of responsefunction for the determination of thermal diffusivity. Curve A, foam concrete; Curve B, insulating board; Curve C, brick tile.
0.030
E
0o 0.025
f
U ,,.e
FU
0.020
Q Z 0
x
"" O.015 W -r" I,-
O.O1(O
2.5
5.0 THICKNESS
169
IN
10.0 cm$
Fig. 8. Variationof thermal conductivity with thickness.
K.N. Agarwaland V. V. Verma
170
/HEAT FLOW METER 60
l
"x
I
I
•
PRACTICAL CURVE
O
THEORETICALCURVE !
55
o~ LU e~
50
t.
)
l,,u r',,
-
t,o
O. I,O '-r
F-
u
z,5
3
0 THICKNESS
fN cm$
Fig. 9, Experimental and theoretical temperature distribution curves in the steady state.
Table 1. Measured values of thermal conductivity of building fabrics I I
I1
Specimen No. and name of the material 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Wall insulating board Thermocole Foam concrete Bartex Insulation Board Soft Board Astrolith Board Mineral Wool Slab Dense concrete Brick tile Window glass
Illll
II
II
I I
I
Density (kg/m 3)
Mean temp. (°C)
Thermal conductivity by the appatatus (Kcal/h degcm)
Thermal conductivity by the hot plate (Kcal/h deg cm)
342,0 22,0 704.0 329-6 249'0 674.0 192.0 2280.0 1820.0 2350.0
42.5 44"3 41.2 59.5 35.0 52.0 41-0 43.8 40.4 59-5
0.046 0.026 0' 123 0.055 0.044 0.093 0.043 1.440 0.672 0.760
0,047 0,027 0"128 0,058 0.041 -0.046 1-360 0.697 0.701
.
.
.
.
.
.
.
•
i i
Table 2. Experimental values of Texp and thermal diffusivity of building fabrics ii
ill|
Specimen No. and name of the material I. 2, 3. 4. 5. 6.
Wall insulating board Thermocole Foam concrete Dense concrete Brick tile Window glass
.i
Sample thickness (cm)
Rise time Texp (s)
1.25 1-24 1"50 1"23 2'50 0-40
471 92 429 201 550 147
ii
j,i
ii
Thermal conductivity Thermal diffusivity Thermal capacity (Kcal/h deg era) (Dx 10- 3 m2/h) (Kcal/m 3) 0-046 0.026 0-123 1.440 0.672 0.760
4"08 19"24 8.03 9"63 13'07 14.12
11-10 1.43 15-4 152-10 51-20 54.90
A Quick Method of Measuring Thermal Conductivity and Thermal Diffusivity of Building Fabrics ments, thermocouples were fixed at the middle point and temperatures were recorded by a recorder. The thermal response curve are shown in figures 6 and 7. Experiments were conducted with six different thicknesses of thermocole to obtain the range of optimum thickness. The optimum range of thickness will also depend upon the value of thermal conductivity of the material to be tested. The variation of the thermal conductivity of thermocole with thickness is shown in figure 8. Experiments were also performed to measure temperature at different points along the thickness of the thermocole in the steady state to examine the effect of the thickness of the sample on the temperature distribution. The temperature distribution obtained from the experiment and calculated from the theory in the steady state are shown in figure 9. The range of optimum thickness for board type of insulating materials like thermocole, wall insulating board, and other wood fiber boards are approximately 4 cm. It has been noted from the .temperature distribution curve that during the steady state, the temperature distribution in the heat flow meter region is different because of thickness of the heat flow meter.
Comparison with the standard results Measured values of conductivity of ten samples ranging from window glass to thermocole are presented in Table 1. Table 2 gives the measured values of T exp for six samples from which the values of diffusivity has been calculated using equation (4). The validity and accuracy of the
1. 2. 3. 4. 5. 6. 7.
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method can be examined from the value obtained for standard sample of wall insulating board. It may be observed that the values of these board type insulating materials, are in close agreement with the values obtained by the standard hot plate method but for the building material like dense concrete and window glass the values are some what higher than those by the hot plate. The accuracy of the method is within _ 5 per cent. This agreement is expected due to comparable contact resistance. Figures 4 and 5 illustrate, that the maximum time of testing for thermocole is 60 min whereas for window glass it is only 25 min. This shows that in most of the cases time of testing will not be more than one hour. As expected, there will be small variation of temperature in the test area. However, average values of T exp were found to give a close agreement between the measured values of diffusivity of the standard sample. In certain cases it was noticed that the thermal response curves (figures 6 and 7) were not linear. It can be due to variation of the temperature of the thermostats and fluctuations in the supply voltage. It can finally be concluded from the various experimental results that the method can be used for the rapid determination of the thermal properties of building fabrics, without the use of complicated electronic controls. Acknowledgements--Theauthors are thankful to Shri N. K. D. Choudhury for his encouragement and suggestions. They are also thankful to Shri B. C. Raychaudhuri for initiating the work and Shri M. P. Carg for his assistance in setting up the apparatus. The paper is published with the permission of the Director, Central Building Research Institute, Roorkee.
