Heat exchange in the surface of lightweight steel roof coatings/Silumos mainai plieniniu vedinamu stogu dangu pavirsiuose.
Banionis, Karolis ; Stankevicius, Vytautas ; Monstvilas, Edmundas 等
1. Introduction
In the continental or colder climate regions, technical and thermal
solutions of lightweight ventilated roofs are based on heat saving
during the cold period of the year. During the process of roof design,
the heat exchange processes which take place during the summer period
are not considered. In summer the problem of overheated premises under
the lightweight ventilated steel roofs is encountered: sun radiation
heats the surfaces of the buildings and for this reason, the indoor
temperature increases (Seduikyte and Paukstys 2008). Moreover, the
surface temperatures of the buildings can easily reach 75-80[degrees]C
(Lee et al. 2009). In summer steel roof coatings heat due to the
intensive solar radiation and this causes additional heat gains in the
premises. The calculation of values of the heat gains requires the
following:
a) to estimate the temperature of the roof coating, i.e. to
evaluate the heat exchange among the exterior, roof coating and
ventilated air gap;
b) to estimate the temperature of the ventilated air gap, i.e. to
evaluate the heat exchange among the roof coating, ventilated air gap
and roof construction, which is situated between the ventilated air gap
and premises;
c) to estimate the thermal behavior of the roof construction,
situated between the ventilated air gap and premises, and the
temperature differences between the ventilated air gap and premises,
i.e. to evaluate the heat exchange between the ventilated air gap and
premises through the roof construction.
Normally, the calculations of rated thermal parameters are carried
out using the interior and exterior air temperatures. Heat flow values
of lightweight ventilated steel roofs are determined by the temperature
differences between the premises and ventilated air gap of the roof, but
not by the temperature differences between the premises and exterior
air. The temperature of the ventilated air gap of the roof is influenced
by the temperature of steel roof coating. The coating has a low thermal
receptivity, thus its temperature quickly reacts to the solar radiation,
long-wave radiation from the sky and other climatic impacts. Daily
variation of climatic impacts causes significant changes in the
temperature of the steel roof coating. Therefore, thermal analysis of
the roof is often time dependent since the external climate temperature,
wind speed and solar radiation vary with time (Al-Sanea 2002).
Similarly, the temperature distribution inside the multilayer
lightweight partitions is effected not only by the temperature
differences of both surfaces of the partition, but also by the direct
solar radiation onto the external surface (Kairys et al. 2006).
Primary comparative calculations of steel and tiling roof coating
parameters indicated that thermal diffusivity of steel coating is
approximately 140 x [10.sup.-7] [m.sup.2]/s and of tilling coating
approximately 6 x [10.sup.-7] [m.sup.2]/s, i.e. thermal diffusivity of
the steel roof coating is 23 times higher than that of the tiling
coating. Raising the steel coating temperature of 1 [m.sup.2] by one
degree requires approximately 16 times less energy than the tiling
coating. The calculation method of unsteady heat exchange employs the
parameter of maximum time step (Barkauskas and Stankevicius 2000). It
indicates the amount of time needed for the heat exchange between the
analyzed surfaces to become steady. In the case of the steel roof
coating of 0.5 mm thickness, the allowable time step is approximately
0.009 seconds, whereas for tiling it is 0.2 seconds; thus, in tiling
layer, the heat exchange becomes steady approximately 22 times slower.
The results of the presented comparative calculations enable to make a
presumption that the ventilated steel roof coating instantly reacts to
the thermal effects of climate due to the rapid heat exchange processes.
Apart from the exterior air temperature, the temperature of roof
coating is influenced by the short-wave and long-wave thermal radiation,
the angle of the surface of the roof and the horizontal projection, and
the short-wave absorption and long-wave absorption coefficients of the
surface. Before calculating the external surface temperature, the heat
exchange in the external surface of the roof coating should be
estimated.
Thermal conductivity of the external surface of the roof coating is
defined as the external heat transfer coefficient. The external heat
transfer coefficient of roof coating is estimated from the constituent
sum of convective and radiative heat transfer coefficients of the
external surface (EN ISO 6946:2008; Oliveti et al. 2003; Al-Sanea 2003)
(see Eq. 1):
[h.sub.se] = [h.sub.r] + [h.sub.c]. (1)
The radiative constituent of heat transfer coefficient of the
exterior surface of the roof is calculated according to Eq. (2) (EN ISO
6946:2008, Biwole et al. 2008; Hadavand et al. 2008a; Hadavand et al.
2008b):
[h.sub.r] = 4 x [sigma] x [T.sup.3.sub.AIR] (1/[[epsilon].sub.sky]
+ 1/[[epsilon].sub.surf]), (2)
where: [h.sub.r]--radiative heat transfer coefficient of the
exterior surface of the roof, W/([m.sup.2]-K); [sigma]--Stefan-Boltzmann
constant, [sigma] = 5.67051 x [10.sup.-8] W/([m.sup.2] x [K.sup.4]);
[T.sub.AIR]--exterior air temperature, [degrees]K;
[[epsilon].sub.sky]--emissivity of long-wave radiation from the sky;
[[epsilon].sub.surf]--emissivity of long-wave radiation of exterior
surface of the roof.
The value of the convective heat transfer coefficient of the
exterior surface of the roof is dependent on the wind speed v (m/s)
([TEXT NOT REPRODUCIBLE IN ASCII] 2006) and is calculated according to
the following Eq. (3.1):
[h.sub.c] = 7.34 X [v.sup.0,656] + 3.78 x [e.sup.-1,91 x v] (3.1)
or given by Cerne and Medved (2007):
[h.sub.c] = 3.1 + 4.1 x v. (3.2)
Under solar radiation, the temperature of exterior surface of the
envelope increases, whereas the effect of long-wave radiation from the
sky reduces it. As it is described by ([TEXT NOT REPRODUCIBLE IN ASCII]
et al. 1956), solar and long-wave radiations have an impact on the
relative exterior air temperature. This temperature [[theta].sub.sol]
([degrees]C) is calculated by ([TEXT NOT REPRODUCIBLE IN ASCII] et al.
