Hourly calculation method of building energy demand for space heating and cooling based on steady-state heat balance equations.
Monstvilas, Edmundas ; Stankevicius, Vytautas ; Karbauskaite, Jurate 等
1. Introduction
The fundamental requirements of the new EPBD directive are aimed at
the further decrease of energy consumption in buildings (Directive
2010/31/EU). Great attention is paid to the ability to construct only
low and very low-energy using buildings in the future. Solar heat gains
admitted inside the buildings make a considerable impact on the indices
of the building energy consumption. These gains take place during the
whole heating season. At the beginning and end of the heating season,
solar thermal radiation is intensive enough and heat gains could cover a
large extent of heat losses in buildings. Therefore, the development of
calculation precision of solar heat gains and real evaluation has a big
influence on the indices of building energy demand (Yohanis, Norton
1999).
The calculation of solar heat gains into buildings has been
improved and is more detailed in the new standard LST EN ISO 13790
(2008) in comparison with its edition of 2004. Heat gains are calculated
according to the annual, monthly and hourly calculation methods. When
yearly and monthly mean value calculation methods are applied, the
average daily data on global solar radiation are used (LST EN ISO 13790
2008; Van Dijk et al. 2005). In other words, these calculation methods
assume that solar thermal heat flow density is the same at every hour of
the day. The hourly calculation method is more detailed because it uses
the data of hourly solar radiation during 24 hours. However, even this
method is not perfect enough. Some additional conditions must be
fulfilled in order to prevent divergences of calculation results (LST EN
ISO 13790 2008), but in the present edition of the mentioned standard,
they are not described.
We have studied the calculation methods of solar gains in a
building and composed a new hourly calculation method which enables
calculating hourly solar heat gains and temperature in the rooms during
the day more precisely as the laws of solar radiation transformation
into long wave thermal energy are taken into account.
2. Theoretical premises
For use within the context of building regulations, and in
particular for checking compliance with a EP requirement (maximum energy
performance level), there is an urgent need for simplified methods that
fulfil a number of basic requirements (Van Dijk et al. 2005; Ginevicius
et al. 2008).
Normally it is considered that heat gains in buildings can occur
due to the internal heat emissions, long wave sky radiation and solar
thermal radiation. These heat gains are different by their nature and
physical properties. Therefore, by setting heat balance equations the
peculiarities and nature of each kind of heat gains have to be taken
into account.
2.1. The assessment of internal heat gains
In most cases, internal heat gains inside the building occur due to
the thermal energy flow from warmer internal surfaces than indoor air
temperature, i.e. due to the emitted heat from humans and various
appliances (domestic electrical appliances, lighting, etc.). Thermal
energy from these warmer internal surfaces is usually delivered by two
ways: by convection and by radiation. Radiant thermal transmission can
be calculated according to the equations of long wave thermal radiation
energy transfer between the surfaces with different temperatures.
Internal heat gains could be precisely calculated if accurate areas
and temperatures of emitting surfaces were known, but this is not the
case. Therefore, for the calculation of energy consumption in buildings
the normative values of internal heat gains are used, which most
frequently are given as energy flow to floor area unit [q.sub.int],
W/[m.sup.2] (LST EN ISO 13790 2008). Heat transfer mechanism of internal
heat gains is the same as in heating devices (radiators and similar
equipment), i.e. it is based on the laws of thermal convection and long
wave thermal radiation. Thus, it can be stated that during the heating
season internal heat gains are decreasing thermal energy flow required
for heating the building in value of [[PHI].sub.in]. Then the decrease
of thermal energy flow for heating [[PHI].sub.in,t], W, at every time
step t can be calculated as follows:
[[PHI].sub.in,t] = [q.sub.in,t] x [A.sub.f], (1)
where: [q.sub.in,t]--internal heat gains at the time step t for
floor area unit of the heated spaces (rooms), W/[m.sup.2];
[A.sub.f]--floor area of the heated spaces (rooms), [m.sup.2].
2.2. The assessment of long wave sky radiation
Different temperatures between the sky dome and enclosures of the
building cause heat exchange between these surfaces. The heat exchange
on the external surfaces of the building enclosures occur as thermal
convection and long wave thermal radiation (ASHRAE 2009; Banionis et al.
2011; LST EN ISO 6946 2008). The surface heat transfer coefficient at
external surfaces of the building envelope [h.sub.se] is determined from
the sum of convective [h.sub.se,c] and radiative [h.sub.se,r] surface
heat transfer coefficients (ASHRAE 2009; Banionis et al. 2011; LST EN
ISO 6946 2008):
[h.sub.se] = [h.sub.se,c] + [h.sub.se,r]. (2)
The hemispherical emissivity value for most of the building product
surfaces, including glass panes, makes up about 0.9 (ASHRAE 2009), which
means that the surfaces absorb almost all energy of the emitted long
wave radiation. Therefore, only a very small part of this radiation
strikes the inside of the building directly even through glazed
surfaces. Long wave radiation from the sky dome is affecting the
external surfaces of the building envelope decreasing the temperature of
those surfaces. During the heating season, due to the reduced
temperatures of external surfaces of the envelope, extra transmission
heat losses occur and the required heating energy flow is enlarged by
the value of [[PHI].sub.r]. This value ([[PHI].sub.r], W) could be
calculated on the basis of calculation principles from LST EN ISO 13790
(2008) and after itemizing the equations (LST EN ISO 13790 2008):
[[PHI].sub.r] = [h.sub.se,r] x [DELTA][[theta].sub.er]/[h.sub.se,c]
+ [h.sub.se,r] x [n.summation over (k=1)] [[[epsilon].sub.lw,se,k] x
[F.sub.r,k] x [U.sub.k] x [A.sub.k]], (3)
where: k--number of appropriate building elements;
[F.sub.r,k]--form factor between the external surface of the building
element and the sky (for unshaded vertical elements [F.sub.r,k] = 0.5,
for unshaded horizontal elements [F.sub.r,k] = 1) (LST EN ISO 13790
2008); [h.sub.se,r]--external surface radiative heat transfer
coefficient could be taken as equal to 5 x [[epsilon].sub.lw],
W/([m.sup.2] x K); it corresponds to the average temperature of
10[degrees]C; [DELTA][[theta].sub.er]--average difference between the
external air temperature and apparent sky temperature; in the sub-polar
areas [DELTA][[theta].sub.er] = 9K, in the tropics
[DELTA][[theta].sub.er] = 13K, in the intermediate zones
[DELTA][[theta].sub.er] = 11K (LST EN ISO 13790 2008);
[[epsilon].sub.lw,se,k]--hemispherical emissivity of external surface of
the element k; [U.sub.k]--thermal transmittance of the element k,
W/([m.sup.2] x K); [A.sub.k]--overall projected area of the element k
with the given orientation and tilt angle [m.sup.2].
