SfB Build. Sci. Vol. 5, pp. 31-40. Pergamon Press 1970, Printed in Great Britain
Ab9 '1 699.86
A Study of Thermal Performance of Concrete Hollow Blocks by an Electrical Analogue Method K. R. RAO PRAKASH CHANDRA
This paper deals with a study of the thermal performance of hollow blocks of different designs and types of concrete, by a two dimensional R-C network analogue method. Steady and periodic thermal characteristics of solid and concrete hollow blocks, along with those of solid and cavity brick wall sections, are presented. The thermal performance of the concrete hollow block wall sections, exposed to a typical summer sol-air temperature diurnal cycle, has been evaluated both for conditioned and unconditioned situations. The hourly variation of heat flow rates and inside surface temperatures of the hollow block sections were compared with those of the solid and cavity brick walls. This study brings out the fact that the widely used hollow block design with two large air spaces is not thermally efficient under tropical climates. Their thermal performance can, however, be improved considerably and be made acceptable by adopting a design with four air spaces arranged in two rows.
INTRODUCTION C O N C R E T E hollow block constructions have been in wide use all over the world for some time. The main advantage in using hollow blocks is the rapidity of construction and increased productivity. It is often claimed that, because of the enclosed air space, hollow blocks also provide better thermal insulation. This need not necessarily be true, especially under tropical climates where the periodic thermal characteristics must also be taken into account. The thermal capacity, which depends upon the weight of the structural element, should be given equal importance. The main factors which determine the thermal performance of a hollow block construction are (i) the type of concrete (dense or lightweight) used for making the blocks (ii) the percentage air space (by volume) and (iii) the number and the disposition of the hollows in the block. A systematic study of the effect of the above factors on the thermal performance of hollow block constructions is necessary to evolve thermally efficient hollow block designs. With this in view a study of the thermal characteristics and the overall thermal performance of hollow block constructions of different design and materials has been carried out by an electrical analogue method.
3 Fig. 1. Types of hollow blocks studied.
hollow blocks have been considered. They are illustrated in figure 1 and described below. Type 1. Two air spaces of 10 cm x I0 cm x 20 cm dimensions in a single row with a web thickness of 10 cm between the hollow spaces. Type 2. Three air spaces of dimensions 10 x 10 x 20 cm in a single row with a web thickness of 2.5 cm between the air spaces. Type 3. Four air spaces of dimensions 10 x 5 x 20 cm arranged in two rows and columns with web thickness of 5 cm and 10 cm between the rows and columns respectively. The overall dimensions of the blocks of all the three types are taken as 40 x 20 x 20 cm. The hollow blocks of type 1 and 3 have 25 per cent air space while the block type 2 has 37.5 per cent of air space. It is the usual practice in hollow
Hollow block types studied For the present study three different designs of *Central Building Research Institute, Roorkee (U.P.) India.
K. R. Rao and Prakash Chandra
block design to provide air spaces as wide as 10 cm, but it has been shown by Rowley and Algren[l] that no additional advantage in thermal resistance of air space is derived by increasing its width beyond 2.5 cm. Hence better thermal performance of hollow blocks can be expected by splitting the air space into smaller widths and arranging them in two or more rows in the direction of heat flow. However, the strength and stability considerations which decide the web thickness between the airspaces will limit the number of rows that could be provided. A comparison of the hollow block types 1 and 3 will bring out the effect of rows on their thermal performance. Materials of hollow blocks in present day practice concrete hollow blocks are made, not only of dense aggregate, but also with lightweight aggregates like cinder, and expanded slag. In order to broaden this study the above three types of hollow block designs made from dense as well as lightweight aggregate concretes are considered. The thermophysical properties of the materials of the blocks are given in Table 1.