1956) as follows:
[[theta].sub.sol] = [[theta].sub.e] + [[alpha].sub.surf] x
[I.sub.t]/[h.sub.se] - 3.6 , (4)
where: [[theta].sub.e]--average exterior air temperature,
[degrees]C; [I.sub.t]--intensity of solar radiation to the surface of
adequate orientation, W/[m.sup.2]; [[alpha].sub.surf]--surface
short-wave absorption coefficient; [h.sub.se]--heat transfer coefficient
of the external surface, W/([m.sup.2] x K) [[alpha].sub.surf] x
[I.sub.t]/[h.sub.se]--equivalent temperature of solar
radiation,[degrees]C; 3.6--decrease of the average relative exterior air
temperature due to the long-wave radiation.
The methodology for calculation of the surface temperature
[[theta].sub.se] is described by Ulgen (2002) and Kaska et al. (2009)
where solar radiation and long-wave radiation from the sky, relative
exterior air temperature, heat exchange in superficial layers and
thermal energy absorption coefficients of surfaces are evaluated. The
equation suggested by (Kaska et al. 2009) is similar to the one proposed
by ([TEXT NOT REPRODUCIBLE IN ASCII] et al. 1956) but there is one
fundamental difference.
In contrast to ([TEXT NOT REPRODUCIBLE IN ASCII] et al. 1956 and
Kaska et al. 2009) it is stated that the impact of solar and long-wave
radiation effect is attributed not to the relative exterior air
temperature evaluation, but to the evaluation of temperature variation
of the surface, affected by these radiations, as follows (ASHRAE 2001):
[[theta].sub.se] = [[theta].sub.e] + [[alpha].sub.suf] x
[I.sub.t]/[h.sub.se] - [[epsilon].sub.surf] x [DELTA]R/[h.sub.se], (5)
where: [DELTA]R--the balance of long-wave radiation (the long-wave
radiation from the sky minus the long-wave radiation of the surface of
the roof coating), W/[m.sub.2]; [[epsilon].sub.surf] x
[DELTA]R/[h.sub.se]--amendment item for the evaluation of exchange
between the long-wave radiation from the sky and the long-wave radiation
of the surface of the roof coating.
In accordance with ASHRAE recommendations (ASHRAE 2001), this
amendment item can be used as a constant and is 4[degrees]C for
horizontal surfaces, i.e. surface temperature declines by 4[degrees]C
due to the long-wave radiation effect. For vertical surfaces this
amendment item is 0[degrees]C (Ulgen 2002).
According to EN ISO 13790:2008 standard, horizontal surfaces fully
take over the effects of long-wave radiation, but these effects are
twice less for vertical surfaces. Kehrer and Schmidt (2008) provide an
amendment for the estimation of long-wave radiation effect due to the
surface lean angle. Thus, the external surface temperature of the
ventilated lightweight steel roofs [[theta].sub.rc.e] should be
calculated according to the following Eq. (6):
[[theta].sub.rc.se] = [[theta].sub.e] [I.sub.[summation]SOL] x
[[alpha].sub.rc.se][H.sub.rc.se] + [DELTA][L.sub.NET] x
[[epsilon].sub.rc.se]/[h.sub.rc.se] x [(cos([beta/2])).sup.2], (6)
where: [DELTA][L.sub.NET]--the balance of long-wave radiation (the
long-wave radiation of the surface of the roof coating minus the
long-wave radiation from the sky), W/[m.sup.2]; [beta]--the angle of the
relevant surface of the roof coating with the horizontal plane.
Together with the climatic thermal effects on the external surface
of the roof coating, heat exchange takes place in the interior surface
of the roof coating. The exchange affects the interior surface of the
roof coating and for this reason, its evaluation is necessary for the
analysis of the consistent patterns of temperature variations of the
surface of the roof coating (Fig. 1).
[FIGURE 1 OMITTED]
For this purpose, the energy balance Eq. (7) could be used to
calculate the temperature of the interior surface of the roof coating
[[theta].sub.rc.si] in the following manner (8):
[[theta].sub.rc.se] - [[theta].sub.rc.si]/[R.sub.rc] =
([[theta].sub.rc.si] - [[theta].sub.ag]) x [h.sub.rc.si.c] +
([[theta].sub.rc.si] - [[theta].sub.ins.se]) x [h.sub.rc.si.r], (7)
[[theta].sub.rc.si] = [h.sub.rc.si.c] x [R.sub.rc] x
[[theta].sub.ag] + [h.sub.rc.si.r] x [R.sub.rc] x [[theta].sub.ins.se] +
[[theta].sub.rc.se]/[h.sub.rc.si.c] x [R.sub.rc] [h.sub.rc.si.r] x
[R.sub.rc] + 1, (8)
where: [[theta].sub.rc.si]--temperature of the interior surface of
the roof coating,[degrees]C; [[theta].sub.ag]--temperature of the
ventilated air gap of the roof,[degrees]C;
[[theta].sub.ins.se]--temperature of the external surface of the roof
thermal insulation layer, [degrees]C; [R.sub.rc]--thermal resistant of
the roof coating, [m.sup.2] x K/W; [h.sub.rc.si]--heat transfer
coefficient of the interior surface of the roof coating, W/([m.sup.2] x
K).