Eq. (3) is used for opaque and transparent building elements.
2.3. The assessment of solar radiation
2.3.1. Heat exchange at external surfaces of enclosures
The values of absorption coefficient for solar radiation
[[alpha].sub.sw] of the surfaces of the building products in most cases
are lesser than the values of long wave hemispherical emissivity
[[epsilon].sub.lw] (ASHRAE 2009; Banionis et al. 2011; Urbikain, Sala
2009). A part of short wave solar radiation is absorbed by both external
opaque and transparent surfaces. Therefore, a part of short wave solar
radiation does not pass inside the building even through glazed
enclosures. Heat exchange at external surfaces of enclosures proceeds as
thermal convection and long wave thermal radiation (ASHRAE 2009;
Banionis et al. 2011; LST EN ISO 6946 2008). Surface thermal
transmittance of external surfaces of enclosures [h.sub.se] is
calculated according to Eq. (2). Due to the impact of solar radiation,
the temperature of external surfaces of both opaque and transparent
enclosures becomes higher than the outdoor air temperature. The
temperature of the inside surfaces of enclosures is increasing as well.
This causes additional heat transfer at internal surfaces of enclosures
which have a mechanism similar to the heat transfer mode in heating
devices (radiators and similar equipment), i.e. it is based on the laws
of thermal convection and long wave thermal radiation. As the external
surfaces of the building are impacted by short wave solar radiation
during the heating season in this way decreasing the transmission heat
losses, the required thermal energy flow for heating is reduced by the
value [[PHI].sub.sol,ab]. on the basis of the calculation principles in
LST EN ISO 13790 (2008). After itemizing the equations given there, this
value [[PHI].sub.sol,ab,t], W, at every time step t could be calculated
as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)
where: [A.sub.k]--area of the element k of a given orientation and
tilt angle, [m.sup.2]; [I.sub.sol,k]--the mean global solar radiation
over the time step of the calculation onto appropriate element k of a
given orientation and tilt angle, W/[m.sup.2]; [F.sub.sh,k]--shading
factor by external obstacles for the surface [A.sub.k];
[[alpha].sub.sw,se,k]--solar radiation absorption coefficient of the
element k of external surfaces of the building.
2.3.2. The assessment of solar thermal energy transfer into the
rooms through transparent elements
Transparent elements of buildings (e.g. glazed areas of windows)
are partly transparent to short wave solar radiation. The transparency
for this radiation is characterized by total solar energy transmittance
[g.sub.gl,k] of the transparent element k (LST EN ISO 13790 2008;
Carmody et al. 2004):
[g.sub.gl,k] = 0.9 x [g.sub.gl,n,k], (5)
where: [g.sub.gl,n,k]--solar energy transmittance for solar
radiation which is normal to the transparent element k; 0.9 correction
factor due to the tilt angle between the solar beam and transparent
element.
The methods currently used for the calculations (LST EN ISO 13790
2008; Nielsen, Svendsen 2005) and research results of external solar
gains (Yohanis, Norton 1999; Kalema et al. 2008; Zinzi et al. 2008;
Carmody et al. 2004; Corrado et al. 2007; Orosa, Oliveira 2010; Sjosten
et al. 2003) do not consider the fact that since solar radiation
penetrates the transparent elements of the building, the wave lengths of
thermal radiation do not change, i.e. the solar radiation remains
short-wave. The same basis is used for the simulation of thermal
behaviour at window surfaces (Jurelionis, Isevicius 2008). The admitted
solar energy inside the building does not directly heat the indoor air.
The heat exchange between the admitted solar energy and indoor air could
only occur in the form of radiation, but air is highly transparent to
the thermal radiation and therefore, this exchange does not occur. The
short wave solar energy admitted into the building could be absorbed
only by the internal surfaces of the rooms. The value of absorption
coefficient for solar radiation [[alpha].sub.sw] for most of the indoor
finishing products comprises about 0.6; thus, the inside surfaces of the
rooms (partitions, floor and ceiling slabs, etc.) absorb only a part of
total solar energy admitted inside the building. As the temperature of
the inside surfaces rises up due to the solar energy admitted indoor,
the convective heat exchange between the mentioned inside surfaces and
indoor air begins, and for this reason, the indoor air is heated up.
During this convective heat exchange, the inside surfaces lose a part of
absorbed thermal energy. Thus, according to the calculation methods and
equations given in LST EN ISO 13790 (2008), only short wave solar energy
flow [[PHI].sub.sol,sw,t], W admitted inside the building at every time
step t can be calculated:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)
where: [F.sub.sh,k]--shading factor of external obstacles for the
window surface [A.sub.wd,k]; [F.sub.sh,gl,k]--shading factor of movable
shading appliances for the window surface [A.sub.wd,k] (mechanically and
electrically controlled external and internal Venetian blinds and
similar equipment); [F.sub.F,k]--ratio of the projected frame area to
the overall projected area of the glazed element; [I.sub.sol,k]--the
mean global solar radiation over the time step of calculation onto
appropriate element k with the given orientation and tilt angle,
W/[m.sup.2].
Solar energy flow [[PHI].sub.sol,lw,t], W, absorbed by the inside
surfaces of the building after passing through the transparent elements
of the building envelope and transformation into long wave thermal
energy, could be calculated at every time step t as follows:
[[PHI].sub.sol,lw,t] = [[alpha].sub.sw,si] x [[PHI].sub.sol,sw,t],
(7)
where: [[alpha].sub.sw,si]--mean solar radiation absorption
coefficient of internal surfaces of the building.
