Building and Environment 45 (2010) 727–738
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A new thermal performance index for dwelling roofs in the warm humid tropics Chitrarekha Kabre
*
Faculty of Architecture, Manipal Institute of Technology, Manipal University, Manipal, Karnataka 576104, India
a r t i c l e
i n f o
Article history: Received 28 May 2009 Received in revised form 18 August 2009 Accepted 19 August 2009 Keywords: Thermal performance index Thermal comfort Ceiling surface temperature Mean radiant temperature Dwelling roof Warm humid tropics
a b s t r a c t
This research aims to find a scientific rating scheme for roof system for the warm humid tropics. The overall air-to-air thermal transmittance ( U -value) -value) or thermal resistance ( R-value) of roof are most widely used properties, but these are based on steady-state heat conduction and do not respond to changing conditions of climate, design and comfort needs. The paper presents a new thermal performance index, which is based on thermal comfort and actual thermal performance of a roof design option. It provides a basis for identifying the optimum roof design for unconditioned and acclimatised regimes. A review of the acceptable limits of ceiling surface temperature is presented. The mathematical modelling for predicting performance of roof based on admittance procedure and derivation of thermal performance index is described. In the proposed scheme the galvanized iron roof is given 0% rating and the roof satisfying the comfort needs for the given climate is rated as 100%. Illustrative examples of built roofs or design options are taken from India and Australia. It clearly shows that the roofs with the highest thermal resistance are not necessarily optimum solutions. 2009 Elsevier Ltd. All rights reserved.
1. Introduction
In designing climate responsive accommodation for the warm humid areas, areas, wher where e ambient ambient air temperatur temperature e and relative relative humidity humidity are both above the desirable comfort level, the indoor conditions can be improved by keeping building open for natural ventilation, thus to outside conditions. As a result the outdoor and indoor air temperatures do not differ much. The primary function of building skin is to control the solar heat loads. It is necessary to shield any window windowss from from direc directt sun penetr penetrati ation, on, and to reduc reduce e the heat heat transm transmitt itted ed throug through h the sunlitwalls sunlitwalls and the roo roof. f. Theeast and west west walls receive a good deal of radiation, but when the angle of incidence dence is small (early morning morning and late afternoon) afternoon) the intensity intensity of radiation is not at its maximum. The north and south walls receive comparatively little radiation and are much easier to shield with overhang overhangs. s. The walls are easily shaded shaded by overhangin overhanging g eaves, eaves, verandas or verdant environment and therefore gradually acquire temperatures near to the air temperature. However, the roof is the most exposed to impacts of solar radiation, as it receives sunlight for practically the whole of the day, and in the tropics the angle of incidence is close to the normal in the hotter parts of the day. Heat gain through roof elevates ceiling surface temperature and causes radia radiant nt heat heat load load on the occupa occupants nts.. The term term ‘roo ‘roof’ f’ includ includes es the roo roof f structure, the outer covering, and layers of insulating materials or membranes and the ceiling. * Tel.: þ 91 820 2924111; fax: þ 91 820 2571071. E-mail address:
[email protected]
0360-1323/$ – see front matter 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2009.08.017
The The ques questio tion n aris arises es,, how how much much radi radian antt heat heat load load can can be permit permitte ted d withou withoutt harmfu harmfull effects effects on the life and work work of the inhabitants? The answer to this question is guided by two conflicting motives: to satisfy comfort needs of the people of the warm humid humid tropi tropics cs and to optim optimise ise the performa performance nce of the roof to provi provide de good good value value of the invest investmen ment. t. In oth other er wor words, ds, find a performance rating for roofs which is high enough to ensure progress and yet realistic enough to be generally attainable. In tropical climates steady-state property, the overall air-to-air thermal transmittance (U -value) -value) or thermal resistance (R-value), alone cannot cannot provide provide a satisfacto satisfactory ry performanc performance e criterion criterion for rating rating roofs since the thermal performance of a roof is a function of the sol-ai sol-airr temper temperatu ature re wave wave form form which which is a functi function on of climat climatic ic factors, factors, surface colour colour and orientatio orientation. n. A performa performance nce criterion criterion based based on the therma rmall comfo comfort rt and actual actual the therma rmall perfor performan mance ce of a roo roof f section would be appropriate. Identification of problem is presented in the next section with a field experiment in India and followed followed by discussion on the stateof-the-art. The sections following it explain derivation and mathematical modelling of the new thermal performance index and its application for exemplar roofs in India and Australia.