Heat exchange in the internal surface of the roof coating is
divided into convective and radiative heat exchange. The former takes
place between the internal surface of the roof coating and the air
moving in the ventilated air gap, while the latter refers to the
exchange through the ventilated air gap between its boundary surfaces,
i.e. between the internal surface of the roof coating and the external
surface of the roof thermal insulation layer. In Eqs. (7) and (8), the
convective heat transfer coefficient of the internal surface of the roof
coating [h.sub.rc.si.c] (W/([m.sup.2] x K)) is calculated by Eq. (3)
where the speed of the air moving through the ventilated air gap is
applied instead of the wind speed. The radiative coefficient of the same
surface [h.sub.rc.si.r] (W/([m.sup.2] x K)) is calculated according to
the following equation, provided by (Ong and Chow 2003; Barkauskas and
Stankevicius 2000; Sadauskiene et al. 2009):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)
where: [C.sub.0]--radiation coefficient of black-body, [C.sub.0] =
5.67 W/([m.sup.2] x [K.sup.4]).
The value of the convective heat transfer coefficient depends on
the speed of the air moving through the ventilated air gap, but the
characteristics of roof construction below the air gap have no effect on
its value. Moreover, following Eq. (9), the radiative heat transfer
coefficient of the surface depends on the long-wave radiation emissivity
of the boundary surfaces of the ventilated air gap and their
temperature. The value of the radiative heat transfer coefficient can be
increased and reduced by changing the long-wave radiation emissivity of
these surfaces: reduced emissivity diminishes the value of the
coefficient and vice versa. One of the solutions for reducing the
radiative heat transfer through the ventilated air gap is to install a
layer with low radiative emissivity in the lower surface of the gap.
When the internal surface of the roof coating is [[epsilon].sub.rc.si] =
0.8 and the lower surface of the ventilated air gap
[[epsilon].sub.ins.se]. is reduced from 0.9 to 0.1, the value of the
radiative heat transfer coefficient can be reduced about 7 times.
However, in this case, a part of the radiative energy would be reflected
from this layer and this amount of energy would increase the temperature
of the interior surface of the roof coating, though it is still unknown
how much this temperature could increase. In theory, according to Eq.
(9), when the temperature of the interior surface of the roof coating
[[theta].sub.ins.se] is reduced, the radiative heat transfer coefficient
also decreases. This suggests that a thermally recipient layer, which
would accumulate a part of thermal energy, installed in the lower
surface of the ventilated air gap, or two gaps installed instead of one
would give the reason for the temperature variation of the roof coating;
however, this presumption has not been studied yet.
In order to investigate the processes and dynamics of heat exchange
between the atmosphere and the surface of the ventilated lightweight
steel roof coating, and to evaluate the reliability of the methodology
for calculating the temperature of the coatings, the experiments were
performed as described below.
2. Objectives of the experiments and construction of experimental
cells
Commonly used constructions of lightweight ventilated roofs with
steel coatings were chosen for experimentation. In such types of roofs,
thermal insulation is usually installed between the wooden frame
elements.
While planning the course of the experimentation, it was determined
that the temperature of the ventilated steel roof coatings may be
affected not only by the climatic impact, but also by the heat exchange
between the coating and the external surface of the thermal insulation
layer of the roof. Aiming at the reduction of heat gains into the
premises through the mentioned types of roofs during the hot season of
the year, the external layers of thermal isolation of the roof could be
equipped with heat reflective coatings, heat receptive layers made of
constructional products, heat receptive layers with heat reflective
coatings, or with more than one ventilated air gap.
The experiments were performed under real climatic conditions,
which imply that the climatic effect was different for every experiment.
If a single experimental cell had been used for the research, the
comparison of the results, obtained at different times, would have been
complicated. For this reason, two experimental cells of identical
construction, S1 and S2 were prepared and their thermal characteristics
were calibrated before the basic experimental stage. Having carried out
the calibration of the cells (first experimental stage) and concluded
that the thermal characteristics of the cells are identical, the
construction of cell S1 was not altered during the whole experimental
period. The construction of cell S2 was changed during the other
experimental stages in order to estimate the impact caused by the
thermal characteristics of roof layers, placed below the ventilated air
gap, on the temperature variation dynamics of the roof coatings, arising
due to the climatic effects. The experimental results of cell S2 were
compared with those of cell S1.
Fig. 2 and Table 1 represents the roof construction of cells S1 and
S2 during the first experimental stage (calibration of cells).
[FIGURE 2 OMITTED]
Heat transmittance coefficient of cells walls is U = 0.18
W/([m.sup.2] x K), cells floor U = 0.18 W/([m.sup.2] x K) and cells roof
U = 0.16 W/([m.sup.2] x K). Profiled dark brown steel leafs were used as
a waterproofing roof coating; their short-wave radiation emissivity of
external surfaces is [[alpha].sub.rc.se] = 0.7, hemispherical long-wave
radiation emissivity of external surfaces [[epsilon].sub.rc.se] = 0.88
and hemispherical long-wave radiation emissivity of internal surfaces
[[epsilon].sub.re.si] = 0.77 (Prado et al. 2005). A 0.6 mm thick
breather membrane non-conductive for air functioned as a
vapour-conductive wind proofing insulation (hereinafter "breather
membrane"). Moreover, 10 mm thick chipboard was used for internal
layer of roof construction. In order to maximally reduce the exterior
air infiltration into the inside of the cells, the junctions of the
premises and their separate layers were made airtight in both cells.
