Journal of Building Engineering 23 (2019) 291–300
Contents lists available at ScienceDirect
Journal of Building Engineering
journal homepage: www.elsevier.com/locate/jobe
A combined analytical model for increasing the accuracy of heat emission
predictions in rooms heated by radiators
T
Karl-Villem Võsaa, Andrea Ferrantellia, , Jarek Kurnitskia,b
⁎
a
b
Tallinn University of Technology, Department of Civil Engineering and Architecture, Ehitajate tee 5, 19086 Tallinn, Estonia
Aalto University, Department of Civil Engineering, P.O.Box 12100, 00076 Aalto, Finland
ARTICLE INFO
ABSTRACT
Keywords:
Water radiator
Heat emission
Energy performance
Analytical models
Computer simulations
Operative temperature
Radiative temperature
The efficiency of heat emitters plays an important role in the improvement of building energy performance,
especially in the context of system and product comparison. In particular, it can be directly related to thermal
comfort via the operative temperature that is effectively sensed by the users.
For the first time in the literature, in this paper we develop a combined analytical model for room and
radiator that computes directly the heat output required to maintain a specific operative temperature. The total
heat balance of the enclosure is used to accurately quantify and compare the heat emission losses of different
radiator types via an analytical calculation of the operative temperature. This determines the efficiency of a
selection of panel radiators with different surface temperature, radiation fraction and number of panels, which
were tested in a chamber conforming to the EN 442-2 standard.
Additionally, we assess the related annual energy consumption in different climates by carrying out annual
simulations in old (without heat recovery) and new (with heat recovery) building types located in Tallinn,
Estonia and Strasbourg, France. In the new building we find a similar performance for all the radiators. In the old
building however, one radiator outperforms the other two with up to 1.38% lower annual energy consumption,
due to smaller rear losses and higher thermal comfort provided by the larger front panel surface.
1. Introduction
In the context of thermal comfort and emission efficiency in buildings, the physical modelling of heat transfer processes is of primary
importance for an accurate assessment of energy saving capabilities
[1–3].
Low- and zero-energy buildings increase the energy performance,
and accordingly demand an increasing heat emission efficiency. A
higher resolution in the related calculations is therefore mandatory
when assessing heat emitters in general, and panel radiators in particular.
Nevertheless, at the moment the manufacturers do not have any
standard methodology for determining the devices' heat emission efficiency. For instance, the authors of [4] found experimentally a fairly
different performance compared to the one listed by the manufacturer.
Obviously, it is of great importance to know whether the radiator type
would lead to a 10% or 1% difference in heating energy demand. A
common high resolution method is therefore needed rather urgently.
Another issue concerns the operative temperature top , namely the
average of mean air- and radiant-temperatures that approaches the
⁎
temperature sensed by the user [1]. Even though it constitutes a fundamental parameter of international thermal comfort standards such as
[2], in the EN 15316-2:2017 top is not adopted for computing heating
system losses from the air temperature (basically due to loss of resolution for radiation effects) [5].
On the other hand, it is now well understood that, depending on the
radiant temperatures in the enclosure, using the top instead of the air
temperature induces sizeable differences in the heat emission losses of
the radiators [6–9].
The operative temperature is also central to high resolution problems in the optimization of heating emissions towards energy saving
and thermal comfort [10,11]: where should we locate the radiator, how
are the size and internal design important? Answers to these questions
require a resolution level that has not been achieved so far; recent experimental studies (see e.g. [4]) were not conclusive, as they found
contrasting results such as differing measured heat emissions in different tests. However it is certain that the radiator design has a critical
impact on its emission losses, as illustrated in Fig. 1.
Attempts to model the heat exchange induced by the heaters' output
in internal spaces have been carried out for a long time [12–16].
Corresponding author.
E-mail address: andrea.ferrantelli@taltech.ee (A. Ferrantelli).
https://doi.org/10.1016/j.jobe.2019.02.009
Received 23 November 2018; Received in revised form 7 February 2019; Accepted 10 February 2019
Available online 13 February 2019
2352-7102/ © 2019 Elsevier Ltd. All rights reserved.