2. Problem Problem identificati identification on
All over the world indigenous and vernacular architecture are replete with appropriate built responses to climate which is also true in India. However, this would not be true in contemporary
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architecture with proliferation of modern technology, which resulted in using ubiquitous building techniques all over the country irrespective of the climate. A wide spectrum of eco-friendly and innovative building systems is being introduced in the housing sector as a consequence of environmental concern. The thermal performance in most of the cases remains undetermined due to lack of empirical evidence or inadequate computational tools. An experiment was conducted by the author to explore the present trends in house-building technology and identify the problem of designing roof for thermal comfort in warm humid zone [1]. For this study Trivandrum (lattitude 8 290 N) and Auroville (lattitude 12 N) were chosen because of the well known construction activities in the contemporary housing. The houses were selected based on the criteria that they were designed by architects and constructed using different conventional or alternative construction materials. The limited accessibility to the houseswas a constraint in the study and the number of samples is not sufficient to draw any statistical conclusion to recommend any design solutions. The experiment comprised of on spot measurement of relevant temperatures in the summer month of March 1998 between 13:30 and 18:00 h. At this time the weather was reasonably clear and the outdoor air temperature in shade varied from 31 to 33 C in Trivandrum and from 30 to 32 C in Auroville. Rooms selected for measurements were of similar area and ceiling height ranged from 2.5 to3.6 m. Since most of the houses were open for ventilation, the indoor and outdoor shade temperatures were observed as same. The internal surface temperatures of walls were also the same as indoor air temperature, but the ceiling surface temperature varied according to roof constructions. For sloping roofs, the side most exposed to sun was chosen for measurement. 2.1. Instrumentation
The instrument used in the study was Twin Input Digital Thermometer (Q1434) supplied by Dick Smith Electronics Pty Ltd. Australia. This instrument is a portable 3 digit, compact-sized digital thermometer using two external K-type thermocouples as temperature sensors. Temperature indication follows National Bureau of Standards and IEC 584 temperature/voltage tables for the two K-type thermocouples. 2.2. Analysis
This experiment reflects wide variations in thermal performance of houses and confirms that the roof played the dominant role because of diverse constructions. Fig. 1 shows the graph of measured air and ceiling surface temperature. The ‘ U ’ value was calculated by the author for all the roofs and is included in the legend to Fig. 1. In both places examples of good and poor roof designs could be observed; the ‘U ’ value ranged from 1.4 to 5.29 W/ m2 K and the excess ceiling temperature ranged from 0 to 15 K. Fig. 2 shows the construction details of some of the roofs studied. Since the roof insulation ranged from resistive to capacitive type the ‘U ’ value cannot provide a satisfactory basis for comparison. Two different types of construction (light, sample no. 6 or heavy, sample no. 33) have U values within the acceptable limit of 2.33 W/ m2 K, but would perform in different ways. In case of lightweight sheet roofs the ceiling temperature dropped by 14 K, from the worst to the best, with timber board ceiling and unventilated attic space, (sample no. 1 and 11 in Fig. 1). The simple Mangalore tile roof in a kindergarten in Auroville (sample no. 22 in Fig. 1) was extremely hot, but the similar roof with ceiling of particle board and timber (sample no. 23–24 and no. 6 in Fig. 1) improved performance three times. Another roof (sample no. 7–8 in Fig. 1) in Trivandrum, using traditional ‘‘fish’’
(fish-tail) clay tiles performedbetter because of overlapping of tiles. There are two or three layers at any cross section and due to low mass this roof cooled down by the evening. In case of heavy roofs, filler slab-Reinforced Concrete slab with clay tiles, (sample no.2–5,14,15,17 & 21in Fig.1) performed better than conventional Reinforced Concrete slab (sample no. 12 in Fig. 1). The reason for the same could be that it consists of air pockets in between tiles. This argument would not apply to the other filler slab using bricks, where light concrete was used as insulation. Conventionally Reinforced Concrete roof are insulated using lime concrete and flat clay tiles (sample no. 9 in Fig. 1). Shell roof construction like ferro cement channel (sample no. 27–28 in Fig. 1) and funicular shell (sample no. 16 in Fig. 1) are being used for economic reasons but without insulation does not perform very well, due to the thin skin. The temperature varied along curvature. White washing improved performance two and half times in case of Reinforced Concrete roofs (no. 18–19). Shading of the roof is one of the time-tested solutions. Two extreme types were noticed, one involved laying of tiles on the Reinforced Concrete roof and the other is construction of ‘insulated’ parasol roof. The examples of the first type are a layer of clay tile over 100 mm Reinforced Concrete roof with an air gap of 25 mm (sample no. 10 in Fig. 1) and three layers of country tiles (Spanish) on 75 mm Reinforced Concrete slab (sample no. 25–26 in Fig. 1). The parasol roof construction is an architects’ innovation using vermiculite concrete as insulation, (sample no. 36 in Fig. 1). Although many examples of parasol roofs exist in vernacular architecture using lightweight skins, the insulation is not necessary. Such a wasteful duplication resulted because the architects could not explain this fact to the client in the absence of quantitative data, since no tool was available to assess the performance of the unorthodox design alternative. 3. A review of comfort limits and overhead radiant heat
There are no physiological field tests available to determine the discomfort caused due to the radiant heat from roofs in the warm humid tropics. However, there are a number of systematic studies based on laboratory experiments, which investigated discomfort caused from heated ceiling panels (used for room heating in cold climates). Munro and Chrenko [2] and Chrenko [3] found that the elevation of the mean radiant temperature at head level due to the radiation overhead was the best parameter for indicating the subjective response of those investigated. All experiments took place at constant air temperature, which means that the operative temperature was increased when the ceiling temperature was increased. The operative temperature is defined as the uniform temperature of an enclosure in which an occupant would exchange the same amount of heat by radiation plus convection as in the existing non-uniform environment. In the studies by McNall and Biddison [4] and by Griffiths and McIntyre [5] the increased temperature of the heated ceiling was balanced by a decrement of the wall temperature to maintain constant operative temperature. Fanger et al. [6] argued that this is not realistic, since in practice the air temperature is usually decreased to balance the increased ceiling temperature. Furthermore, since the subjects were tested in groups, all of them were not necessarily thermally neutral. Thermal neutrality for a person is defined as a condition in which he or she prefers neither a higher nor a lower ambient temperature level. Thermal neutrality is a necessary condition for a person to attain thermal comfort. It is a further requirement that no local warm or cool discomfort is experienced on any part of the body. Overhead radiation for a heated ceiling can create such local discomfort: either warm
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Fig. 1. Spot measurements of ceiling and indoor air temperature in contemporary dwellings in Trivandrum and Auroville (India) – March 1998. (All dimensions in mm), ( U value in W/m2 K).