Thermal insulation layers of walls and floor were made from 200 mm of
expanded polystyrene foam panels. Two air conditioning devices of 400 W
cooling capacities were also installed inside the cells. The orientation
of roof surfaces of both cells was identical: south direction, whereas
the surface lean angle towards the horizontal projection was 2[degrees].
The values of thermal conductivity coefficients of the constructional
products used for the cells were evaluated by experimentations performed
following LST EN 12667: 2002 and employing a device which meets ISO
8301:1991 requirements. The image of the cells is presented in Figs 3-7.
[FIGURE 3 OMITTED]
The construction of cell S2 was changed in the other experimental
stages as presented in Table 2.
In the roof constructions of the cells, the thermocouples were
installed on the internal surface of the roof, in the middle of the
ventilated air gap of the roof, on the external surface of the breather
membrane, on the junction of the chipboard and polyethylene film, and on
the internal surface of the chipboard. Additionally, two heat flux
meters were installed on the internal surface of the roof of each cell.
The internal temperature of the cells was measured by a digital meter
TReg01, which was also used for its control, and a thermocouple T20. A
digital meteorological station was set up near the cells for registering
the exterior air temperature, diffuse solar radiation, total solar
radiation, the balance of long-wave radiation, wind speed and other
exterior air parameters.
During the experiments, a constant temperature of 10[+ or
-]0.5[degrees]C which was lower than the exterior air temperature was
maintained in the cells S1 and S2 all the time.
[FIGURE 4 OMITTED]
[FIGURE 6 OMITTED]
3. Meteorological data
The digital meteorological station, set up near the experimental
roof cells, registered the following climatic parameters: diffuse and
total solar radiation, long-wave radiation from the sky, exterior air
temperature, relative humidity of the exterior air, wind speed, wind
direction and atmospheric pressure.
[FIGURE 5 OMITTED]
[FIGURE 7 OMITTED]
The values of total solar radiation and balanced long-wave
radiation, registered during the experiments, are presented in Figs 9,
10 and Table 3.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
4. The experimental results
The experiments were carried out in Lithuania in the month of July
because it has the highest average monthly air temperature. At this
time, the average daily amplitude of the exterior air temperature is
10.2[degrees]C and the maximum daily amplitude of the exterior air
temperature is 18.7[degrees]C (RSN 156-94). During the experimentation,
the average daily amplitude of the exterior air temperature was
10.5[degrees]C. Thus, it could be stated that the selected periods
corresponded to the permanent monthly amplitude of the exterior air
temperature in the experimental location (see Table 4).
The results show that during the experimentation, the average daily
temperature of the roof coating was higher, from 5.9-11.3[degrees]C,
than the exterior air temperature, while during the daylight hours, it
was also higher, from 9.7[degrees]C-17.3[degrees]C. In the night time
hours, the average temperature of the roof coating was lower, from
3.2[degrees]C-3.9[degrees]C, than the exterior air temperature, which
was due to the long-wave radiation from the sky.
During the experiment No. 1, the difference between the average
daily temperatures of the roof coating in the cells S1 and S2 was
-0,2[degrees]C, whereas during the experiments No. 2, No. 3, No. 4 and
No. 5, these temperature differences were -0.7[degrees]C,
-1.0[degrees]C, -0.7[degrees]C and -0.6[degrees]C respectively. This
suggests that constructional changes of the roof, which theoretically
should have an impact on the reduction of heat flows through the
construction of the roof during the hot period of the day, increases the
average daily temperature of the internal surface of the roof coating.
5. Experimental evaluation of theoretical presumptions
All data from the experimental cells and meteorological station
were recorded every second; their average 1 minute value was calculated
and stored in the data logging memory. Then they were transferred to the
computer and processed by the Microsoft Excel. Tables 5 and 6 present
the measured and calculated average hourly and daily results of roof
coating temperatures and inaccuracies in their calculation.
Judging from the data, presented in Table 5, the absolute
inaccuracy of the average hourly temperature of the interior surface of
the roof coating, calculated by Eq. (8), is from -4.9 to +6.8[degrees]C.
The data, presented in Table 6, suggests that the absolute
inaccuracy of the average daily temperature of the roof coating,
calculated by Eq. (8), is from -0.6 to +1.6[degrees]C.
The calculations by Eq. (8) employed the experimental data on the
temperature of the ventilated air gap, the speed of air moving in the
ventilated air gap (for the evaluation of the convective heat exchange
in the surface layers) and the temperature of the top surface of the
thermal insulation layer of the roof. Then the results of the
calculations by Eqs. (6) and (8) were compared in order to evaluate the
impact of heat exchange intensity in the interior surface of the roof
coating on the temperature of the coating. The heat exchange was
determined to have the greatest impact when the temperature of the roof
coating is the highest. However, the heat exchange reduces the
temperature of the internal surface of the roof only approximately in
0.003[degrees]C (the difference between the calculation results by Eqs.
(6) and (8)). This implies that the radiative heat exchange between the
surfaces of the ventilated air gap have no impact on the temperature of
the ventilated steel roof coating; this type of coating takes over the
thermal climatic effects in the extreme manner.
Thermal climatic effects on the steel roof coating can be divided
into the following components of the temperature effects: exterior air
temperature, the component of the short-wave solar radiation temperature
and the component of the long-wave solar radiation temperature (Fig.
11).
During the experiment No. 3, the daily value variation of
temperature components was calculated, using Eq. (6) and average hourly
values of the climatic parameters, and presented in Fig. 12. It shows
that
the short wave solar radiation and the exterior air temperature have
the greatest effect on the temperature variation of the roof coating.
Due to the thermal effects of the solar radiation, this experiment
estimated the temperature of the coating up to 25[degrees]C higher than
the value of the exterior air temperature (Fig. 13, 14:00 h). During the
experiment, the effect of long-wave solar radiation was minor and
reduced the temperature of the coating only by approximately
1-4[degrees]C.