Table I. Therrnophysh'al properties q/ concrete~ and brh'A Material
Thermal conductivity (kcal/m."C.h)
I. Dense concrete 2. Cinder concrete 3. Expanded slag aggregate 4. Brick
Density Specific heat (kg]m 3) (kcal/kg.°C)
0- 347 0-744
The general differential equation, for heat conduction through an isotropic medium is given as:
while for current flow through a non-inductive transmission line is given by equation
Fig. 2. R - C network analyser.
dE 1 V zE ~ RC
Study o f Thermal Performance o f Concrete Hollow Blocks
The similarity of these two equations suggests that an analogy between thermal and electrical systems exists and that the heat transfer through building sections can conveniently be studied by an equivalent electric network representation in the laboratory. Several workers[2-5] have successfully used the electric analogue method to solve problems of steady and transient heat flow through bodies of complex shape under different boundary conditions. For some time a R-C network analyser has been in operation at the Central Building Research Institute, Roorkee, mainly for determining the periodic heat flow characteristics of building sections. A solid section can be represented as a onedimensional lumped R-C circuit of "T" type configuration, but a hollow block due to the presence of air spaces and solid bridges needs a two dimensional representation. Therefore the existing network has been modified suitably for handling two-dimensional heat flow problems as well. This is shown in figure 2. The two-dimensional resistance capacitance circuit network representation of a
hollow block is shown in figure 3. The scaling factors used for computing equivalent electrical resistance and capacitance values for the analogue representation of the hollow block sections are given in Table 2. The experimental procedure adopted for the determination of steady and periodic characteristics by the electrical analogue method has been described in an earlier paper. THERMAL CHARACTERISTICS Although a hollow block is more accurately represented by a two dimensional R-C network, it is worthwhile to find out the errors introduced by treating it as an equivalent solid (one dimensional) network as this simplifies the procedure considerably. The steady state heat transmission factor (U value) and the periodic thermal characteristics (transfer and driving point functions) for all the three types of blocks of dense and lightweight concretes, were determined for both two dimensional and equivalent solid network representations. These are given in Table 3. Thermal characteristics for other commonly used wall sections such as solid concrete blocks, brick and cavity wall were also determined and included in Table 3 for a comparison. It can be seen from the data presented in Table 3 that for any given type of material, hollow block type 3 (the one having four air spaces in two rows) is far superior to other types of blocks and also superior to the solid block of the same material of equal thickness. It may also be noted that the most commonly used block with two air spaces (type 1) is thermally inferior to the solid block of the same thickness. The improvement obtained in thermal characteristics by increasing the number of air spaces is much greater for dense concrete blocks, than for lightweight concrete blocks. The thermal characteristics (steady and periodic) of the hollow blocks discussed above provide the basic indication of their relative thermal behaviour and are independent of climatic factors. However, the actual thermal performance of a building
Fig. 3. Electrical network representation of a hollow block (type 1).
Table 2. Scalingfactors.
Capacity Inside and outside filmresistances Temperature
°C/kcal.m2.hr kcal/°C.m2 °C/kcal.m2.hr
~ F ~
R T / R e 1-89xI0 s f~ CT/Ce 10- 9 F R T / R e 1"89x 105 °c/v T/t
K. R. Rao and Prakash Chandra
Table 3. Steady state andfundamental periodic thermal characteristics of hollow blocks Material
Solid block (20 cm)
Hollow block types 1
1. Dense concrete
U TFI* 2 DF2* 2' qb' U TFI 2
2. Cinder concrete
DF2 2' 4' 3. Expanded slag agg. U TFl 2 ¢t DF2 2' qb' 4. Brick wall (22.5 cm) U TF1 J. qb DF2 2' ~' 5. Cavity brick wall1" U TFI ~ DF2 2' ~b'
2.500 0-183 87-0 0.449 28.0 1.913 0-153 85.0 0.557 23.0 1.279 0.083 108.0 0.631 19.0 1.993 0.143 93.0 0.531 24.0 1.806 0.175 70.0 0.604 26.0
2"599 0.266 68.0 0.461 24-0 1.788 0.166 66-0 0'565 20.0 1.285 0.103 69.0 0-748 18'0
2.599 0-232 62"0 0'470 20"0 1'788 0"169 68.0 0.602 22'0 1.285 0'093 74.0 0.730 14.0
2-105 0"176 78.0 0.536 26.0 1.400 0.100 73.0 0.638 21.0 1.089 0.049 82-0 0.800 15.0
2-105 0.182 79.0 0'536 15.0 1.400 0.108 80-0 0-652 18.0 1.089 0-066 85.0 0.755 14.0
2.400 0.196 59.0 0"547 26'0 1.666 0'142 70-0 0-666 16"0 1.236 0,112 56.0 0.818 15.0
2-400 0.203 62.0 0.559 22.0 1.666 0-150 76-0 0.661 20-0 i.236 0-110 67-0 0-775 14.0
* TFI and DF2 are vectorial quantities. Units for U-values are k.cal/m 2.°C.h. t 7.5 cm bricks + 5.0 cm air space + 7"5 cm brick.