No.
Roof type
U
No.
Roof type
U
1. 2.
Red Mud Polymer (RMP) 100 Filler slab þ 12 cement render outside
4.98 3.94
19. 20.
3.62 2.59
3. 4. 5.
100 Filler slab þ 12 cement render both sides 100 Filler slab þ 12 cement render both sides 100 Filler slab þ 12 cement render both sides
3.94 3.94 3.94
21. 22. 23.
6.
Mangalore tile on wooden rafter þ Anjali wood ceiling 10 Fish clay tile (2 layers) on wooden rafters
1.83
24.
4.88
25.
4.88 3.07
26. 27.
Same as no. 18, whitewash 100 Reinforced Concrete þ 75 lime concrete (brick bats) þ 20 clay tile 100 Filler slab. 25 external & 12 internal cement render 15 Mangalore tiles þ Reinforced Concrete rafters 15 Mangalore tiles þ 18 particle board ceiling þ Reinforced Concrete rafters 15 Mangalore tiles þ Reinforced Concrete rafters þ 18 particle board ceiling 10 Country clay tiles (3 layers) on 10 thick wooden slab on 75 rafters 10 Country clay tile (3 layers) on 70 Reinforced Concrete slab 25 Ferrocement channel
1.96
28.
1.49
29.
7. 8. 9.
3.62
30.
13.
Same as no. 7 100 Reinforced Concrete þ 50 lime concrete (brick bats) þ 20 clay tile 100 Reinforced Concrete þ 12 cement render þ 25 air gap þ Mangalore tile Aluminium sheet (26 gauge) þ 600 Air cavity þ 20 Anjali wood ceiling 100 Reinforced Concrete slab þ 12 cement render on both sides !00 Filler slab þ 12 cement render outside
3.86
31.
14.
100 Filler slab þ 12 cement render both sides
3.63
32.
15.
100 Filler slab þ 12 cement render both sides
3.63
33.
16.
2.45
34.
17.
Funicular shell þ 100 lime concrete þ 50 gravel concrete þ 12 cement render 100 Filler slab þ 12 cement render outside
3.86
35.
18.
100 Reinforced Concrete þ 12 cement render on both sides
3.62
36.
10. 11. 12.
25 Ferrocement channel þ 75 lime concrete (brick bats) þ 30 cement screed 25 Stone slab on Reinforced Concrete joist þ hot bitumen þ 50 vermiculite þ 25 cement screed þ ceramic tile 25 Clay tile þ 125 cement vermiculite(1:6) þ 50 Reinforced Concrete þ 50 brick jelly þ broken ceramic tiles, no shade 25 Ferrocement channels þ 75 lime concrete (brick bats) þ 30 cement screed with glazed tiles 25 Ferrocement channel þ 75 lime concrete (brick bats) þ 30 cement screed with broken ceramic tiles 120 Filler slab (brick) þ 50 expanded vermiculite þ 30 cement screed with ceramic tiles 50 Reinforced Concrete þ 15 lime concrete (brick bats) þ 25 mortar þ 15 terra-cotta tiles 25 Clay tile þ 125 cement vermiculite(1:6) þ 50 Reinforced Concrete þ 50 lime concrete (brick bats) þ broken ceramic tiles Same as no. 30, shaded
3.42 5.29 1.69 1.69 3.94 3.79 3.86 2.56 1.87 1.40 2.55 2.55 1.62 3.51 1.40 1.40
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Fig. 2. Construction details of some of the sample roofs selected for spot measurements in Trivandrum and Auroville (India).
discomfort at head or cold discomfort at the feet (or both). They conducted experiments to find the limits of overhead radiation to which person in thermal neutrality can be exposed without feeling discomfort at any part of the body. This simulates many cases in practice where people modify their clothing to keep them thermally neutral. In these experiments the air and wall temperature (rather than just the wall temperature) were lowered to keep the subjects neutral when exposed to overhead radiation. They suggested two parameters for practical use: the ceiling temperature
and the radiant asymmetry. The radiant asymmetry is defined as the difference in radiant temperatures seen by a small flat element looking in opposite directions. This study suggested that five percent feeling uncomfortable corresponds to a radiant temperature asymmetry of 4 K which agrees well with the limit suggested by Chrenko (‘‘elevated mean radiant temperature’’ ¼ 2.2 K) although he predicted more than 20% feeling uncomfortable at his limit. Fig. 3 gives the allowable ceiling temperature as a function of the angle factor to the ceiling [7].