The use of solar radiation absorption coefficient
[[alpha].sub.sw,si] of inside surfaces of the building and the mechanism
of transformation of short wave thermal radiation into long wave thermal
radiation energy have not yet been regarded in the calculation methods
of energy demand for heating or cooling of the buildings (LST EN ISO
13790 2008; Nielsen, Svendsen 2005) nor in the research results
(Yohanis, Norton 1999; Kalema et al. 2008; Josikalo, Kurnitski 2007;
Zinzi et al. 2008; Carmody et al. 2004; Corrado, Fabrizio 2007; Orosa,
Oliveira, 2010; Sjosten et al. 2003; Seduikyte, Paukstys 2008). Perhaps,
by this reason the difference in the values of solar heat gains obtained
by the calculation on the basis of LST EN ISO 13790 (2008) and
experimental studies is observed; according to Kalema et al. (2008), the
solar gain utilization factor is too low for very light buildings having
no massive surfaces; as Josikalo and Kurnitski (2007) state, in the 2004
version of the standard LST EN ISO 13790, the numerical parameters of
heat gains are reasonably applicable for residential buildings, but not
for office buildings. Josikalo and Kurnitski (2007) claim that the
evaluation methods are acceptable, especially for the existing
buildings, and according to Motuziene and Juodis (2010) to office
buildings as well, but the results obtained show the annual best values
when windows are installed in northern wall. Such item is disputable.
2.4. Hourly calculation method of building heat gains. Energy
demand for heating the buildings
Time step at the calculation is assumed to be equal to one hour,
i.e. [DELTA]t = 1 h. It is considered that during this time step heat
transfer settles into a steady-state mode. The required thermal energy
flow at every time step t for heating the building is determined as
follows:
[[PHI].sub.H,t] = [H.sub.tot] x ([[theta].sub.i,t] -
[[theta].sub.e,t]) - [[PHI].sub.int,t] + [[PHI].sub.r,t] -
[[PHI].sub.sol,ab,t]; (8)
[H.sub.tot] = [H.sub.tr] + [H.sub.ve]; (9)
[H.sub.tr] = [summation]([U.sub.k] x [A.sub.k]); (10)
[H.sub.ve] = [[rho].sub.a] x [c.sub.a] x [summation] (n x V x
[b.sub.ve]), (11)
where: [[theta].sub.i,t] and [[theta].sub.e,t]--respectively,
indoor and outdoor air temperature at time step t,[degrees]C;
[H.sub.tot]--total heat transfer coefficient of the building, W/K;
[H.sub.tr]--transmission heat transfer coefficient of the building, W/K;
[H.sub.ve]--ventilation heat transfer coefficient of the building, W/K;
n--mean air change rate for ventilation, [h.sup.-1]; V--inside volume of
the building, [m.sup.3]; [b.sub.ve]--temperature adjustment factor if
the supplied air temperature is not equal to the temperature of external
environment; this value will be determined in accordance with LST EN ISO
13790 (2008); [[rho].sub.a] x [c.sub.a]--heat capacity of air per
volume, [[rho].sub.a] x [c.sub.a] = 0.34 Wh/([m.sup.3] x K).
For the determination of short wave solar gains admitted into the
building, the following presumptions are made:
--all solar radiation absorption coefficients [[alpha].sub.sw] are
the same for all inside surfaces;
--solar energy flow [[PHI].sub.sol,sw] impacts are even to all
inside surfaces, therefore, the temperature changes of all surfaces are
the same;
--external surface temperature [[theta].sub.m,surf] of the
effective thermal capacity layer d varies in the rooms (LST EN ISO 13790
2008; Carmody et al. 2004), but the temperature of the opposite internal
plane [[theta].sub.m,i] bordering this layer stays constant (see Fig.
1);
--temperature profile between the outer surface and opposite
internal plane bordering the effective thermal capacity layer is
considered to be linear (see Fig. 1);
--thermal energy flow [[PHI].sub.m] absorbed/released by effective
heat capacity of the building during the time step [DELTA]t is
proportional to the change of mean temperature [[theta].sub.d] of heat
capacity layer (see Eq. (12));
--initial time step t corresponds to the beginning of the day.
[FIGURE 1 OMITTED]
Thermal energy flow [[PHI].sub.m,t] absorbed (see Fig. 2) or
released (see Fig. 3) by the effective heat capacity layer of the rooms
can be calculated at every time step t:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (12)
where: [C.sub.m]--effective heat capacity of the building, Wh/K;
for buildings with high effective heat capacity [C.sub.m] = 102 x 8 x
[A.sub.f] Wh/K, with very low capacity--[C.sub.m] = 22.2 x [A.sub.f]
Wh/K (LST EN ISO 13790 2008).
With the enlargement of solar thermal energy flow (Fig. 2) admitted
into the building, the thermal balance of flows settles at the outer
surface of the effective heat capacity layer of the building
[[PHI].sub.m-i,t] = [[PHI].sub.sol,lw,t]--[[PHI].sub.m,t], and with the
decrease of the admitted solar energy flow (Fig. 3), the thermal balance
[[PHI].sub.m-i,t] = [[PHI].sub.sol,lw,t] + [[PHI].sub.m,t] also settles
at this surface.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
As the solar energy flow admitted into the rooms increases, the
indoor surface temperatures are increased too. If heat gains are
sufficient to heat the building, the internal surfaces of the rooms have
to emit such thermal energy flow which is required to heat the building
up to [[theta].sub.i,H,ds] indoor temperature. Until the thermal energy
flow from the surfaces [[PHI].sub.m-i,t] is less than required to heat
the building:
[[PHI].sub.H,t] [greater than or equal to] [[PHI].sub.m-i,t],
[[theta].sub.i,t] = [[theta].sub.i,H,ds], (13)
i.e., until the internal surfaces transmit the thermal energy into
the ambience with the design indoor air temperature
[[theta].sub.i,H,ds], the emitted energy flow from them at every time
step t, t+1, t+2 ... can be calculated as follows:
[[PHI].sub.m-i,t] = [h.sub.si] x [A.sub.m,tot] x
([[theta].sub.m,surf,t] - [[theta].sub.i,H,ds]), (14)
where: [A.sub.m,tot]--the total area of internal surfaces of the
rooms, [m.sup.2] could be taken as [A.sub.m,tot] = 4.5 x [A.sub.f] (LST
EN ISO 13790 2008).
Flow [[PHI].sub.m-i,t] from Eq. (3) is calculated in the following
manner: the temperatures of the surfaces are calculated at every time
step t according to Eqs. (16) and (19) and the flows into the rooms with
temperature [[theta].sub.i,H,ds] are calculated according to Eqs. (14)
and (21), i.e. in Eq. (21) the temperature is taken as
[[theta].sub.i,t+j] = [[theta].sub.i,H,ds]. At every time step t,
[[PHI].sub.m-i,t] corresponds to the higher values calculated according
to Eqs. (14) and (21).