Journal of Building Engineering 23 (2019) 291–300
K.-V. Võsa, et al.
Nomenclature
T
t
top
tMRT
tin
tout
tln
ta
te
tse
tsi
tr
qri
qre
qci
qce
qcr
qw
qbw
Absolute temperature [K]
Temperature [°C]
Operative temperature [°C]
Mean radiant temperature [°C]
Supply water temperature [°C]
Radiator outlet temperature [°C]
Logarithmic mean temperature difference [°C]
Indoor air temperature [°C]
External temperature [°C]
Temperature of external surfaces [°C]
Temperature of internal surfaces [°C]
Radiator surface temperature [°C]
Net radiative heat exchanged between radiator and internal surfaces [W]
Net radiative heat exchanged between internal and
F r si
Ar
Asi
Ase
d
cp
Regarding these earlier works, Inard et al. presented in [17] a zonalmethod representation of thermal exchanges in enclosed spaces. They
found in particular that on the view point of energy consumption and
thermal comfort, distributed heat sources (a hot-water heated floor and
an electrical heated ceiling) presented a slight advantage over localized
sources (a hot-water radiator and an electrical convector). This constitutes a remarkable precursor of actual numerical studies, e.g. with
standard IDA ICE models [18].
Focusing on radiators, Harris investigated in [19] the effect of a
reflecting metal foil inserted behind the central heating radiators. Experiments performed in an environmental chamber showed a 30% decrease of the heat loss through the area of wall immediately behind the
radiator.
The above methodology is therefore extremely useful for investigating the complex processes involved in the physics of space
external surfaces [W]
Convective heat exchanged at internal surfaces [W]
Convective heat exchanged at external surfaces [W]
Convective heat transferred from the radiator [W]
Heat loss through the external wall [W]
Radiator back wall losses [W]
Total radiator heat output [W]
Total exchange factor from radiator to internal surfaces [-]
Radiator panel area [m2]
Internal surfaces area [m2]
External surface area [m2]
Emissivity [-]
Thickness [m]
Density [kg/m3]
Thermal conductivity [W/mK]
Specific heat at constant pressure [J/kg K]
heating. Specifically, there is a compelling need to quantify efficiently
the performance differences from different types of radiators [4,20–22].
Several attempts to do so have been made in the recent past: an analytical model for comparing the efficiency of different radiators was
first introduced in [4] and further developed in [23]. Both studies
considered a 11-type, a 22-type parallel connected and a 22-type serial
connected panel radiators with similar standard heat outputs, with laboratory measurements performed in a test chamber corresponding to
the standard EN 442-2:2003 [24]. The energy saving capability of the
radiators was measured in [4] at the same operative temperature.
In [23], new laboratory measurements with updated devices were
combined with new calibrations, where the heat outputs were instead
adjusted to the difference between top and the average T of the cooled
surfaces. This methodological refinement allowed to identify the most
performing radiator in the 11-type, due to its larger panel surface area.
Unfortunately, all these encouraging results do not comprise the
direct calculation of a specific operative temperature as induced by the
radiator surface temperature and heat output. Since these are easily
controlled parameters of each device, they constitute a reliable means
for comparing different emitters.
As a novel result in the literature, we accomplish this task in the
present paper, by extending the methodology developed in [23] from
the EN 442-2 test chamber to a real room, both windowed and windowless. We formulate an analytical steady-state heat transfer model
that calculates the heat balance for both room and radiator in the enclosure, assuming adiabatic internal walls and heat flux only through
the external wall.
The operative temperature is determined from formulas listed in ISO
7726:1998 [2], while for computing the convective heat transfer
coefficients we use two different methods. The first one comes directly
from the measurement-based Cconv obtained in [23], while the second
method uses the Detailed Natural Convection Algorithm (DNCA) of the
simulation software IDA ICE, which is based on phenomenological
formulas [18]. Since both calculation methods use the same DNCA
model, this comparison is made as a cross check of the calculation.
Heat transfer in the same room with identical size and steady-state
conditions is also studied numerically with IDA ICE. We find that using
the Cconv values results in a general 5–6% overestimation of the radiators heat output when compared to using the DNCA and IDA ICE values,
which instead give similar results overall.1 As explained in Section 2.2,
this is due to average cooling water temperatures being used in the
analytical model, instead of measured surface temperatures.