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thermal perforamnce index (TPI) is ranked on a scale of A (good) to E (extremely poor). The thermal performance index (TPI) is calculated for a typical summer design day in a hot dry climate (Roorkee, India) with surface absorption coefficient (0.7) based on the unsteady state harmonic method [11]. The thermal performance index (TPI) values for typical roof sections are included in the Bureau of Indian Standards [12]. A number of correction factors are provided to convert thermal performance index (TPI) values for different climatic zones. However, thermal performance index (TPI) do not account for the variations in comfort needs and thermal performance of roof in different climates. A good performance for hot dry climate would be different from the one for warm humid. A good performance for Indian subjects would be different from the one for Australian subjects accounting for acclimatisation factor. 4. Methodology 4.1. Comfort limits
Auliciems [13] formulated an adaptive, (psycho-physiological), an empirical model of thermal perception. This model relates people’s vote to some measurable environmental factors. Auliciems reported the strong correlations between thermal neutrality and mean monthly outdoor DBT and expressed by the equation of the regression of neutrality, t n, upon the mean monthly outdoor temperature, t m as follows:
t n ¼ 17:6 þ 0:31$t m
(1)
Auliciems states that it is possible to determine neutralities for all parts of the world within the range 17–31 C. A study by Nicol and Roaf [14] in Pakistan, the regression equation was found to be, Fig. 3. The allowable temperature of a heated ceiling above air temperature as a function of angle factor. Source: Fanger et al. [6], Fig. 9, p.155.
Conditions under a roof heated by the sun are sufficiently similar to those under heated panels to justify the use of the same parameters for rating thermal performance of roofs: the ceiling temperature and the mean radiant temperature. However, the acceptable limits defined for temperate and cold climates, in the above mentioned studies, would need to be redefined for tropical climates since the inhabitants of temperate or cold climates are used to welcome radiation from open fires and other heating appliances and are less likely to feel discomfort from radiation than the people in tropical climates where radiant heat from roof is dominant problem. Koenigsberger and Lynn [8] referred to Chrenko’s study, but they prescribed that the ceiling temperature should not rise more than 4.45 K above the air temperature, this would correspond to 0.723 K elevation of the mean radiant temperature which in turn allows 0.556 K increase in CET (Corrected Effective Temperature) in the assumed room. They used a steady-state method to calculate ceiling temperatures with certain assumptions to choose from different roofing materials. The Corrected (Normal) Effective Temperature takes into account the temperature, humidity, and rate of movement of the air as well as radiation from solid surroundings. It is equal to the ‘temperature of still air, saturated with watervapour, in which an equivalent sensation of warmth was experienced by subjects in a long series of tests,’ [9]. Chandra [10] described thermal performance index (TPI) of walls and roofs section, derived from inside surface temperature and peak heat gain for unconditioned and conditioned buildings respectively. A rating of 100 thermal performance index (TPI) of roof corresponds to 38 C peak inside surface temperature in an unconditioned environment taking base temperature as 30 C. The
t n ¼ 17:0 þ 0:38$t m
(2)
An ASHRAE sponsored study on adaptive models compiled an extensive database from past field studies to study, develop, and test adaptive models, [15]. Theadaptive models are useful to specify building temperatures set points throughout the year. In general, the value of using an adaptive model to specify set points or guide temperature control strategies is likely to increase with the freedom that occupants are given to adapt (e.g. by having flexible working hours, locations, or dress codes). For the purpose of this study the expressions given by Auliciems and Nicol and Roaf will be used for Australia and India respectively. The thermal neutrality is used as a threshold to calculate the potential overheating that can be caused by a given roof. Although there are different opinions about the lowest and highest limits of neutrality, for the purpose of this study the neutrality limits given by Auliciems are accepted as: 18 < t n < 28 C. The width of the comfort zone is taken 4 K for unconditioned environment. 4.2. Mathematical modelling of thermal performance of roof
Climatic data as gathered at airports and meteorological stations are usually published as averages of various data recorded over several years. This research is primarily be concerned about the early design stages when designer may usually refer to monthly mean values which are readily available to every user. Therefore, monthly mean values will be used and the hourly values will be generated based on standard algorithm [7]. Thermal performance of roof is a function of thermo-physical properties of roof materials and outdoor and indoor environmental conditions. In the ‘harmonic’ solution the transient conduction equations are solved analytically in building thermal energy calculation with a periodic temperature boundary condition on one
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side of the slab and a constant temperature boundary condition on other side. This approach gives the temperature or energy pattern for a building assuming it has reached the stable, or equilibrium, state for some given cycle of weather and usage. The ‘‘admittance’’ procedure, developed by Danter [16] and adopted by the Institution of Heating and Ventilating Engineers (IHVE) [17] is typical of this type of solution. It is a comprehensive procedure and as described there (without the complications of harmonics other than that of period 24 h and with only reference to time lag). In order to predict the heat transmitted through a roof and consequently its effect on indoor comfort; it is necessary to find the following parameters: Sol-air temperature Ceiling temperature Mean radiant temperature and shape factor