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
[FIGURE 13 OMITTED]
The temperature components of long-wave solar radiation effect and
exterior air vary quite equally during 24 hours (Fig. 13). Dynamic
temperature variation of roof coating during 24 hours is determined by
the intensity of solar radiation effect. In practice, it is important to
evaluate the amount of time required by the temperature of the roof
coating to react to the solar thermal effects. Fig. 13 presents the
diagrams showing the temperature of the internal surface of the roof
coating and total short-wave solar radiation during the experiment No.
3. The data suggest that due to the low thermal emissivity, steel roof
coatings quickly react to the thermal effects of solar radiation and
their temperature variation repeat the complexion of the solar radiation
intensity variation. The data obtained from the other experiments are
very similar to the ones presented in Fig. 13.
5. Conclusions
1. Steel roof coatings take over the effects of thermal solar
radiation quickly due to the low thermal susceptibility of the steel
roofs. The temperature variation of the coatings repeats the complexion
of the solar radiation intensity variation.
2. Radiative heat exchange between the boundary surfaces of the
ventilated air gap has almost no impact on the temperature of the
ventilated steel roof coating. This type of coatings takes over thermal
climatic effects in the extreme manner.
3. Calculation methodology was used for the estimation of the
temperature of the ventilated steel roof coating. This methodology
assesses long-wave radiation from the sky, solar radiation, exterior air
temperature and heat exchange in the ventilated air gap, and enables a
precise calculation of the surface temperatures of the coating. The
absolute error of the calculation is from 0.6 [degrees]C to
+1.6[degrees]C.
4. Short-wave solar radiation and exterior air temperature have the
major impact on the temperature variation of the roof coating during 24
hours. Long-wave radiation from the sky has a lesser effect on the
temperature of the coating, reducing it to approximately 1-4[degrees]C.
doi: 10.3846/13923730.2011.556180
References
Al-Sanea, S. A. 2002. Thermal performance of building roof
elements, Building and Environment 37(7): 665-675.
doi:10.1016/S0360-1323(01)00077-4
Al-Sanea, S. A. 2003. Finite-volume thermal analysis of building
roofs under two-dimensional periodic conditions, Building and
Environment 38(8): 1039-1049. doi:10.1016/S0360-1323(03)00068-4
ASHRAE. Handbook of fundamentals. 2001. American Society of
Heating, Refrigerating and Air-Conditioning Engineers. Atlanta, GA.
Barkauskas, V.; Stankevicius, V. 2000. Pastatu atitvaru silumine
fizika [Building physics]. Kaunas: Technologija.
Biwole, P. H.; Woloszyn, M.; Pompeo, C. 2008. Heat transfers in a
double-skin roof ventilated by natural convection in summer time, Energy
and Buildings 40(8): 1487-1497. doi:10.1016/j.enbuild.2008.02.004
Cerne, B.; Medved, S. 2007. Determination of transient
two-dimensional heat transfer in ventilated lightweight low sloped roof
using Fourier series, Building and Environment 42(6): 2279-2288.
doi:10.1016/j.buildenv.2006.04.022
EN ISO 6946:2008 Building components and building elements. Thermal
resistance and thermal transmittance. Calculation method. Brussel, 2008.
EN ISO 13790:2008 Energy performance of buildings--Calculation of
energy use for space heating and cooling. Brussel, 2008.
Hadavand, M.; Yaghoubi, M.; Emdad, H. 2008a. Thermal analysis of
vaulted roofs, Energy and Buildings 40(3): 265-275.
doi:10.1016/j.enbuild.2007.02.024
Hadavand, M.; Yaghoubi, M. 2008b. Thermal behavior of curved roof
buildings exposed to solar radiation and wind flow for various
orientations, Applied Energy 85(8): 663-679.
doi:10.1016/j.apenergy.2008.01.002
Kairys, L.; Stankevicius, V.; Karbauskaite, J. 2006. Heat flux
through the timber walls under summer climate conditions in Eastern
Europe, Journal of Civil Engineering and Management 12(1): 77-82.
Kaska, O.; Yumrutas,, R.; Arpa, O. 2009. Theoretical and
experimental investigation of total equivalent temperature difference
(TETD) values for building walls and flat roofs in Turkey, Applied
Energy 86(5): 737-747. doi:10.1016/j.apenergy.2008.09.010
Kehrer, M.; Schmidt, T. 2008. Radiation effects on exterior
surfaces, in Proc. of the 8th Symposium on Building Physics in the
Nordic Countries: Selected papers, vol. 1. June 16-18, 2008, Copenhagen,
Denmark. Copenhagen: Danish Society of Engineers, 207-212.
Lee, S.; Park, S. H.; Yeo, M. S.; Kim, K. W. 2009. An experimental
study on airflow in the cavity of a ventilated roof, Building and
Environment 44(7): 1431-1439. doi:10.1016/j.buildenv.2008.09.009
LST EN 12667:2002 Thermal performance of building materials and
products Determination of thermal resistance by means of guarded hot
plate and heat flow meter methods--Products of high and medium thermal
resistance. 2002.
Oliveti, G.; Arcuri, N.; Ruffolo, S. 2003. Experimental
investigation on thermal radiation exchange of horizontal outdoor
surfaces, Building and Environment 38(1): 83-89.
doi:10.1016/S0360-1323(02)00010-0
Ong, K. S.; Chow, C. C. 2003. Performance of a solar chimney, Solar
Energy 74(1): 1-17. doi:10.1016/S0038-092X(03)00114-2 Prado, R. T. A.;
Ferreira, F. L. 2005. Measurement of albedo and analysis of its
influence the surface temperature of building roof materials, Energy and
Buildings 37(4): 295300. doi:10.1016/j.enbuild.2004.03.009
RSN 156-94 Statybine klimatologija [Building climatology]. Vilnius,
1995.