section, when exposed to a specific weather condition, is o f practical interest. This is judged by the resultant temperature and heat flow variations at the inside surface due to the thermal variations at the exposed surface. The heat exchange p h e n o m e n o n at the exposed surface is usually expressed by a single equivalent temperature variation k n o w n as sol-air temperature. The procedure for obtaining the inside surface temperature and heat flow variations o f a building section exposed to a given sol-air temperature diurnal cycle is explained below. Let the Fourier representation o f the diurnal variation of the sol-air and indoor air temperatures be expressed as steady state and periodic components as given in equations (3) and (4). The meaning o f the symbols is given in the nomenclature.
t~ = La(m)+ ~ ~ . cos (tonz- ~,)
ti~ = t~a(m)+ ~ tlan COS (09,'r- ~/.)
Then the diurnal inside surface temperature (j~) and heat flow ( ~ ) variations for a general case o f unconditioned enclosure can be obtained f r o m equations (5) and (6) respectively.
n U tis = ~ [tsa(m) - t,a(m)] +,=,~"2.~a . cos (og.T - ~. - ~.) n
+ y~ ,vj , . . cos (co.~-%-~'.)
qis = ( t i s - t,.)hi
In the case o f a conditioned enclosure qo(rn) in equation (5) is to be replaced by t~,c, the temperature at which the indoor air is kept constant, and the third term becomes zero. This will result then as: .L" U (ts,(m)-t,,c)+ L 2.is,. cos ( t o . r - ~ , - ~ b , ) tis n=l
(7) F o r the purpose of illustrating the thermal performance of wall section made o f hollow concrete blocks o f different materials and designs over a diurnal cycle, a typical sol-air temperature waveform for west orientation on a s u m m e r day (16th May) at Roorkee, India (Latitude 29051 ' N) has been considered. The diurnal variations o f the shade air, sol-air, and indoor air temperatures used in the illustrative example are shown in figure 4. The Fourier representation o f sol-air and indoor air temperatures is given by equations (8) and (9).
Study of Thermal Performance of Concrete Hollow Blocks
dense, cinder and expanded slag concretes, when exposed to a sol-air temperature diurnal cycle as represented by the equation (8) and indoor air temperature kept constant at 25°C, were obtained and are presented in figures 5(a), (b), (c) respectively.
rio = 25"C
/ / - N~////Type 3 / ,~,/V/s°ud
? ® ~ 45 -
25 ~ ZG
,o__ .<\'.... i
Fig. 4. Hourly sol-air (West orientation), shade air and indoor air temperatures on a typical summer day.
12 16 Time, h
Fig. 5(a). Effect of hollow block design on the heat flow rate for dense concrete.
ts= = 35.0+ 15.80 cos (15r-232 °) + 6.80 cos (30~- 103°) + 4.51 cos (45z- 5°) + 2.35 cos (60T - 242 °) (8)
tia = 33.1 +2.75 cos (15v-252 °) + 0.35 cos (30z- 69 °) +0.37 cos (45z- 73 °) +0.13 cos (60T- 129 °) (9)
£ As both conditioned and unconditioned enclosures occur in practice, it is necessary to evaluate the thermal performance of any building section for the above situations separately. It is known that in the case of a conditioned enclosure, i.e. indoor air temperature maintained constant, the U-value and the transfer function are the only characteristics that come into the picture, whereas for the unconditioned case, the internal driving point function would also play a significant part. The main point of interest for a conditioned building is the cooling load contributed by the building section. On the other hand, for the unconditioned building (inside air temperature variable) the inside surface temperature of the building section is the main factor to be considered, as this will also determine the mean radiant temperature of the enclosure. THERMAL
Conditioned interior The hourly heat flow rates, through solid and all three types of hollow block wall sections made of
~" 3o o "6 -~" 2o
\ I "~\CJ
Fig. 5(b). Effect of holloN block design on the heat flow rate for ci,~der concrete.