Numerical computations with the IDA ICE software are then used in
an analogous transient computation that spans a full solar year. We
Fig. 1. Radiator surface temperatures and relation to losses.
1
292
These are remarkably close in the case of windowless room.
Journal of Building Engineering 23 (2019) 291–300
K.-V. Võsa, et al.
consider both an old (without heat recovery) and a new (with heat
recovery) building, with boundary conditions from climate data for
Tallinn (North-Eastern Europe) and Strasbourg (Central Europe). We
find that the 22-type serial-connected panel radiator has up to 0.14%
and 1.38% lower energy consumption in the defined new and old
building types, respectively. The higher front panel surface temperature
resulted in the best thermal comfort out of the considered cases, while
the lower rear panel temperature corresponds to a lower additional rear
heat loss. Due to heat recovery, annual energy consumption differences
in the new building were only up to 0.14%. This corresponded to a setpoint difference of only 0.01 °C or less, too small for standardisation or
practical calculation purposes.
The present article is organized as follows: in Section 2.1 we briefly
summarize the experimental setup and results from [23] that are used
in this study. In Section 2.2 we illustrate our steady-state analytical
model and compare the different results with our choices for the convection coefficients and the IDA ICE computation. In Section 2.3 we
describe the annual numerical simulation, and our conclusions are finally drawn in Section 4.
Air temperature
sensor at
controller
Anemometer
h=1.50m
Black globe
thermometer
h=1.50m
Air temperature
sensors
h=0.05m, 0.60m,
0.75m, 1.50m,
2.95m
Temperature
and mass
flow
sensors
Fig. 3. Sketch of the EN442 test chamber [23].
2. Method
2.1. Experimental setup and measurements
In this paper we are interested in comparing three different types of
radiators:
• 11-type panel - single radiative panel configuration with convective
fin behind the panel.
• 22-type panel, parallel-connected - double radiative panel config•
uration with two convective fins in-between. Water flows in parallel
through both panels.
22-type panel, serial-connected - double radiative panel configuration with two convective fins in-between. Water flows through the
front (room-side) panel first.
These are illustrated in Fig. 2. The measurement data here discussed
were obtained in a test chamber shown in Figs. 3 and 4, which conforms
to EN 442-2 requirements [24]. The walls, floor and ceiling of the test
chamber are made from sandwich panels, whose internal surface temperatures can be controlled. The panels consist of four components: a
combination of smooth and undulation steel sheets form channels for
cooling water, with the smooth sheet facing the interior of the test
room. The undulating steel sheet is covered with an 80 mm layer of
insulating foam, and the insulation layer with an external sheet whose
thickness is 0.6 mm. The minimum overall thermal resistance of each
wall, floor and ceiling is 2.5 m2 K/W.
The temperatures of internal surfaces are controlled by regulating
the water flow inside the flow channels, in order to achieve the desired
heat outputs of the radiators. The test room is independent of the environment, since the only opening is an entrance door, also insulated as
described above. Radiators are placed symmetrically on the wall opposite the entrance door, with supply and return lines at the same end.
The chamber air temperature was controlled by a thermostatic radiator valve equipped with a PI-type controller, set to maintain 20 °C air
temperature at the point of occupancy (assumed to be at the centre of
the room at h=0.75 m). Two sets of tests were conducted for each of
the radiators with projected heat outputs of 380 W and 580 W. The
cooling water flow rate for the cooled walls was adjusted for the first
Fig. 4. Sensor setup in the EN442 test chamber [23].
tested radiator in each set, until the desired heat output was reached.
The flow rate in the circulation pump was then fixed and used as a
reference flow rate for the other radiators in the same test set.
Temperature sensors were installed for all the cooled surfaces, radiator front panel surface and on the insulation surface behind the radiator, as in Fig. 4. The air temperature was measured in the room
centre at different heights. Additionally, we measured the heat flux
behind the radiator to compare the heat losses with different rear panel
temperatures.