e$DI l ¼ 95 ð95 15Þ m=8
Fig. 4 shows a comprehensive picture of the variables involved in predicting the performance of a roof and their interaction. 4.2.1. Sol-air temperature (tsa) Sol-air temperature was first introduced by Mackey and Wright [18] and later modified by several researchers. A precise definition of sol-air temperature is ‘‘the equivalent outdoor temperature that will cause the same rate of heat flow at the surface and the same temperature distribution through the material, as results from the outdoor air temperature and the net radiation exchange between the surface and its environment’’, [19]. The sol-air temperature is given as
t sa ¼ t oa þ
1 I g $a e$DI l f o
emittance surfaces such as polished metals. DI l ¼ net long wave radiation exchange between a black body at outside air temperature and the outside environment (W/m2). The term ( t sa t oa) is often referred to as ‘‘sol-air excess’’ temperature, especially in British literature. Although there is an abundant literature on precise computation of the term DI l, the degree of accuracy depends on the availability of data on sky cover and other atmospheric factors. A reasonable approximation was proposed by Loudon [20] at Building Research Station. For a horizontal surface, e$DI l may be taken as 95 W/m2 for a cloudless sky, 15 for an overcast sky, and intermediate values proportional to the cloud amount for partially clouded skies. Therefore,
(3)
where, t sa ¼ Sol-air temperature C, t oa ¼ Outdoor air temperature C, I ¼ Total solar radiation (direct þ diffuse) incident on the g surface (W/m2), a ¼ Absorptance of the material for short wave or solar radiation, f o ¼ Outside film or surface conductance (W/m2 K), e ¼ emittance of surface, for low temperature radiation usually taken as 0.9 for most building surfaces, but only 0.05–0.2 for low
(4)
m ¼ cloud cover in oktas, m ranges from 0 to 8, m ¼ 0 denotes clear sky; m ¼ 8 denotes completely overcast sky. Using this equation, the long wave component of sol-air temperature ranged from 1.65 to 4.24 C for Trivandrum. This is comparable to the recommended value of 3.9 C by ASHRAE [7] ch. 28, p. 28.5, if seasonal variation in cloud cover is accounted. 4.2.2. Ceiling surface temperature (tc ) The ‘‘admittance procedure’’ of the UK Building Research Establishment is based on the calculation of the 24-h mean heat flow through an element,
(5)
Q ¼ A$U $ðt sa t ai Þ
(where, t sa is the 24-h mean sol-air temperature of the outside surface and t ai , the indoor temperature, is taken as constant), followed by the calculation of the deviation from this mean foreach hour q,
~ ¼ A$U m t saðqfÞ t sa Q
(6)
where, A ¼ area(m2), U ¼ air-to-air thermaltransmittance ¼ 1=RT (W/
Fig. 4. Scheme to illustrate the flow of information needed to predict the performance of roof when subjected to sinusoidal excitation.
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Fig. 5. Flat and pitched rectangular roof and centre of a room.
m2 K), R T ¼ total thermal resistance (m2 K/W), m ¼ decrement factor (non-dimensional), f ¼ time lag (h), t ai ¼ 24 h average inside air temperature ( C), t sa ¼ 24 h average of sol-air temperature ( C), t saðqfÞ ¼ sol-air temperature of surface, hours before ( C). The expression for inside surface temperature of a roof section can be derived from the equations of internal heat flow Q c at the inside surface of a wall at time q (in W/m2), [21,22].
h
Q c ¼ U ðt sa t ai Þ þ m t sðqfÞ t sa
i
(7)
The ceiling surface temperature can be found from,
(8)
Q c ¼ hc ðt c t ai Þ þ hr 3ðt c t sur Þ
where, hc ¼ convective coefficient, hr ¼ radiation coefficient, e; ¼ emittance, t ai ¼ inside air temperature at time q, t c ¼ ceiling surface temperature at time q, t sur ¼ average temperature of inside surface seen by roof, f ¼ time lag.
Rsi
T 4mrt ¼ T 14 $F p1 þ T 24 $F p2 þ / þ T N4 $F pN
If the average inside surface temperature of all surfaces excluding roof is
(9)
t sur ¼ t ai
(13)
where, T mrt ¼ absolute mean radiant temperature, K, T N ¼ absolute temperature of surface N, K, F pN ¼ angle factor between a person and surface N. As the sum of the angle factors is unity, the fourth power of mean radiant temperature equals the mean value of the surrounding surface temperatures to the fourth power, weighted by the respective angle factors. The angle factor normally depends on the position and orientation of the person. The relationship between MRT and shape factor is mathematically defined and illustrated in the American National Standard [23]. In a warm humid climate when windows are opened for ventilation it can be assumed that the surface temperatures of walls and floor is the same as the indoor air temperature and only the ceiling temperature is elevated due to solar radiation, then the equation (13) can be simplified as 4 ð1 F c Þ T 4mrt ¼ T c4 F c þ T ai
1 ¼ m2 K=W hc þ ehr
(14)
where, T c ¼ absolute surface temperature of ceiling, K, T ai ¼ absolute indoor air temperature, K, F c ¼ angle factor between a person and ceiling. The shape factor can be defined in terms of the solid angle subtended by the roof. The solid angle at point O is the sum of the
Substituting this in equation (8) we get,
Q c ¼ hc ðt c t ai Þ þ hr eðt c t ai Þ
(10)
from which,
t c ¼ t ai þ
Q c ¼ t ai þ Q c $Rsi ðhc þ ehr Þ
(11)
substituting the Q c from equation (7) the ceiling surface temperature can be calculated as follow,
h
t c ¼ t ai þ U $Rsi ðt sa t ai Þ þ m$ t saðqfÞ t sa
i
(12)
4.2.3. Mean radiant temperature (tmrt ) and shape factor ( Fc ) Mean radiant temperature is the uniform temperature of an imaginary enclosure in which radiant heat transfer from the human body equals the radiant heat transfer in the actual non-uniform enclosure. Measurement of the globe temperature, air temperature, and the air velocity can be combined to estimate the mean radiant temperature. The mean radiant temperature can also be calculated from measured values of the temperature of surrounding walls and surfaces and their position with respect to the person. As most building surfaces have a high emittance e, all the surfaces in the room can be assumed to be black [7] (ch. 8, p. 8.10). The following equation is then used:
Fig. 6. Ceiling surface temperature of flat GI (galvanized iron) roof in Trivandrum (India) and Cairns (Australia).