It may be noted from figure 5(a), that in the case of dense concrete blocks, the thermal performance is improved in accordance with the increase in the number of airspaces. Considerable reduction in heat flow rate is obtained by dividing the same air volume into four hollow spaces (type 3) arranged in two rows instead of the usual two hollows (type 1)
K. R. Rao and Prakash Chamh'a Conditioned,
t : = 2 5°C
As the brick is the most commonly used walling material it is of some interest to compare the thermal performance of hollow concrete blocks with 22.5 cm solid and 20 cm cavity brick walls under identical exposure conditions. This comparison for types 1 and 3 blocks is shown in figure 6(a) and (b), respectively. It can be seen from figure 6(a), that the Conditioned,
/ -/~.,~, ,",.Type3
' Solid 60
~ ,, = 2
Fig. 5(c). Effect of hollow block design on the heat flow rate for expanded slag concrete.
in a single row. In the case of the lightweight hollow blocks, as seen from figures 5(b) and (c), block type 2 is slightly inferior to block type 1 unlike the case of dense concrete blocks. However, block type 3 is superior to block types 1 and 2 as is the case with dense concrete blocks. This may be explained as follows. As mentioned earlier, the thermal behaviour of a building section under periodic conditions depends on its thermal resistance as well as the thermal capacity. In a hollow block, a part of solid portion is replaced by the air. For dense materials the thermal resistance of the solid part removed is less than that of the air space introduced but there is a reduction in thermal capacity of the block. However, if the increase in the overall thermal resistance is large enough, so that it overweighs the effect of the loss of thermal capacity, the overall thermal behaviour improves. If the total air space is divided into more hollow spaces and arranged in two rows (in the direction of heat flow) the thermal resistance of the air space will be increased considerably and hence its efficiency will be further increased. In the ease of lightweight concrete blocks, the thermal resistance offered by the solid portion is sufficiently large and there may not be a significant change in the overall thermal resistance by the introduction of air spaces if arranged in a single row. Further, the thermal capacity is reduced by replacing the solid portion by air space and this leads to relatively poor thermal performance. However, if the air spaces are divided and arranged in two rows as in type 3, considerable improvement in thermal behaviour can be achieved for lightweight concrete blocks as well.
\\ i E x p o n d e d .\.. ~,~slogconc.
Fig. 6(a). A comparison of the thermal perJormance of hollow block type t, solid and cavity brick walls.
t : : 25°C
60 / Solid brick.
50 -J:: c~
~¢ • .-/J~V Cinder
~. z o
Fig. 6(b). A comparison of the thermal performance of hollow block type 3, solid and cavity brick walls.
most commonly used dense concrete blocks [i.e. type (1)] are the poorest of all, whereas the cinder concrete blocks more or less match with the cavity brick wall but are slightly inferior to the solid brick wall. It is interesting to note (figure 6b) that by changing the hollow block design from type 1 t o
Study of Thermal Performace of Concrete Hollow Blocks type 3, a dense concrete block wall approximates to a cavity brick wall and the cinder concrete block will give a better performance than the solid brick wall. As regards the expanded slag concrete block, even type 1 is superior to solid brick wall and it is further improved in the case of type 3.
20 o 50
19 ° 21
The range of heat flow rates for solid and hollow blocks of dense, cinder and expanded slag concrete along with the solid and cavity brick walls are shown in figure 7 as a bar diagram. This indicates that there is not much difference in minima while there is considerable variation in the maximum. It may be more appropriate to compare the integrated heat flow over a complete diurnal cycle rather than just maximum and minimum ranges. Such a comparison is made in figure 8 as a histogram.
Unconditioned interior The hourly inside surface temperature variation of the dense, cinder and expanded slag concrete
22 o ~
Expanded Slog conc.
CB SB Brick
Fig. 7. Diurnal ranges of heat flow through different types of hollow and solid block concrete walls.
//_ _'~ y cor~ L,,":"R~,%so,~d b.ek
Fig. 9(a). Inside surface temperature variations for hollow concrete blocks of type 1.
Dense / /Solid brick / ~ \ / J ~ C J/ inderconc.
I ,.f'-'~ /
- 3<,S o
S Cinder con,
CB SB Expanded Slog conc.
Fig. 8. Histogram of integrated heat flow (over 24 h) through different types of hollow and ,*olid block concrete walls.
Fig. 9(b). Inside surface temperature variations for hollow concrete blgcks of type 3.