Eventual errors from the calibration of different measuring devices
were reduced by swapping the same temperature sensors, radiator
valve and controllers over in-between tests, in order to reproduce
uniform conditions for each and every test. Furthermore, averages of
measurements were aggregated from the datasets only after the sensor
readings stabilized from the initial excitations. Eventually, the measured differences among the three radiator types were found to be
greater than those due to any design differences or measurement errors.
Fig. 2. Water flow directions in the tested radiators.
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For further details we remand to [23], where experimental modalities
and the full results are thoroughly described and analysed.
2.2. Steady-state analytical model
As we are interested in comparing radiators at the same operative
temperature rather than that of air, in this paper we make a significant
extension of an analytical model which was proposed in [4,23] for the
test room. Now the heat balance in the room includes also the heat
output of the radiator: the model is able to compute the radiator surface
and return temperatures as well as the heat output.
In contrast, in [23] these values were taken from the measurements
and used as input data for the model. The study at hand therefore
constitutes a clear advance in the formulation, also because it extends
the comparison of radiators to real rooms under steady-state conditions.
Moreover, we use this analytical model to validate the IDA ICE simulation discussed in Section 2.3.
The operative temperature is defined as the uniform temperature of
an enclosure in which an occupant would exchange the same amount of
heat by radiation plus convection as in the existing non-uniform environment [2]. In most practical cases where the relative velocity is
small (< 0.2 m/s) or where the difference between mean radiant and air
temperature is small (< 4 °C), the operative temperature can be calculated with sufficient approximation as the mean value of air and mean
radiant temperature (MRT) [2],
top =
ta + tMRT
.
2
Fig. 5. Sketch of the heat balance for the analytical model.
F si se =
qri =
Fsi se =
as
1/ Fr si + (1/ r
1)
Tse4 ),
(10)
ts ),
(11)
ts ) 0.32.
hc =
1.810(ta ts )1/3
1.382 |cos ( )|
hc =
9.482(ta ts )1/3
otherwise
7.283 + |cos ( )|
=
if
90°,
(12)
n
tln
tln, n
n
,
(13)
where the logarithmic difference of temperatures is calculated as
tln =
tin tout
.
t
ta
ln in
tout ta
(14)
Supply water at temperature tin = 75 °C was used for all the analytical solutions. On the other hand, the radiator heat output can be
formulated with Fig. 6,
(5)
= qri + qcr + qbw .
Alternatively, when differing internal wall temperatures are considered, the view factors in Table 1 can be used.
The radiation heat rate from internal to external surface is calculated similarly,
qre = Asi F si se (Tsi4
The general Newton's cooling law with air temperature ta is written
where = 0° for floors and = 180° for ceilings.
The radiator heat output is calculated according to the characteristic
equation established in [24] as
(3)
5
Asin = 3·12 + 2·16 = 68 m2.
(9)
Here we use the room average Cconv value, obtained experimentally
in [23]. Alternatively, convective heat transfer coefficients were also
calculated according to the IDA ICE Detailed Natural Convection Algorithm (DNCA), holding as [18]
(4)
n=1
Ase
A
Fse si = se .
Asi
Asi
hc = Cconv (ta
and the internal surfaces can be considered as a single surface with their
areas summed up,
Asi =
si = se = 0.90 . Since the external wall
where the convective heat transfer coefficients were calculated from
[26] as
with surface emissivity values r = 0.95 and si = 0.90 representing typical values for a white aluminium panel and a room with a white
finish, where Ar and Asi are, respectively, the radiator panel and internal surfaces areas. As the defined front panel surface only sees internal surfaces whose temperatures are assumed to be equal, the view
factor becomes
Fr si = 1 ,
(7)
(8)
qc = hc As (ta
(2)
1
1) + (Ar / Asi )(1/ si
,
thus from the reciprocity theorem we obtain
The total exchange factor F r si is obtained from [25],
F r si =
1)
Fse si = 1 ,
(1)
Tsi4 ).
1
1) + (Asi / Ase )(1/ se
and surface emissivity values
only sees internal walls,
In our laboratory measurements, the air temperature was maintained at 20 °C. A windowless and windowed room with identical dimensions to the EN442-2 test chamber are considered, and internal
surfaces are assumed to be adiabatic. In other words, all heat emitted to
the room is lost through the exterior wall (as illustrated in Fig. 5).