REFERENCES Book of A.S.T.M. Standards, part III, pp. 1084-1092. A.S.T.M. Bulletin, Publication on thermal conductivity (1957). M. CUTTLERand G. T. CI-IENEY,J. appl. Phys. 34, 1902 (1965). T.Z. HARMATTY,J. appL Phys. 35, 1190 (1964). B. K. SAXENA,Ind. J. Tech. 2, 27 (1964). M.B. DASS and M. A. HOSSAIN,Br. J. appl. Phys. 17, 87 (1966). H.S. CARLAWand J. C. JAEGAR,Conduction of Heat in Solids, 2nd Edn. pp. 99-102 (1959).
Une m6thode simple a 6t6 6tablie ayant pour but une prompte d6t6rmination de la conductivit6 thermique et de la diffusivit6 thermique des mat6riaux de construction et de l'isolation. La conductivit6 thermique a 6t6 mesur6e dans son 6tat ferme h l'aide d'un calorim6tre, intercal6 dans un ensemble faisant l'6chantillon double, tandis que le mesurage de la diffusivit6 thermique a 6t6 fait moyennant l'enregistrement de la suite des temp6ratures lues dans le point du milieu de l'6chantillon double. Par un c6t6, cet 6chantillon 6rant en contact direct avec la source de la temp6rature constante pendant que la temp6rature de l'autre c6t6 eut 6t6 maintenue sur le niveau d'ambiance. L'analyse th6orique a montr6 que la fonction de la r6ponse thermique n'est q'une fonction exponentielle retard6e, avec le temps de mont6e exprim6 par le rapport. Les mesurage de la conductivit6 thermique et de la diffusivit6 thermique d'un 6chantillon d'usage courant (planche isolatrice des tours) provenant de National Bureau of Standards U.S.A. (Bureau National de l'Unification des Etats Unis d'Am6rique), ainsi que d'autres mat6riaux de construction prouvaient que la m6thode puisse ~tre suivie par les laboratoires s'occupant d'essayage des mat6riaux de construction et d'isolation, de l'usage courant, dans le diapason des temp6ratures au dessous de 100°C, avec une pr6cision de lecture + 5 %, et, se servant d'un simple dispositif exp6rimental. Eine einfache Methode zur schnellen Bestimming der W~irmeleit--und der W~rmediffusionsf/ihigkeit von Bau--und Isolationsstoffen wurde ausgearbeitet. Die W/irme-
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K. N. Agarwal and V. V. Verma
leitf~ihigkeit wurde im gleichbleibendem Zustand gemessen mittels Einfiihrung eines W~irmeflul3meters in Doppelprobesanordnung, w~ihrend die Messung der Diffusionsf~ihigkeit durch Registrierung des Temperaturzustandes im Mittelpunkt des Doppelprobestiickes erfolgte. Eine der Seitenfl~iche des Probestiickes ist im Kontakt mit einer konstanten Temperaturquelle, w~ihrend die andere Seitenfl~iche auf dem umgebenden Temperaturniveau gehalten ist. Eine theoretische Analyse bewies, dab die thermische Empfindlichkeitsfunktion eine verz/3gerte Exponentialfunktion ist, yon einer Steigzeit, die durch das Verh~iltnis bestimmt ist. Messungen der W/irmeleitf~ihigkeit und der W~irmediffusionsf/ihigkeit eines Standardmusters (Wandisolationsplatte) des National Bureau of Standards, U.S.A. (Landesbtiro der Industrienormen, Vereinigte Staaten von Amerika) und andere Baustoffe haben gezeigt, dal3 die Methode angewandt werden kann in kaboratorien ftir Prtifung von Bau--und Isolationsstoffe fiir den allgemeinen Gebrauch, in einem Temperaturbereich unter 100°C mit einer ~o, mit Anwendung einer einfachen Prtifungsvorrichtung. Toleranz von + 5 °/ _