K. R. Rao and Prakash Chandra
~9 ~ 200
r : l
5 S I
Expanded slog conc.
Inside smface temperature ranges o)" different types o[ hollow and solid block concrete walls.
hollow block types 1 and 3, and of the solid and cavity brick walls, for the same sol-air temperature exposure and a typical indoor air temperature variation (shown in figure 4), were determined and are presented in figures 9(a) and (b). It may be observed that, while for a given type of concrete the change in design of the hollow block from type 1-3 improves its thermal performance, it is not as large as in the case of conditioned enclosure. The maximum and minimum ranges of the surface temperatures of different walls, with the variable indoor air temperature are shown in figure 10. The numbers given at the ends of the bars indicate the time of occurrence of maximum and minimum temperatures. It is known that if the temperatures of the enclosing surfaces exceed 30°C, they would impair the radiant heat loss from the human body and thus augment the discomfort conditions in an enclosure. In an earlier paper (10) it has been shown that the degree hours above 30°C will serve as a good index for the rating of thermal performance of building sections. A comparison of the degree hours of the solid and hollow concrete blocks and solid and cavity brick walls is given in the form of a histogram (figure 1 I). The number at the top of each strip indicates the number of hours the surface temperature exceeds 30°C in a day. It is obvious that the lower the figure of degree hours obtained, the better is its thermal performance. It is interesting to note that the degree hours for the unconditioned case follow
the same general pattern of the integrated heat flow of the conditioned situation for solid and hollow concrete blocks.
88 24 21
.E ~, 8 4 e~ E3
Expanded Slog conc.
Fig. 11. Histogram of degree h (base 3 0 ° C ) of inside surface of hollow and solid block concrete walls.
Study of Thermal Performance o f Concrete Hollow Blocks
CONCLUSIONS T h e m a i n conclusions d r a w n f r o m this s t u d y a r e : 1. U n d e r t r o p i c a l climates the c o m m o n l y used h o l l o w b l o c k s o f dense concrete having two h o l l o w s o f 10 c m wide air spaces are t h e r m a l l y inferior to 22.5 cm b r i c k wall, while the lightweight concrete h o l l o w blocks c o m p a r e well. 2. T h e r e is c o n s i d e r a b l e scope in i m p r o v i n g the t h e r m a l p e r f o r m a n c e o f hollow concrete blocks by increasing the n u m b e r o f hollows a n d a r r a n g i n g t h e m in rows a n d columns. Both for c o n d i t i o n e d a n d u n c o n d i t i o n e d situations the t h e r m a l p e r f o r m a n c e o f a h o l l o w dense c o n c r e t e b l o c k wall can be m a d e equal to o r even slightly b e t t e r t h a n a 22.5 c m b r i c k wall by a d o p ting four h o l l o w s (type 3) instead o f the usual two hollows (type 1) design. 3. T h e i m p r o v e m e n t o b t a i n e d in the t h e r m a l p e r f o r m a n c e by increasing the n u m b e r o f air spaces is m u c h m o r e in the case o f dense concrete b l o c k s t h a n for the lightweight aggregate concrete blocks. 4. T h e a p p r o x i m a t e r e p r e s e n t a t i o n o f a hollow b l o c k as an equivalent solid ( R - C ) n e t w o r k w o u l d i n t r o d u c e errors o f the o r d e r o f 5 per cent.
Acknowledgment This work was carried out as part of the research programme of Central Building Research Institute and is published with the permission of the Director.