If [[PHI].sub.H,t] [greater than or equal to] [[PHI].sub.m-1,t],
then at the initial time step which corresponds to the beginning of the
day, the thermal exchange balance equation for outer surfaces of
effective heat capacity layers of the rooms could be expressed in the
following manner:
[h.sub.si] x [A.sub.m,tot] x ([[theta].sub.m,surf,t] -
[[theta].sub.i,H,ds]) + [C.sub.m] / [DELTA]t x 0,5 x
([[theta].sub.m,surf,t] - [[theta].sub.m,surf,t-1]) =
[[PHI].sub.sol,lw,t], (15)
and temperature [[theta].sub.m,surf,t] could be calculated from Eq.
(15):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (16)
where: [[theta].sub.m,surf,t-1] = [[theta].sub.i,H,ds].
When heat flow from the internal surfaces of the rooms becomes
higher than it is required for heating, the inside air temperature
begins to increase. In this case the surfaces transmit thermal energy
flow into the ambience with enlarged air temperature of the rooms, in
other words, the condition of Eq. (13) is not fulfilled. It is
considered that this occurs at the time step t+j, and the temperature of
the rooms is [[theta].sub.i,t+j]. At that moment such balance of thermal
flows settles down:
--balance of heat exchange between the heat flow required to heat
the rooms up to the temperature [[theta].sub.i,t+j] and the flow from
the internal surfaces of the rooms into the rooms with
[[theta].sub.i,t+j] temperature:
[H.sub.tot] x ([[theta].sub.i,t+j] - [[theta].sub.e,t+j) -
[[PHI].sub.int,t+j] + [[PHI].sub.r,t+j] - [[PHI].sub.sol,ab,t+j] =
[h.sub.si] x [A.sub.m,tot] x ([[theta].sub.m,surf,t+j] -
[[theta].sub.i,t+j]); (17)
--balance of heat exchange between the heat flows from the internal
surfaces plus effective heat capacity layer and solar long wave thermal
flow from internal surfaces:
[h.sub.si] x [A.sub.m,tot] x ([[theta].sub.m,surf,t+j] -
[[theta].sub.i,t+j]) + [C.sub.m] / [DELTA]t x 0,5 x
([[theta].sub.m,surf,t+j] - [[theta].sub.m,surf,t-1+j]) =
[[PHI].sub.sol,lw,t+j]. (18)
The Eqs. (17) and (18) comprise an equation system and its solution
enables calculating the temperatures of internal surfaces
[[theta].sub.m,surf,t+j] and indoor air temperatures [[theta].sub.i,t+j]
of the rooms at the time step t+j:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (19)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20)
By knowing the internal surface temperature
[[theta].sub.m,surf,t+j] of the rooms at the time step t+j and the
indoor air temperature [[theta].sub.i,t+j] of the rooms, the heat flow
between the internal surfaces and indoor air could be calculated as
follows:
[[PHI].sub.m-i,t+j] = [h.sub.si] x [A.sub.m,tot] x
([[theta].sub.m,surf,t+j] - [[theta].sub.i,t+j]). (21)
The heat flow from the heating system [[PHI].sub.H,nd,t], which is
required to maintain the design indoor air temperature
[[theta].sub.i,H,ds], could be calculated in such manner:
if [[theta].sub.i,t] = [[theta].sub.i,H,ds], [[PHI].sub.H,nd,t] =
[[PHI].sub.H,t] - [[PHI].sub.m-i,t], if [[theta].sub.i,t] >
[[theta].sub.i,H,ds] [[PHI].sub.H,nd,t] = 0. (22)
Total daily amount of energy [Q.sub.H,nd,day], required to heat the
rooms up to the design indoor air temperature [[theta].sub.i,H,ds], is
calculated by the following formula:
[Q.sub.H,nd,day] = [24.summation over (t=1)] ([[PHI].sub.H,nd,t] x
[DELTA]t). (23)
The total rate of heat gains [[PHI].sub.gn,H,t] at every time step
t required to heat the rooms up to the design indoor air temperature
[[theta].sub.i,H,ds], is calculated in such manner:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (24)
The following formula is used for calculating the total daily
amount of heat gains [Q.sub.gn,H,day], required to heat the rooms up to
the design indoor air temperature [[theta].sub.i,H,ds]:
[Q.sub.gn,H,day] = [24.summation over (t=1)] ([[PHI].sub.gn,H,t] x
[DELTA]t). (25)
2.5. Hourly calculation method of building heat gains. Energy
demand for cooling the building
The calculation of energy demand for cooling is similar to the
calculation method of energy demand for heating the building. First of
all, the design indoor air temperature [[theta].sub.i,C,ds] is chosen,
i.e. the maximal allowable indoor temperature. Usually for the
calculations of energy needed for cooling it is considered to be
26[degrees]C. The calculations are performed as follows:
--indoor air temperature [[theta].sub.i,t] at every time step t is
calculated according to Eqs. (13)-(19). If the condition of Eq. (13) is
fulfilled, this temperature will be equalled to [[theta].sub.i,C,ds], if
not--to the temperature [[theta].sub.i,t+j];
--if [[theta].sub.i,t] [less than or equal to]
[[theta].sub.i,C,ds], there is no need to cool the rooms;
--if [[theta].sub.it] > [[theta].sub.i,C,ds], the rooms ought to
be cooled, and the required cool flow at every time step t is calculated
using the following formula:
[[PHI].sub.C,nd,t] = [H.sub.tot] x ([[theta].sub.i,t] -
[[theta].sub.i,C,ds]). (26)
Total daily amount of cooling energy [Q.sub.gn,C,day], required to
cool the rooms down to the design indoor air temperature
[[theta].sub.i,C,ds], is calculated in such manner:
[Q.sub.C,nd,day] = [24.summation over (t=1)]([[PHI].sub.C,nd,t] x
[DELTA]t). (27)
3. The analysis of calculation results obtained by various methods
The analysis of calculation results acquired by the described
hourly calculation method and the hourly and monthly calculation methods
was performed. The calculation model was chosen on the basis of extreme
impact of heat gains to thermal energy demand for heating or cooling.