Sadauskiene, J.; Buska, A.; Burlingis, A.; Bliudzius, R.; Gailius,
A. 2009. The effect of vertical air gaps to thermal transmit-tance of
horizontal thermal insulating layer, Journal of Civil Engineering and
Management 15(3): 309-315. doi:10.3846/1392-3730.2009.15.309-315
Seduikyte, L.; Paukstys, V. 2008. Evaluation of indoor environment
conditions in offices located in buildings with large glazed areas,
Journal of Civil Engineering and Management 14(1): 39-44.
doi:10.3846/1392-3730.2008.14.39-44
Ulgen, K. 2002. Experimental and theoretical investigation of
effects of wall's thermophysical properties on time lag and
decrement factor, Energy and Buildings 34(3): 273278. doi:
10.1016/S03787788(01)00087-1
[TEXT NOT REPRODUCIBLE IN ASCII]. [Phokin, K. PH. Thermal physics
of building partitions]. MocKBa: ABOK-ITPECC.
[TEXT NOT REPRODUCIBLE IN ASCII] [Shklover, A. M.; Vasilev, B. Ph.;
Ush-kov, Ph. V. Essential thermal technology of residential and public
buildings]. [TEXT NOT REPRODUCIBLE IN ASCII].
Karolis Banionis (1), Vytautas Stankevicius (2), Edmundas
Monstvilas (3)
Institute of Architecture and Construction of Kaunas University of
Technology, Tunelio g. 60, LT-44405 Kaunas, Lithuania
E-mails: (1) karolis_banionis@yahoo.com (corresponding author); (2)
v.stankevicius@ktu.lt; (3) asi_monstvilas@yahoo.com
Received 29 Dec. 2009; accepted 13 Jul. 2010
Karolis BANIONIS. PhD student of Civil Engineering, Researcher at
the Laboratory of Thermal Building Physics of the institute of
Architecture and Construction, KTU. Research interests: heat transfer,
thermal impacts of solar radiation.
Vytautas STANKEVICIUS. Doctor Habil, Full Professor, Chief
Researcher at the Laboratory of Thermal Building Physics of the
institute of Architecture and Construction, KTU. Research interests:
heat transfer, technical properties of thermal insulation products.
Edmundas MONSTVILAS. Doctor, Senior Researcher at the Laboratory of
Thermal Building Physics of the institute of Architecture and
Construction, KTU. Research interests: heat transfer and thermal
insulation, technical properties of thermal insulation products.
Table 1. Construction elements composing roof constructions
of the cells
Material Thickness, Thermal conductivity,
mm W/(m x K)
Roof steel cover 0.55 50
Breather membrane 0.6 0.13
Mineral wool 200 0.034
Polyethylene film 0.2 - *
Chipboard 10 0.13
Heat reflective film (1) 0.4 - *
Cement-sawdust board (2) 14 0.213
Note: (1) used in 2, 3, 5 experimental stages;
(2) used in 3, 4 experimental stages;
* R = 0.02 [m.sup.2] x K/W.
Table 2. Roof construction of cell S2 in different experimental
stages
Experiments Changes of cell S2 construction in
different experimental stages
2 A 0.3 mm thick heat reflective coating
(Fig. 4) with a hemispherical long-
wave radiation emissivity coefficient
[[epsilon].sub.h] = 0.09 was mounted
over the breather membrane.
A 14 mm thick cement/sawdust board
3 ([lambda] = 0.213 W/m x K) with heat
reflective coating (Fig. 5) and a
hemi/spherical long/wave radiation
emissivity coefficient
[[epsilon].sub.h] = 0.09 was mounted
over the breather membrane. Heat
capacity of the board per area is
26572 J/([m.sup.2] x K).
4 A 14 mm thick cement/sawdust board
([lambda] = 0,213 W/m x K) without
additional coatings (Fig. 6) was
mounted over the breather membrane.
Heat capacity of the board per area is
26572 J/([m.sup.2] x K).
Two air gaps, separated by a heat
5 reflective coating with two heat
reflecting surfaces (Fig. 7), were
installed over the breather membrane.
The hemispherical long-wave radiation
emissivity coefficient of these
surfaces of the coating is
[[epsilon].sub.h] = 0.09. The height
of the air gap between the breather
membrane and heat reflective coating
is 35 mm, whereas the height of the
air gap between the heat reflective
coating and roof coating is 40 mm.
Table 3. Values and normative climatic data measured during the
experiments of climatic parameters
Parameters Exp. Exp. Exp. Exp. Exp.
No. 1 No. 2 No. 3 No. 4 No. 5
Average daily exterior air 22.5 21.5 22.8 23.3 20.2
temperature, [degrees]C
Average daily wind speed, m/s 2.3 1.2 1.8 1.9 1.3
Average daily total solar 331 327 242 307 225
radiation, W/[m.sup.2]
Average daily diffuse solar 79 80 128 94 105
radiation, W/[m.sup.2]
Average daily relative 65 67 62 67 71
exterior air humidity, %
Average daily long-wave 388 385 404 394 388
radiation from the sky to the
top surface of the roof [down
arrow], W/[m.sup.2]
Average daily long/wave 438 438 439 442 428
radiation from the top
surface of the roof to the
sky [up arrow], W/[m.sup.2]
Average daily long/wave -50 -53 -35 -48 -40
radiation balance, W/
[m.sup.2]
Daylight period 17.4 17.2 16.9 16.7 16.0
[[tau].sub.n], hour.