= Temperature z = Time x = Thermal conductivity Density P = Specific heat s = (.D = A n g u l a r velocity h l = Inside convective heat transfer coefficient U = Overall heat t r a n s m i s s i o n coefficient R0 = Outside film resistance R A = A i r space resistance R~ = Inside film resistance R = Resistance o f solid p a r t C -- T h e r m a l capacity q = H e a t flow rate 2 = The a m p l i t u d e d e c r e m e n t factor for transfer function The a m p l i t u d e d e c r e m e n t f a c t o r for internal 2' = driving p o i n t function ~ = The phase lag for transfer function tp' = The phase lag for internal driving p o i n t o f function t
Subscripts i o s
= = = sa = ia = is = os = n = m = a =
Inside Outside Solid Sol-air Insideair Inside surface Outside surface Harmonic Mean A i r space
REFERENCES 1. F. B. ROWLEY, and A. B. ALCREN, Thermal resistance of air spaces, Trans. ASHVE, 35, 165 (1929). 2. V. PASCHKIS,Periodic heat flow in building walls determined by Electrical Analogue method, Trans. ASHVE, 48, 75 (1942). 3. H. BUCHBERG,Electric Analogue prediction of the thermal behaviour of an inhabitable enclosure, Trans. ASHVE, 61,339 (1955). 4. K. S. CHAr~, and K. R. RUSTON, The simulation of boundary conditions in heat conduction problems in a resistance capacitance electrical analogue, J. scient, lnstrum., 41, 535 (1964). 5. A. F. ROaERrSON, and DANIEL GROSS, An electrical analogue method for transient heat-flow analysis, J. Res. National Bureau of Standards, 61, 105 (August 58). 6. K. R. RAO, and M. G. DANGE, Studies on the thermal behaviour of a concrete roof panel by electrical analogue method, Indian Constr. News, Dec. 61-Jan. 62, 105. 7. K. R. RAt), and M. G. DANCE, Electrical analogue study on the periodic heat flow through a brick wall, IndianJ. Tech., 6, 5, 138 (1968). 8. K. R. RAO, and PRAKASH CHANDRA,Digital computer determination of thermal frequency response of building sections, Build. Sci., 1, 299 (1966). 9. O. C. MACKEY,and L. T. WRIGHT, Periodic heat flow-homogeneous walls and roofs, Trans, ASHVE, 49, 148 (1943). 10. K . R . RAO,S. P. JAIN and K. N. AGARWAL,Degree hour rating o f thermal performance of enclosures, Syrup. Environmental Phys. as Applied to Buildings in Tropics, C.B.R.L Roorkee, Feb. 25-27, (1969).
K. R. Rao and Prakash Chandra
Cet expos6 traite de l'6tude de la performance thermique de blocs creux de diffdrents types et prdparations de bdton par une m6thode analogique de rdseau R C ~ deux dimensions. On pr6sente les caract6ristiques thermiques statiques et p6riodiques de blocs creux solides et en b6ton, en mfime temps que celles de sections de murs solides et "~ cavit6 en brique. On a fait une 6valuation de la performance thermique de sections de mur creux en b6ton exposdes ~ un cycle de temp6ratures diurnes sol-air d'un 6t6 typique dans les situations conditionn6es et non conditionn6es. Les variations horaires des rdgimes d'6coulement de chaleur et des tempdratures de la surface interne des sections en blocs creux ont 6t6 compardes "fi celles des tours solides et i~ cavit6 en brique. Cette 6tude fait ressortir le fait que la conception tr6s r6pandue des blocs creux avec deux grands espaces a6r6s n'est pas thermiquement efficace dans les climats tropicaux. Leur performance thermique peut cependant fitre consid6rablement am61ior6e et rendue acceptable en adoptant une configuration comportant quatre espaces a6rds placds en deux rang6es. Diese Abhandlung besch/iftigt sich mit dem Studium des thermischen Benehmens von hohlen Betonblt~cken verschiedener Ausffihrung und Form mittels einer zweidimensionalen R-C Netzwerknachbildungsmethode. Es werden feste und periodische Thermaleigenschaften von massiven und hohlen Betonbl~Scken zusammen mit denen von massiven und Hohlziegelwand--Abschnitten gezeigt. Das W~irmebenehmen von Wandabschnitten aus hohlen Betonbl6cken, die einem typischen sommerlichen Tagesablauf in Bezug auf Sonne-Luft Temperatur ausgesetzt waren, wurde sowohl ffir bedingte wie natfirliche F/ille ausgewertet. Die stfindliche ~nderung der W/irmeflussgeschwindigkeiten und Temperatur der inneren Oberfl/iche der Hohlblock abschnitte wurden mit denen der massiven und Hohlziegelw/inde verglichen. Dieses Studium ergab die Tatsache, dass das allgemein benutzte Hohlblockmuster mit zwei grossen Luftrgumen im tropischen Klima wfirmem~issig nicht wirtschaftlich ist. lhre W~irmewirtschaftlichkeit kann allerdings durch Anwendung eines Entwurfs mit vier, in zwei Reihen angeordneten, Luftrfiumen erheblich verbessert und annehmbar gemacht werden.