The model was constructed as a part of the building with only one
external wall. The whole area of this wall was occupied by windows.
Adjacent rooms of this part of the building kept up the same temperature
as in the modelled rooms. In other words, there was no heat exchange at
every considered time step between the modelled and the adjacent rooms.
3.1. Data of the chosen model
Data on the rooms: floor area [A.sub.f] = 100 [m.sup.2] (10 x 10
m); height 2.5 m; volume V = 100 [m.sup.3]. Data on the windows:
vertical; South oriented; area [A.sub.w,k] = [A.sub.sol,k] = 25
[m.sup.2]; U = 1.3 W/([m.sup.2] x K); [[epsilon].sub.lw,e.s.] = 0.9;
[[alpha].sub.w,e.s.] = 0.12; [F.sub.r,k]=0.5; [F.sub.sh,k]=1;
[F.sub.sh,gl,k] = 1; [F.sub.f,k] = 0.2; [g.sub.gln,k] = 0.5. Other data:
[h.sub.se,c]= 25 W/([m.sup.2]-K); [h.sub.si]=7.7 W/([m.sup.2]-K);
[[alpha].sub.sw,i.s.] = 0.6; [C.sub.m] = 10280 Wh/K; n = 0.5 [h.sup.-1];
[b.sub.ve] = 1; natural ventilation; [[theta].sub.i,H,ds] =
20[degrees]C; [[theta].sub.e,t], = 5.5[degrees]C; [g.sub.int,t] = const
= 1.2 W/[m.sup.2]; [DELTA][[theta].sub.er] = 10 K; according to Eq. (3)
calculated [[PHI].sub.r] = const = 22.31 W. The calculation of the
global solar radiation [I.sub.sol,k,t] in April according to the
suggested hourly calculation method is based on the Lithuanian climate
data. They are presented in Table 1 below together with the calculation
results. For the calculations according to the method of (LST EN ISO
13790 2008), [I.sub.sol,k] = 113 W/[m.sup.2].
3.2. Energy demand for heating. The analysis of results acquired by
the presented hourly calculation method and the hourly method of LST EN
ISO 13790 (2008)
The method presented in this article uses the monthly mean hourly
solar radiation data as well as the mean hourly data of other heat
gains. Monthly mean heat gains or indices of energy use are established
according to the calculation regarding each day of the month (e.g. 30
days of April). In case of our calculation model, the calculation
results during the month, in comparison with the results of the first
day of the month (Table 1), vary only slightly. The results of the
calculation for heating energy flow demand [[PHI].sub.H,nd,t] during
each day of April are presented in Fig. 4, as well as the results
acquired according to the LST EN 13790 (2008) hourly method.
[FIGURE 4 OMITTED]
The LST EN 13790 (2008) method does not specify whether one- or
several-day calculations should be considered when establishing the
values of hourly energy demand during the day. Therefore, aiming at a
better analysis of this method, the heat flow energy demand for heating
the rooms [[PHI].sub.H,nd,t] was calculated during the same period of 30
days. It was difficult to evaluate the results of the calculation, as
they vary from 700 W heating energy flow demand to about 100 W cooling
energy flow demand during the first few days. For the comparison of
results acquired by these two different calculation methods the results
of the first few days of the month were used.
The first day results calculated according to the LST EN 13790
(2008) method show the 7169 Wh/day amount of heating energy demand. This
result is close to the result acquired by the hourly calculation method
presented in this paper (9486 Wh/day). The differences in the
calculation results for the following days acquired by the mentioned
calculation methods markedly grow. It is shown in detail in Fig. 5 where
the calculation results of the first three days are displayed. Data in
Fig. 6 expressing the results of our calculation method from 0 to 24
hour correspond to the results given in Table 1.
[FIGURE 5 OMITTED]
The LST EN 13790 (2008) method uses daily mean solar radiation data
for calculations, but indoor temperature during the day is calculated by
hours and varies in a considerably wide range. The calculation results
of the indoor temperature calculated by our and LST EN 13790 (2008)
methods are presented in Fig. 6. The difference between the calculation
results is not significant, but in accordance with the data presented
earlier, it is seen that it makes an essential impact on the calculation
results of energy demand for heating and cooling of the rooms. The
energy demand for heating diminishes with every following day. According
to the calculation results from Fig. 6, presenting the LST EN 13790
(2008) calculation method, the indoor temperature is increasing and
energy demand for heating is decreasing every day (Figs. 4 and 5). This
shows that the LST EN 13790 (2008) method has to apply additional
conditions not described by this method in order to avoid divergences of
the calculation results.
[FIGURE 6 OMITTED]
3.3. Energy demand for heating. The analysis of results acquired by
the presented hourly calculation method and the LST EN ISO 13790 (2008)
monthly calculation method
The results acquired using the LST EN 13790 monthly calculation
method are the following: the sum of transmission and ventilation heat
losses during the day makes up 26100 Wh/day; heat gains 26674 Wh/day;
[[tau].sub.H,0] = 15; [[alpha].sub.H,0] = 1; t = 137.04; [[alpha].sub.H]
= 10.14; [[gamma].sub.H] = 1.02; [[eta].sub.H,gn] = 0.90; the amount of
heat gains utilized for heating of the building makes up 26674 0.9 =
24006 Wh/day; energy demand for heating of the building makes up 26100 -
24006 = 2094 Wh/day. The calculation result (2094 Wh/day) is more than 4
times lesser than the monthly mean result obtained by our hourly
calculation method (9486 Wh/day). Moreover, this result (2094 Wh/day)
differs from the first day result (7169 Wh/day) obtained by the LST EN
ISO 13790 (2008) hourly method calculation too.
The difference between our and LST EN 13790 (2008) monthly methods
emerges due to the differences in estimation of solar heat gains inside
the rooms:
--monthly method presented in LST EN ISO 13790 (2008) assumes that
the whole amount of solar radiation admitted indoor turns into long wave
thermal energy. In other words, it is assumed that solar radiation
absorption coefficient of inside surfaces of the rooms is
[[alpha].sub.sw] = 1. When calculating energy indices for heating, the
method takes into account the fact that solar heat gains may be higher
than the heat losses in certain times of the day and at these times
heating of the rooms is not required. It means that all solar heat gains
are not used to heat the rooms, i.e., it is assumed that only a
[[eta].sub.H,gn] part of solar heat gains is related to the energy
demand for heating;
--the hourly calculation method presented in this paper assumes
that only a part [[alpha].sub.sw] of solar heat gains admitted indoor is
used for heating the rooms, i.e., this part is expressed by solar
radiation absorption coefficient of indoor surfaces. Energy indices for
heating of the building are calculated according to Eqs. (24) and (25)
for each hour of the day and the hourly indoor and outdoor temperatures
are taken into account. Therefore, there is no need to apply any
correctives to the calculation results of solar heat gains.