Night time period 6.6 6.8 7.1 7.3 8.0
[[tau].sub.n], hour.
Parameters Measured Normative
in July climatic data
Average daily exterior air 18.7 17.4
temperature, [degrees]C
Average daily wind speed, m/s 1.7 3.1
Average daily total solar 222 215
radiation, W/[m.sup.2]
Average daily diffuse solar 114 103
radiation, W/[m.sup.2]
Average daily relative 75 76
exterior air humidity, %
Average daily long-wave 382 n/a
radiation from the sky to the
top surface of the roof [down
arrow], W/[m.sup.2]
Average daily long/wave 416 n/a
radiation from the top
surface of the roof to the
sky [up arrow], W/[m.sup.2]
Average daily long/wave -34 n/a
radiation balance, W/
[m.sup.2]
Daylight period 16.6 16.0
[[tau].sub.n], hour.
Night time period 7.4 8.0
[[tau].sub.n], hour.
Table 4. Measurement data of the exterior air and roof coating
temperatures
Parameters Cell No. 1 ("S1")
24 Daylight Night
hours hours time
hours
Experiment No. 1 (calibration of cells)
Exterior air temperature, [degrees]C 22.5 23.5 20.0
Interior surface temperature of the roof
coating, [degrees]C 29.9 34.8 17.0
Temperature difference between the
interior surface of the
roof coating and exterior air,
[degrees]C 7.4 11.3 -3.0
Experiment No. 2
Exterior air temperature, [degrees]C 21.5 22.5 18.8
Interior surface temperature of the roof
coating, [degrees]C 32.1 38.7 15.2
Temperature difference between the
interior surface of the roof coating
and exterior air, [degrees]C 10.6 16.2 -3.6
Experiment No. 3
Exterior air temperature, [degrees]C 22.8 24.0 20.1
Interior surface temperature of the roof
coating, [degrees]C 28.7 33.7 16.9
Temperature difference between the
interior surface of the roof coating
and exterior air, [degrees]C 5.9 9.7 -3.2
Experiment No. 4
Exterior air temperature, [degrees]C 23.3 24.5 20.5
Interior surface temperature of the roof
coating, [degrees]C 29.4 35.0 16.6
Temperature difference between the
interior surface of the roof coating 6.1 10.5 -3.9
and exterior air, [degrees]C
Experiment No. 5
Exterior air temperature, [degrees]C 20.2 20.8 19.0
Interior surface temperature of the roof
coating, [degrees]C 27.9 34.0 15.8
Temperature difference between the
interior surface of the roof coating
and exterior air, [degrees]C 7.7 13.2 -3.2
Parameters Cell No. 2 ("S2")
24 Daylight Night
hours hours time
hours
Experiment No. 1 (calibration of cells)
Exterior air temperature, [degrees]C 22.5 23.5 20.0
Interior surface temperature of the roof
coating, [degrees]C 29.7 34.6 17.0
Temperature difference between the
interior surface of the
roof coating and exterior air,
[degrees]C 7.2 11.1 -3.0
Experiment No. 2
Exterior air temperature, [degrees]C 21.5 22.5 18.8
Interior surface temperature of the roof
coating, [degrees]C 32.8 39.8 15.0
Temperature difference between the
interior surface of the roof coating
and exterior air, [degrees]C 11.3 17.3 -3.8
Experiment No. 3
Exterior air temperature, [degrees]C 22.8 24.0 20.1
Interior surface temperature of the roof
coating, [degrees]C 29.7 35.2 16.8
Temperature difference between the
interior surface of the roof coating
and exterior air, [degrees]C 6.9 11.2 -3.3
Experiment No. 4
Exterior air temperature, [degrees]C 23.3 24.5 20.5
Interior surface temperature of the roof
coating, [degrees]C 30.1 35.9 16.7
Temperature difference between the
interior surface of the roof coating 6.8 11.4 -3.8
and exterior air, [degrees]C
Experiment No. 5
Exterior air temperature, [degrees]C 20.2 20.8 19.0
Interior surface temperature of the roof
coating, [degrees]C 28.5 35.3 15.1
Temperature difference between the
interior surface of the roof coating
and exterior air, [degrees]C 8.3 14.5 -3.9
Table 5. Measured and calculated average hourly temperatures of the
steel roof coatings of Cell No. 2
Time of Exp. No. 1 Exp. No. 2
the day
M C E M C E
00:00 18.0 18.8 0.8 12.9 14.5 1.6
01:00 17.7 18.4 0.7 12.9 14.7 1.8
02:00 16.6 17.3 0.7 12.1 13.8 1.7
03:00 15.7 16.6 0.9 13.4 13.6 0.2
04:00 15.2 16.0 0.8 12.9 12.9 0.0
05:00 15.4 16.6 1.2 13.3 13.6 0.3
06:00 18.1 19.7 1.6 15.1 18.4 3.3
07:00 21.1 22.5 1.4 19.6 26.4 6.8
08:00 29.0 31.1 2.1 31.9 36.9 5.0