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F c ¼
U 4p
(17)
4.3. The new thermal performance index (TPI *)
It has beenshown thatthermal sensationwithin buildingsdepends not only on air temperature, but it is also strongly influenced by the surrounding surface temperatures. This can be measured by the MRT (mean radiant temperature): a solid-angle weighted mean temperature of thesesurfaces.The conceptof environmentaltemperature (t env) was proposed by theUK Building Research Station in themid-60s[20], and later adopted by CIBSE [24], it is defined mathematically as,
t env ¼
2 1 t mrt þ t ai 3 3
(18)
where, t mrt ¼ Mean radiant temperature, t ai ¼ Indoor air temperature. The effect of MRT (mean radiant temperature) depends on clothing. In warm climates (with light clothing) it is about twice as significant as the Dry Bulb Temperature which gave rise to the environmental temperature [25]. However, in cooler climates (people with heavier clothing) it has about the same influence as the Dry Bulb Temperature, hence the dry resultant temperature.
t drt ¼ Fig. 7. Acceptable ceiling surface temperature for two places Trivandrum (India) and Cairns (Australia).
four angles subtended by the four rectangles AEPG, DFPG, CFPH, and BEPH. According to Chrenko [3] (pp. 377–378) the solid angle U in steradians at O is given by the formula,
ac bc bd ad U ¼ tan1 þ tan1 þ tan1 þ tan1 Zp1 Zp2 Zp3 Zp4
(15)
where, Z ¼ the distance from O to P, a ¼ AG ¼ BH, b ¼ GD ¼ HC, c ¼ EB ¼ FC, d ¼ AE ¼ DF, p1, p2 , p3 , and p4 are the distance from O to the four corners of the ceiling, Fig. 5, p 1 ¼ OB, p 2 ¼ OC, p 3 ¼ OD, p4 ¼ OA. For P in the centre of the ceiling the expression becomes:
ac U ¼ 4 tan1 Zp
(16)
The shape factor can be expressed as a ratio of the 4 p steradians,
1 1 t mrt þ t ai 2 2
(19)
For tropical climates the environmental temperature can be adopted to assess the indoor conditions. According to current adaptability theory thermal comfort is a function of monthly mean air temperature. In practice people would try to attain thermal neutrality by modifying clothing, air movement, etc. Therefore, similar to Fanger’s experiments, to ensure thermal comfort the environmental temperature should be within the upper and lower limits of thermal neutrality and if air temperature is taken to be at mean, the equation (18) becomes,
t env ¼
2 1 t mrt þ t m 3 3
(20)
By substituting the required comfortable environmental temperature the allowable increase in the mean radiant temperature can be found, equation (21),
t mrt ¼
t env 3 t m 2
(21)
Then the acceptable ceiling surface temperature (t cm in ) for a given shape factor (F c) can be found from the expression,
Table 1 Analysis of acceptable ceiling temperature for two locations, Trivandrum (India) and Cairns (Australia).
Trivandrum (India) Latitude 8.5 N Two hottest months Temperature, maximum ( C) Temperature, minimum ( C) Temperature, mean ( C) Thermal neutrality ( C) Upper limit of thermal neutrality ( C) Acceptable mean radiant temperature ( C) Acceptable ceiling temperature ( C) Peak sol-air temperature Excess of ceiling temperature over mean air temperature (K) Excess of peak sol-air temperature over mean air temperature (K) Average acceptable excess of ceiling temperature (K) over mean air temperature Average maximum Excess of ceiling temp. (K) over mean air temperature
March 32.50 24.20 28.35 27.77 29.77 30.48 38.48 54.8 10.13 26.45 9.0 25.0
Cairns (Australia) Latitude 16.9 S April 32.40 25.10 28.80 27.93 29.93 30.51 37.17 52.93 8.42 24.18
January 30.50 24.00 27.30 26.00 28.00 28.45 33.02 49.60 5.77 22.35 6.0 22.0
February 30.20 24.00 27.10 26.00 28.00 28.45 33.60 48.80 6.50 21.70
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Fig. 8. Thermal performance of pitched (30 ) roofs (light and heavy construction), Trivandrum, India. Note: Absorptivity
4 T 4mrt ¼ T c4 $F c þ T m ð1 F c Þ
(22)
The rise of ceiling temperature above the air temperature causes the elevation of mean radiant temperature. Consequently, the temperature difference between the ceiling and air temperature can be taken as the criterion to assess the performance of a roof. The acceptable elevation of ceiling temperature (Dt cm in ) above the mean air temperature can be given as,
Dt c min ¼ t cm in t m
(23)
Similarly the maximum elevation of ceiling temperature (Dt cm ax ) that can occur for a GI (galvanised iron) roof, ‘‘everyone’s benchmark for the worst roof,’’ in a given climate. However, the ceiling surface temperature of GI (galvanised iron) roof nearly same as solair temperature, Fig. 6. The peak sol-air temperature will be used.