For more particular analysis of both methods mentioned above
additional calculations using different monthly mean outdoor
temperatures were carried out. It was assumed that solar radiation
absorption coefficient of indoor surfaces is the same as in the LST EN
13790 (2008) method, i.e., [[alpha].sub.sw] = 1 according to our hourly
method. In all calculations the data on solar radiation were taken from
Table 1. The calculation results are given in Table 2. This table also
contains the results calculated according to the hourly method of LST EN
13790 (2008).
The results in Table 2 show that the results of our hourly method
are much closer to the results of the LST EN 13790 monthly method than
to the results of the LST EN 13790 hourly method.
3.4. Energy demand for cooling. The analysis of results acquired by
the presented hourly calculation method and LST EN ISO 13790 (2008)
hourly method
For summertime calculations the data of July from Lithuanian
climate database were used, i.e., [[theta].sub.i,C,ds] = 26[degrees]C;
[[theta].sub.e,t]=16.72[degrees]C, the other income data are the same as
for the calculations of heating energy demand. The monthly mean of July
and the data on solar radiation [I.sub.sol,k,t] are given in Table 3
below together with the calculation results obtained by our hourly
calculation method. For the calculations according to the LST EN ISO
13790 (2008) method, [I.sub.sol,k] = 122 W/[m.sup.2].
The calculation results of the required cooling energy flow
[[PHI].sub.C,nd,t] on each day of July are presented in Fig. 7. The data
expressing the results of our calculation method from 0 to 24 hour
correspond to the results in Table 3.
According to the LST EN 13790 (2008) hourly method, the calculation
results reflecting the first few days of July are varying from 400 W
energy flow for heating to about 600 W energy flow for cooling. To
compare the results of different calculation methods the calculation
results of the first few days were used. The first day calculation
results according to the LST EN 13790 (2008) hourly method shows cooling
energy demand of 1743 Wh/day. This result is close to the result of the
first day cooling energy demand calculated by our hourly calculation
method (1412 Wh/day). Our method gives value of 2109 Wh/day as monthly
mean cooling energy demand. The differences in calculation results by
the use of these different methods during the following days of July
grow markedly.
3.5. Energy demand for cooling. The analysis of results acquired by
the presented hourly calculation method and LST EN ISO 13790 (2008)
monthly method
The results acquired using the LST EN 13790 (2008) monthly
calculation method are the following: the sum of transmission and
ventilation heat losses during the day makes up 16704 Wh/day; heat gains
28582 Wh/day; [[tau].sub.C,0] = 15; [[alpha].sub.C,0] = 1; [tau] =
137,04; [[alpha].sub.C] = 10.14; [[gamma].sub.c] = 1.71;
[[eta].sub.c,ls] = 0.998.
Taking into account the dimensionless utilization factor for heat
losses [[eta].sub.c,ls], the sum of transmission and ventilation heat
losses during the day makes up 16704-0.998 = 16670 Wh/day; energy demand
for cooling the building makes up 28582 - 16670 = 11912 Wh/day.
[FIGURE 7 OMITTED]
The calculation result of cooling energy demand (11912 Wh/day)
differs from the monthly mean result of our hourly calculation method
(2109 Wh/day) by more than 5 times. Additionally, this result (11912
Wh/day) is almost 7 times higher than the first day calculation result
(1743 Wh/day) obtained by the LST EN 13790 (2008) hourly method.
Similarly as in case of heating energy demand calculations, the
differences between our and LST EN 13790 (2008) monthly methods emerge
due to the different assessment of solar heat gains admitted indoors.
The monthly method in LST EN 13790 (2008) assumes that the whole
amount of solar radiation admitted indoors turns into long wave thermal
energy. In other words, it is assumed that solar radiation absorption
coefficient of inside surfaces of the rooms is [[alpha].sub.sw] = 1.
The hourly calculation method (LST EN 13790 2008) takes into
account the fact that with the enlargement of solar heat gains, the
indoor temperature rises; likewise, the heat losses of the rooms
increase in the calculation of energy demand for cooling. It means that
not all solar heat gains are related to cooling energy demand, i.e., it
is assumed that a (1-[[eta].sub.C,ls]) part of transmission and
ventilation heat losses are not related to the energy required for
cooling of the rooms.
Our hourly calculation method determines energy indices for cooling
of the building according to Eqs. (26) and (27) for each hour of the day
and the hourly indoor and outdoor temperatures are taken into account as
well. Therefore, there is no need to introduce any correctives to the
calculation results.
For more particular analysis of both methods mentioned above
additional calculations using different monthly mean outdoor
temperatures were carried out. It was assumed that solar radiation
absorption coefficient of indoor surfaces is the same as in the LST EN
13790 (2008) method, i.e., [[alpha].sub.sw] = 1 calculation according to
our hourly method. In the calculations, the data of solar radiation was
taken from Table 3. The calculation results are given in Table 4 which
also contains the results received applying the hourly method of LST EN
13790 (2008).
Table 4 shows that the results of our hourly method for cooling
energy need are much closer to the results of the LST EN 13790 (2008)
monthly method than to the results of the LST EN 13790 (2008) hourly
method.
4. Experimental check-up
The check-up of the considered calculation methods was carried out
in the rooms with one external wall at interjacent floor. The rooms were
equipped with office furniture and floor covering of linoleum. The
colour of all internal surfaces was assumed to be pale grey. The other
partitions were facing the rooms with similar indoor climate. Thus, the
heat exchange with other rooms was negligible and was not taken into
account.