09:00 36.1 38.1 2.0 44.8 46.7 1.9
10:00 39.8 41.6 1.8 51.8 52.2 0.4
11:00 40.0 41.6 1.6 56.7 56.4 -0.3
12:00 46.4 47.6 1.2 58.4 58.3 -0.1
13:00 49.2 49.3 0,1 62.4 58.5 -3.9
14:00 51.0 51.5 0.5 57.6 55.2 -2.4
15:00 48.2 49.4 1.2 55.2 53.4 -1.8
16:00 44.9 46.4 1.5 53.6 50.6 -3.0
17:00 41.7 43.8 2.1 44.9 43.7 -1.2
18:00 36.0 38.8 2.8 40.5 40.6 0.1
19:00 30.6 33.8 3.2 32.1 34.1 2.0
20:00 25.4 27.4 2.0 24.3 26.5 2.2
21:00 21.5 22.9 1.4 20.0 22.0 2.0
22:00 19.2 20.3 1.1 17.8 20.0 2.2
23:00 18.2 19.3 1.1 17.4 19.9 2.5
00:00 17.0 18.2 1.2 18.9 20.0 1.1
Time of Exp. No. 3 Exp. No. 4
the day
M C E M C E
00:00 11.8 14.4 2.6 12.6 15.8 3.2
01:00 13.2 15.2 2.0 12.4 15.0 2.6
02:00 12.4 14.1 1.7 13.7 15.2 1.5
03:00 14.6 16.0 -1.4 13.7 14.2 0.5
04:00 14.1 15.0 -0.9 13.6 13.8 0.2
05:00 15.0 15.8 -0.8 13.6 14.7 1.1
06:00 17.9 18.6 -0.7 14.8 17.8 3.0
07:00 20.6 21.0 -0.4 18.5 24.8 6.3
08:00 27.7 27.8 -0.1 27.4 31.7 4.3
09:00 28.4 28.4 0.0 34.6 37.3 2.7
10:00 28.7 27.8 0.9 41.1 43.0 1.9
11:00 46.3 41.9 4.4 43.9 44.5 0.6
12:00 52.3 46.7 5.6 49.7 48.4 -1.3
13:00 51.6 47.7 3.9 50.1 48.9 -1.2
14:00 57.8 51.3 6.5 48.1 46.9 -1.2
15:00 49.3 46.6 2.7 48.6 46.0 -2.6
16:00 41.2 39.9 1.3 46.5 44.9 -1.6
17:00 36.5 36.0 0.5 43.3 42.7 -0.6
18:00 36.7 36.0 0.7 38.5 38.8 0.3
19:00 34.4 34.0 0.4 32.9 33.8 0.9
20:00 26.9 27.6 -0.7 28.3 29.3 1.0
21:00 22.6 23,8 -1.2 24.4 24.9 0.5
22:00 21.3 22.6 -1.3 22.0 23.1 1.1
23:00 21.4 22.6 -1.2 21.5 22.6 1.1
00:00 21.4 22.4 -1.0 21.2 21.9 0.7
Time of Exp. No. 5
the day
M C E
00:00 17.6 18.3 0.7
01:00 16.9 17.8 0.9
02:00 15.9 17.2 1.3
03:00 16 16.9 0.9
04:00 15.9 16.5 0.6
05:00 15.6 16.1 0.5
06:00 16.4 16.6 0.2
07:00 17.3 18.8 1.5
08:00 18 19.2 1.2
09:00 25.8 23.9 -1.9
10:00 37.6 35.6 -2.0
11:00 48.1 44.9 -3.2
12:00 46.4 41.5 -1.9
13:00 46.9 44.0 -2.9
14:00 56.3 53.0 -3.3
15:00 50.5 46.4 -3.3
16:00 48.9 44.1 -4.8
17:00 43.2 39.6 -3.6
18:00 39.0 37.0 -2.0
19:00 31.5 31.8 0.3
20:00 22.6 24.6 2.0
21:00 15.2 19.1 3.9
22:00 15.0 18.1 3.1
23:00 14.2 17.1 2.9
00:00 11.7 15.7 4.0
Note: M--measured temperature, C--calculated temperature,
E--absolute calculation error (the difference between the
temperature of the interior surface of the roof, calculated
by equation (7), and the measured temperature)
Table 6. Measured and calculated average daily temperatures of the
steel roof coatings
Parameters Experiment Experiment
No. 1 No. 2
"S1" "S2" "S1" "S2"
Measured daily average temperature
of the interior surface of the
roof, [degrees]C 29.9 29.7 32.1 32.8
Calculated daily average
temperature of the exterior
surface of the roof by equation
(6), [degrees]C 31.2 31.2 33.7 33.7
Calculated daily average
temperature of the interior
surface of the roof by equation
(7), [degrees]C 31.2 31.2 33.7 33.7
Absolute calculation error: the
difference between the calculated
temperature of the interior
surface of the roof by equation
(7) and the measured temperature,
[degrees]C 1.3 1.5 1.6 0.9
Parameters Experiment Experiment
No. 3 No. 4
"S1" "S2" "S1" "S2"
Measured daily average temperature
of the interior surface of the
roof, [degrees]C 28.7 29.7 29.4 30.1
Calculated daily average
temperature of the exterior
surface of the roof by equation
(6), [degrees]C 29.1 29.1 31.0 31.0
Calculated daily average
temperature of the interior
surface of the roof by equation
(7), [degrees]C 29.1 29.1 31.0 31.0
Absolute calculation error: the
difference between the calculated
temperature of the interior
surface of the roof by equation
(7) and the measured temperature,
[degrees]C 0.4 -0.6 1.6 0.9
Parameters Experiment
No. 5
"S1" "S2"
Measured daily average temperature
of the interior surface of the
roof, [degrees]C 27.9 28.5
Calculated daily average
temperature of the exterior
surface of the roof by equation
(6), [degrees]C 28.1 28.1
Calculated daily average
temperature of the interior
surface of the roof by equation
(7), [degrees]C 28.1 28.1
Absolute calculation error: the
difference between the calculated
temperature of the interior
surface of the roof by equation
(7) and the measured temperature,
[degrees]C 0.2 -0.4
Note: "S1"--Cell No. 1, "S2"--Cell No. 2.