For the purposes of radiation calculation, the radiator is modelled as
an infinitely thin surface laying on the external wall. Radiation from the
top, bottom and sides of radiator is not considered. The net radiative
heat exchanged between radiator at Tr and internal surfaces at Tsi can be
calculated from the common long-wave radiation equation,
Ar F r si (Tr4
1/ Fsi se + (1/ si
(15)
Having calculated qri from Eq. (2) and assuming qbw = const (measured during the laboratory test), convection from the radiator can be
calculated by rearranging Eq. (15),
qcr =
(6)
qri
qbw ,
(16)
while convection values calculated from Eqs. (10) and (16) have to be
equal for heat balance at the air node,
with the total exchange factor
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Journal of Building Engineering 23 (2019) 291–300
K.-V. Võsa, et al.
Table 1
View factors from radiator to room surfaces, valid for a 4 m×4 m×3 m room
with radiator placed at h = 0.15 m above the floor on the centreline of the room.
Surface
Table 2
CEN TC130 WG13 standard room and boundary condition definitions. The
room dimensions are x = 4.0 m, y = 4.0 m and z = 3.0 m.
Radiator size
Opposite wall
Floor
Ceiling
Sidewalls
1.40 m × 0.60 m
2.30 m × 0.60 m
0.1704
0.4111
0.1420
0.1382
0.1672
0.4058
0.1386
0.1442
(17)
where -values are taken from [23]. The steady-state heat loss through
the external wall is calculated by simple one-dimensional conduction as
A
qw = se tse
Rw
te ,
3 m2
1.08 W/mK
30%
1.20 W/mK
0.64
3 m2
2.34 W/mK
30%
2.00 W/mK
0.76
qre = qri + qci ,
1.0 h 1
18 °C
0.8, texh 0 °C
25 °C
20 °C
South
3.8 W/m2
1.0 h 1
outdoor temperature
–
25 °C
20 °C
South
3.8 W/m2
(22)
(23)
are simultaneously satisfied. The analytical model itself, along with the
mean radiant temperature calculation, is implemented in numerous
Excel worksheets according to the described formulae. The iterative
process within the model is handled with the OpenSolver VBA add-on.
The convection component was addressed with three different approaches: using in the analytical model the Cconv -value derived from the
test chamber measurements [23], the DNCA module for convection
[18], and numerically, with IDA ICE simulations.
(19)
2
Windowed area
Window
Window frame fraction
Frame
Window g-value
ACH
= qcr + qri + qbw = qce + qre + qbw ,
(18)
tln ,
Old building
calculated according to Eq. (1) as the average of air and mean radiant
temperature, since the air velocities in the test chamber were low.
Having established all the governing equations and dependencies,
the analytical model can now be iteratively solved by changing air
temperature ta , interior surface temperature of internal walls tsi and
radiator outlet temperature tout . This should be done until the target
operative temperature top = 20 °C and the heat balance equations for
nodes e and c in Fig. 6, written as
The radiator front panel surface temperature is estimated as
tr = ta +
New building
Supply air temperature
Heat recovery efficiency
Cooling setpoint (air)
Heating setpoint (operative)
Window orientation
Internal gains
Fig. 6. Analytical model heat balance nodes. a - radiator, b - indoor air, c adiabatic internal surface, d - internal surface of external wall, e - external
surface of external wall.
qcr = qci + qce .
Boundary condition
2
where Rw = 0.700 m K/W and Rw = 2.114 m K/W correspond to the
thermal resistances of the walls in windowless and windowed rooms,
respectively, with the same external temperature te = 20 °C . The
windowless room roughly represents the laboratory test chamber with
only one external wall, while the windowed room represents the new
building type described in Tables 2 and 3.