The main characteristics of the selected rooms: orientation N-E,
(azimuth 58[degrees]), heated area [A.sub.f] = 18.18 [m.sup.2], height
2.85 m, [[alpha].sub.sw,si] = 0.6, [C.sub.m] = 1868 Wh/K;
windows--vertical, [A.sub.wd,k] = 7 [m.sup.2], [U.sub.wd] = 1.9
W/([m.sup.2] x K), [[epsilon].sub.lw,wd,se] = 0.9,
[[alpha].sub.sw,wd,se] = 0.12, [F.sub.r,wd] = 0.5, [F.sub.sh,wd=] 0.9,
[F.sub.F] = 0.26, [g.sub.gl,n,wd] = 0.55, [h.sub.se,c] = 25 W/([m.sup.2]
x K), his = 7.7 W/([m.sup.2] x K); the area of external wall [A.sub.w] =
7.39 [m.sup.2], [U.sub.w] = 1.0 W/([m.sup.2] x K),
[[epsilon].sub.lw,w,se] = 0.9, [[alpha].sub.sw,w,se] = 0.12, [F.sub.r,w]
= 0.5, [F.sub.sh,w] = 0.9.
Other data: the vents in the rooms were sealed, so air infiltration
was eliminated (n = 0 [h.sup.-1]); indoor air temperature was maintained
at 16[degrees]C ([[theta].sub.i,H,ds] = 16[degrees]C).
Outdoor air parameters were registered by a climate station near
the building every minute. Solar radiation to the horizontal surface was
measured directly and then recalculated for the considered azimuth.
Indoor air temperature was measured in four places.
Electric air heater of 19.8 W power was used in the rooms, and
internal heat gains were assumed to be continuous and equal to 1.1 W.
The measurements of mean indoor temperature and outdoor air
parameters of four days period were taken for the analysis at the
check-up of the calculation precision and are presented in Fig. 8.
The comparison of the calculation results according to our method
and the hourly method presented in LST EN 13790 (2008) with experimental
data is given in Fig. 9.
On the basis of the result comparison, it could be stated that the
trends of temperature changes in the rooms are described more accurately
when the suggested method is used than by the standard hourly method of
LST EN ISO 13790 (2008). It ought to be admitted that both calculation
methods, hourly from LST EN ISO 13790 (2008) and the one introduced in
this paper, are used for the design purposes mostly, for this reason,
the generalized thermal-technical data of the rooms (the area of
internal surfaces, effective heat capacity of the building, solar
radiation absorption coefficient) are applied. Because of this, the
obtained results describe the principal trends of temperature change in
the rooms in regard to the thermal-technical properties of the building
construction, indoor air parameters, and climate impact.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
The temperature in the considered rooms during the day ought to
vary gradually due to the heat gains from outside according to the
calculation results, while the actual temperature changes occur almost
at the same time with alteration of solar radiation flux. A certain part
of surfaces in real rooms have low heat capacity, they quickly become
warm or cool, and heat is instantly transferred to the indoor air by
convection or radiation. The surfaces with high heat capacity (massive)
slowly respond to the short-tempered temperature changes in the rooms
caused by the surfaces of low heat capacity. Therefore, both the
properties of finish materials and equipment, and the generalized
thermal-technical data of the considered rooms have a significant
influence on the actual trend of temperature change. This must be taken
into account in case of design and analysis of thermal behaviour and
energy demand for heating or cooling of the rooms.
5. Conclusions
The methods currently used for the calculations of external solar
heat gains do not consider the fact that the rate of solar thermal
radiation energy admitted indoors through transparent elements of the
building is not adequate to the rate of thermal energy absorbed by the
rooms. The rate of transition of radiated solar short wave thermal
energy into the long wave thermal energy depends on the solar radiation
absorption coefficient of the inside surfaces of the rooms. The value of
solar radiation absorption coefficient of internal surfaces has a great
impact on the amounts of absorbed external heat gains in the rooms.
Therefore, according to the calculations applying the hourly method
introduced in this paper and estimating the solar radiation absorption
coefficient of indoor surfaces, the determined energy demand for heating
of the rooms is greater, and lesser for cooling than the values obtained
by the monthly calculation method of LST EN ISO 13790 (2008) usually
applied in practice.
The method proposed in this paper differs from others because it
estimates physical laws of transition of short wave solar radiation
admitted indoors into long wave thermal energy. This method is also
different from most of others because it uses hourly monthly mean data
for each hour of the day rather than daily mean global solar radiation
data.
The calculation of internal heat gains and sky dome radiation by
our method is linked to the physics of phenomena and the related values
of the mentioned gains slightly differ from the method of LST EN ISO
13790 (2008).
The proposed hourly calculation method enables calculating the
indoor temperature each hour of the day and hourly energy demand for
heating and cooling of the rooms.
After the analysis of different calculation methods of energy
demand for buildings, it was determined that if the whole solar
radiation passed indoors through glazed fenestration and were taken as
external heat gains, i.e., as it is given in the LST EN ISO 13790 (2008)
method, the calculation results of monthly mean energy demand for
heating and cooling of the building would only slightly differ from the
calculation results of the monthly method of LST EN ISO 13790 (2008).
doi: 10.3846/13923730.2012.689994
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Edmundas Monstvilas (1), Vytautas Stankevicius (2), Jurate
Karbauskaite (3), Arunas Burlingis (4), Karolis Banionis (5)
Institute of Architecture and Construction of Kaunas University of
Technology, Tunelio g. 60, LT-44405 Kaunas, Lithuania
E-mails: (1)
[email protected]; (2)
[email protected];
(3)
[email protected] (corresponding author); (4)
[email protected];
(5)
[email protected]
Received 14 Sept. 2011; accepted 16 Jan. 2012
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.
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.
Jurate KARBAUSKAITE. PhD. 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.
Arunas BURLINGIS. PhD. 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.
Karolis BANIONIS. PhD. 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.