Dt cmax ¼ t cmax t m ¼ t samax t m
(24)
From these two expressions the performance of a given roof can be rated. For the hottest month find the peak ceiling surface temperature for a given roof andthe elevation (Dt c) above the mean
¼
0.7, all dimensions in mm. ‘Dec. fact’ is Decrement Factor.
air temperature. The new thermal performance index (TPI*) of the given roof can be given as, *
TPI ¼
Dt cmax Dt c 100 Dt cmax Dt cmin
(25)
This new index would indicate in percentage terms how much performance is achieved on a scale with the range of acceptable elevation and the worst elevation for a given roof in a particular climate. The acceptable elevation of ceiling temperature (Dt cm in ) above the mean air temperature depends on the mean air temperature, thermal neutrality, the dimension of the roof or room, the position of the occupant (or height of the environmental point), the surface temperature of walls and floor. 5. Results and analysis
The methodology is demonstrated for two locations Trivandrum (India) and Cairns (Australia). The acceptable ceiling surface temperatures are calculated for two hottest months setting the environmental temperature to the upper thermal neutrality limit,
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Fig. 9. Thermal performance of pitched (25 ) tile roofs (light construction) Cairns, Australia. Note: Attic space is ventilated, absorptivity Decrement Factor.
when there is very little air movement. These calculations are performed for eight shape factors ranging from 0.17 to 0.24 and averages are calculated. The shape factors are calculated for a point located at a distance for 1.2,1.35 and 1.5 m from square roof of sides 3.0, 3.3 and 3.6 m, most likely to be in the living space of a house. Fig. 7 shows acceptable ceiling temperature for these two locations. Table 1 presents the analysis of acceptable ceiling temperature in these two locations. From this analysis it can be observed that the acceptable rise in mean radiant temperature (t mrt) above mean air temperature in these locations ranged from 0.25 to 1.92 K. The average acceptable ceiling temperature for Trivandrum is 37.8 C and for Cairns is 33.3 C, this is due to not only the difference in the climate but also because of the different expressions used for thermal neutrality. Consequently, the acceptable rise in ceiling temperature above mean air temperature (Dt cmin ) for Trivandrum is 9 K and for Cairns is 6 K. Thus performance rating of same roof in two different locations will be different. If the peak ceiling
¼
0.7, all dimensions in mm. ‘Dec. fact’ is
temperature is 37 C and mean air temperature is 27 C (the difference between two is 10 K), the index is calculated from equation (24) as follows,
TPI ðTrivandrumÞ ¼ TPI ðCairnsÞ ¼
25 10 100 ¼ 93:75% 25 9
22 10 100 ¼ 75% 22 6
With high air speed in humid climate the comfort temperature would be three or four degrees above still air value [26]. Consequently, air movement due to a fan could be accounted by raising the upper limit thermal neutrality to 3 K. At terrestrial temperature the emissivity of internal surfaces of the room would be practically not less than 90% [27]. The radiant exchange within an enclosure with surfaces of high emissivity is practically the same as if all surfaces were thermally black owing to the rapid damping out of
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reflected energy [3] p. 378. Consequently, colour of internal surfaces need not be accounted in the calculations. The new thermal performance index (TPI*) is calculated for a number of roofs common in India and Australia [28]. Thermal performance of ten examples is presented, case no. 1–5 in Trivandrum (India), Fig. 8 and case no. 6–10 in Cairns (Australia), Fig. 9. First sinusoidal characteristic of a given roof section is determined and then the sinusoidal temperature response is calculated, from which the new thermal performance index (TPI*) is estimated. The new thermal performance index (TPI*) of tile roof in Trivandrum is improved from 0% to 110.18% by simply adding timber ceiling with ventilated attic space (case 2). While as the new thermal performance index (TPI*) of concrete roof is improved from 54.06% to 116.75% by adding tiles over the roof to shade (case 5). Fig. 9 illustrates some of the tile roofs (light construction) in Australian houses. Tile roof with attic space and ceiling board provides better performance when treated with different insulation (resistive and or reflective). The new thermal performance index (TPI*) of tile roof with reflective attic space is 108.75% (case 8) and an addition of bulk insulation of 2R improves it to 112.7% (case 10). Here it is relevant to mention that the surface of opaque roofing material has three properties determining behaviour with respect to radiant heat exchange, namely its absorptivity, reflectivity and emissivity. Radiation impinging on roof surface may be absorbed or reflected, being fully absorbed by a perfectly black surface and fully reflected by a perfect reflector. The emissivity is the relative power of a material to emit radiant energy. For any specific wavelength, absorptivity and emissivity are numerically equal, but both may vary for different wavelengths. The magnitude of sol-air temperature is influenced by factors within the designer’s control: absorbance and surface air conductance (see equation (3)). The absorptivity decreases and the reflectivity increases with the lightness of colour. But colour does not indicate the behaviour of a surface with respect to longer wave radiation. Black and white paints have different absorptivities for solar radiation and a black surface becomes much more heated on exposure to the sun. But the long wave emissivities of the two colours are equal.
Whitewash surface ¼ absorptivity of 0 :1 0:3 for shortwave radiation ¼ emissivity of 0 :95 for longwave lengths This is a good radiator, readily losing heat to colder surfaces, and at the same time is a good reflector for solar radiation.
6. Conclusions and further development
Building component properties may be interpreted as ‘‘lowlevel’’ performance indicators, whereas room performance descriptions may be interpreted as ‘‘high-level’’ behavioural properties [29]. Thermo-physical properties (for example U value, shading coefficient) may be defined as attributes of discrete components whereas energy performance (for example environmental temperature, heat gain or loss) may refer to room properties. Furthermore, simple and ‘user-friendly’ indices may be derived on the basis of these properties to encourage energy efficient design, for instance five star energy efficiency ratings for windows and dwellings. Although the new thermal performance index (TPI*) is developed for specific conditions prevalent in the warm humid tropics in unconditioned and acclimatised environment. The new thermal performance index (TPI*) is potentially applicable to any complex
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situation. The future development of the the new thermal performance index (TPI*) is planned along the following lines: Integrate other parameters: change in ventilation rate, colour, cloud cover, diffuse radiation etc. and perform a parametric study. Widen the scope of application to other climatic regimes and conditioned environment. Validate the calculation results with the simulation software such as Autodesk Ecotect (rc2) 5.6 and with field experimentation.