Table 1. Calculation results of indices related to the thermal energy
for heating
Equation no: (4) (6)
Time, [I.sub. [[PHI].sub. [[PHI].sub.
h sol,k,t]; sol,ab,t]; sw,ab,t];
W W W
1 0.00 0
2 0.00 0
3 0.00 0
4 0.00 0
5 2 0.26 18
6 14 1.85 126
7 43 5.68 387
8 120 15.86 1080
9 209 27.63 1881
10 294 38.87 2646
11 343 45.35 3087
12 368 48.65 3312
13 369 48.78 3321
14 332 43.89 2988
15 268 35.43 2412
16 194 25.65 1746
17 108 14.28 972
18 38 5.02 342
19 12 1.59 108
20 0.00 0
21 0.00 0
22 0.00 0
23 0.00 0
24 0.00 0
Equation no: (7) (8) (13), (16),
(19)
Time, [I.sub. [[PHI].sub. [[PHI].sub. [Q.sub.m,
h sol,k,t]; sol,lw,t]; H,t]; surf,t] or
W W W [Q.sub.m,
surf,t+j];
[degrees]C
1 0 990 20.00
2 0 990 20.00
3 0 990 20.00
4 0 990 20.00
5 2 11 990 20.00
6 14 76 988 20.01
7 43 232 984 20.03
8 120 648 974 20.09
9 209 1129 962 20.19
10 294 1588 951 20.31
11 343 1852 944 20.48
12 368 1987 941 20.68
13 369 1993 941 20.88
14 332 1793 946 21.03
15 268 1447 954 21.12
16 194 1048 964 21.12
17 108 583 976 21.03
18 38 205 985 20.87
19 12 65 988 20.69
20 0 990 20.49
21 0 990 20.30
22 0 990 20.18
23 0 990 20.11
24 0 990 20.06
Total: 23397
Equation no: (13), (20) (22) (24)
Time, [I.sub. [Q.sub.i,t] [[PHI].sub. [[PHI].sub.
h sol,k,t]; or H,nd,t; gn,H,t;
W [Q.sub.i,t+j]; W W
W
1 20.00 990 98
2 20.00 990 98
3 20.00 990 98
4 20.00 990 98
5 2 20.00 985 102
6 14 20.00 955 133
7 43 20.00 871 217
8 120 20.00 646 442
9 209 20.00 312 776
10 294 20.34 0 951
11 343 20.52 0 944
12 368 20.71 0 941
13 369 20.90 0 941
14 332 21.05 0 946
15 268 21.13 0 954
16 194 21.13 0 964
17 108 21.04 0 976
18 38 20.88 0 985
19 12 20.70 0 988
20 20.51 0 990
21 20.32 0 990
22 20.00 370 717
23 20.00 620 468
24 20.00 769 319
Total: 9486 15134
Table 2. Energy demand for heating, calculation results by three
different calculation methods at various outdoor temperatures
Monthly mean temperature, [degrees]C
-10 0 5.5 10 15
Amount of daily mean energy 27142 9922 1179 146 56
demand for heating
[Q.sub.H,nd,day] according
to our method (monthly mean
value), Wh/day
Amount of daily mean energy 30811 15558 7169 305 -7322
demand for heating
[Q.sub.H,nd,day] according
to the LST/EN ISO 13790
hourly method (first day
value), Wh/day
Utilization factor for heat 1 0.99 0.9 0.67 0.34
gains [[eta].sub.H,gn]
Amount of daily mean energy 27336 9669 2094 110 0,1
demand for heating
[Q.sub.H,nd,day] according
to the LST/EN ISO 13790
monthly method, Wh/day
Table 3. Calculation results of indices related to thermal energy for
cooling
Equation no: (4) (6)
Time, [I.sub. [[PHI].sub. [[PHI].sub.
h sol,k,t] sol,ab,t]; sol,sw,t];
W/[m.sup.2] W W
1 0.00 0
2 0.00 0
3 0.00 0
4 3 0.40 27
5 20 2.64 180
6 47 6.21 423
7 76 10.05 684
8 131 17.32 1179
9 218 28.82 1962
10 298 39.40 2682
11 346 45.74 3114
12 362 47.86 3258
13 357 47.20 3213
14 326 43.10 2934
15 274 36.22 2466
16 206 27.23 1854
17 126 16.66 1134
18 75 9.92 675
19 43 5.68 387
20 16 2.12 144
21 2 0.26 18
22 0.00 0
23 0.00 0
24 0.00 0
Equation no: (7) (8) (13), (16),
(19)
Time, [I.sub. [[PHI].sub. [[PHI].sub. [Q.sub.m,
h sol,k,t] sol,lw,t]; H,t]; surf,t] or
W/[m.sup.2] W W [Q.sub.m,
surf,t+j];
[degrees]C
1 0 598 26.00
2 0 598 26.00
3 0 598 26.00
4 3 16 598 26.00
5 20 108 596 26.01
6 47 254 592 26.04
7 76 410 588 26.07
8 131 707 581 26.12
9 218 1177 569 26.24
10 298 1609 559 26.44
11 346 1868 553 26.69
12 362 1955 550 26.95
13 357 1928 551 27.21
14 326 1760 555 27.42
15 274 1480 562 27.58
16 206 1112 571 27.66
17 126 680 582 27.66
18 75 405 588 27.61
19 43 232 593 27.51
20 16 86 596 27.40
21 2 11 598 27.27
22 0 598 27.14
23 0 598 27.0109
24 0 598 26.8843
Total: 13973
Equation no: (13), (20) (26)
Time, [I.sub. [Q.sub.i,t] [[PHI].sub.
h sol,k,t] or [Q.sub. C,nd,t];
W/[m.sup.2] i,t+j]; W
[degrees]C
1 26.00 0.0
2 26.00 0.0
3 26.00 0.0
4 3 26.00 0.0
5 20 26.00 0.0
6 47 26.00 0.0
7 76 26.00 0.0
8 131 26.00 0.0
9 218 26.27 -20.4
10 298 26.47 -35.3
11 346 26.72 -53.7
12 362 26.97 -73.0
13 357 27.22 -91.5
14 326 27.43 -107.3
15 274 27.58 -118.8
16 206 27.66 -124.8
17 126 27.66 -124.4
18 75 27.60 -120.1
19 43 27.51 -113.5
20 16 27.40 -104.9
21 2 27.27 -95.3
22 27.14 -85.7
23 27.02 -76.3
24 26.89 -67.0
Total: -1412
Table 4. Energy demand for cooling, calculation results by three
different calculation methods at various outdoor temperatures
Monthly mean temperature,
[degrees]C
12 16.72 20 24
Amount of daily mean energy 4190 11609 16773 23083
required for cooling
[Q.sub.C,nd,day] according to our
method (monthly mean value),
Wh/day
Amount of daily mean energy -5457 1743 6746 12847
required for cooling
[Q.sub.C,nd,day] according to the
LST-EN ISO 13790 hourly method
(first day value), Wh/day
Utilization factor for heat gains 0.965 0.998 1 1
[[eta].sub.H,gn]
Amount of daily mean energy 4486 11908 17782 24982
required for cooling
[Q.sub.C,nd,day] according to the
LST-EN ISO 13790 monthly method,
Wh/day