Acknowledgements
The author would like to thankfully acknowledge the financial assistance of AusAID (Australian Agency for International Development) for this research as part of her PhD course in the University of Queensland. She also thankfully acknowledges Dr. Richard Hyde, Professor, Faculty of Architecture, Design and Planning, University of Sydney and Dr. S. V. Szokolay, Honorary reader, Department of Architecture, University of Queensland for their supervision in this research. Finally special thanks must be given to Mr. Tapan Kumar Ghoshal, a mechanical engineer for his extensive support in this research. References [1] Kabre C. Contemporary roofs in the warm-humid tropics of India. In: Proceeding of the 16th International Passive and Low Energy Architecture (PLEA) conference, Brisbane, PLEA International in assoc. with the Dept of Architecture, the Univ. of Queensland, Brisbane; 1999. p. 387–392. [2] Munro AF, Chrenko FA. The effect of radiation from the surroundings on subjective impressions of freshness. Journal of Hygiene 1949;47:288–96. [3] Chrenko FA. Heated ceilings and comfort. Journal of Heating and Ventilating Engineers 1953;20(209):375–96. [4] McNall Jr PE, Biddison RE. Thermal and comfort sensations of sedentary persons exposed to asymmetric radiant fields. ASHRAE Transactions 1970;76(1):123. [5] Griffiths IS, McIntyre DA. Subjective response to overhead thermal radiation. Human Factors 1974;16(3):415–22. [6] Fanger PO, Banhidi L, Olesen BW, Langkilde G. Comfort limits for heated ceilings. ASHRAE Transactions 1980;86:141–56. [7] ASHRAE. Fundamentals handbook (SI). New York: American Society of Heating, Refrigerating and Air-Conditioning Engineers; 2001. [8] Koenigsberger O, Lynn R. Roofs in warm and humid tropics. Paper Architectural Association, no. 1. London: Lund Humphries for the Architectural Association; 1965. [9] Bedford T. Environmental warmth and its measurement. M.R.C. War Memorandum. London: HMSO; 1940 (17). [10] Chandra P. Rating of wall and roof sections – thermal considerations. Building and Environment 1980;15:245–55. [11] Suman BM, Saxena BK. Role of roof treatment in thermal design of buildings. Architectural Science Review 1992;35:111–4. [12] BIS. Handbook of functional requirements of buildings (other than industrial building) SP:41(S&T). New Delhi: Bureau of Indian Standard; 1987. [13] Auliciems A. Psycho-physiological criteria for global thermal zones of building design. International Journal of Biometeorology 1982;26(Suppl.):69–86. [14] Nicol F, Roaf S. Pioneering new indoor temperature standards. Energy and Buildings 1996;23:169–74. [15] de Dear R, Brager G, Cooper D. Developing an adaptive model of thermal comfort and preference, final report ASHRAE RP-884. Sydney: Macquarie Research Ltd. Macquarie University. Available from: http://aws.mq.edu.au/rp884/ashrae_rp884_home.html ; 1997. [16] Danter E. Periodic heat flow characteristics of simple walls and roofs. Journal of Heating and Ventilating Engineers 1960 July:136–46. [17] IHVE guide book A. London: Institution of Heating and Ventilating Engineers; 1970. [18] Mackey CO, Wright LT. Summer comfort factors as influenced by the thermal properties of building materials. ASHVE Transactions Heating, Piping & AC Section 1943;49:148–74. [19] Rao KR, Ballantyne ER. Some investigation on the sol-air temperature concept, no. 27. Melbourne: Division of Building Research Technical Paper; 1970. [20] Loudon AG. Summertime temperatures in buildings. Garston Watford; 1968. [21] Szokolay SV. Personal note, 17 October 1997. [22] Szokolay SV. Personal note, 20 May 1999.
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[23] ANSI/ASHRAE 55. Thermal environmental conditions for human occupancy, ASHRAE Standard an American National Standard. American Society of Heating, Refrigerating and Air-Conditioning Engineers Inc.; 1992. [24] CIBSE. Section A5: thermal response of buildings. In: CIBSE guide A: design data. 4th ed. London: The Chartered Institution of Building Services; 1979. [25] Szokolay SV. Introduction to architectural science: the basis of sustainable design. Oxford: Architectural Press, Elsevier; 2008. p. 18. [26] Nicol F. Climate and thermal comfort in India. In: Krishan A, Baker N, Yannas S, Szokolay SV, editors. Climate responsive architecture: a design handbook for energy efficient buildings. New Delhi: Tata McGraw-Hill Publishing Company Limited; 2001. p. 66. ch. 3.
[27] Koenigsberger OH, Ingersoll TG, Mayhew A, Szokolay SV. Manual of tropical housing and building, Part one: climatic design. 3rd ed. , London: Longman Group Ltd; 1974. p. 73. [28] Kabre C. Computer aided design of climate responsive dwelling (roofs) in the climatic and technological context of India and Australia. Ph.D. thesis, Department of Architecture, University of Queensland, Brisbane, Australia, 2000. [29] Mahdavi A. ‘‘Open’’ simulation environments: a ‘‘preference-based’’ approach. In: Proceedings of the 5th International Conference on Computer Aided Architectural Design Futures 93, North-Holland. US: CMU; 1993. p. 195–214.