To compensate for the larger panel surface area of the 11-type radiator,2 R-values of Rw = 0.666 m2 K/W and Rw = 2.011 m2 K/W were
used instead, to keep the ratio Ase / Rw constant for all radiators. Since
the proposed model considers the window and wall together as one
single external wall element, the R-value for the windowed case was
calculated as the weighted average R-value of the external wall
R w = 2.50 m2 K/W and window Rwin = 1.116 m2 K/W. From global heat
balance in the room (Fig. 6), heat loss through the external wall can be
formulated as
2.3. Annual simulation
The operative temperature was calculated with the angle factors and
equations from [2]. Angle factors between a small plane element and
the cooled surfaces were used to calculate the plane radiant temperature, as described in Annex C of the standard. The mean radiant temperature was calculated from the plane radiant temperatures in six directions and the projected area factors for a person in the same six
directions, given in Annex B [2]. The operative temperature was
Numerical simulations of heat transfer processes in the new and old
building rooms described above, corresponding to a European reference
room defined in CEN TC130 WG13 and shown in Figs. 7 and 8, were
performed for Tallinn (Estonian TRY climate file, [27]) and Strasbourg
(ASHRAE IWEC climate file, [26]) with the IDA ICE 4.7 simulation
software [18]. The numerical computation setup and material properties used are reported in Tables 2 and 3.
The layout and components of the IDA ICE room model are shown in
Fig. 9. The room model is capable of calculating detailed radiation heat
transfer between all surfaces, external and internal building envelope
elements, the radiator and various connections between the nodes.
For the new building type, design conditions with temperatures 55/
45/20 °C were used for determining the heat load in the two locations.3
This produced design heat loads of 274 W and 241 W. Consequently,
smaller radiators had to be used in the new building simulations (see
Table 4). For the old building, radiator sizes tested in the laboratory
were suitable at 75/65/20 °C design conditions. Radiator supply water
temperature curves used in the simulation were constructed based on
the design conditions (assuming also constant flow) and are shown in
Fig. 10. Additionally, an ideal convector (all heat is released into the
air) was also simulated for comparison.
2
Such a large size is not realistic for ordinary installations, but is required for
matching the heat output of the 22-type radiator.
3
Namely, (supply/return/room) T at fixed external air temperatures of
−21 °C and −15 °C in Tallinn and Strasbourg, respectively.
qw =
(20)
qbw .
Accordingly, the internal surface temperature of the external wall can
be calculated by rearranging Eq. (19) as
tse = te +
qw Rw
Ase
.
(21)
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Table 3
CEN TC130 WG13 standard room and boundary conditions definitions - layer
thermal properties for new and old building.
Building element
External wall, new
Gypsum
Light insulation/wood frame
Internal wall, new
Gypsum
Light insulation/wood frame
Internal ceiling/floor, new
Parquetry
Screed
Heavy insulation
Insulation/wooden joists
Gypsum
External wall, old
Brick
Internal wall, old
Brick
Internal ceiling/floor, old
Parquetry
Concrete
d [mm]
k [W/mK]
[kg/m3]
cp [J/kgK]
26
195
0.22
0.052
970
90
1090
2000
26
95
0.22
0.037
970
20
1090
750
10
25
25
100
26
0.14
0.80
0.035
0.044
0.22
500
1800
30
56
970
2300
800
1200
1700
1090
400
0.43
1200
700
150
0.60
1500
900
10
180
0.14
1.20
500
2000
2300
880
Fig. 9. Simulated room layout in IDA ICE.
Table 4
Radiator catalogue parameters for annual simulation model, new building type.
tln = 29.720 K according to EN 442-2.
Location
Type
n [W]
n
Size [m2]
STRA
11
22-par.
22-ser.
11
22-par.
22-ser.
251
244
248
279
293
298
1.2981
1.3094
1.2776
1.2981
1.3094
1.2776
0.90 × 0.30
0.50 × 0.30
0.50 × 0.30
1.00 × 0.30
0.60 × 0.30
0.60 × 0.30
TAL
0.82
0.81
0.95
0.82
0.81
0.95
Fig. 7. Simulated new building.
Fig. 10. Supply water temperature curves.
Table 5
Radiator catalogue parameters for the steady-state model.
cording to EN 442–2 [24].
Type
Rated output
11
22-par.
22-ser.
2341
2393
2332
n [W]
tln = 49.833 K ac-
Radiator exponent n
Size [m2]
1.3115
1.3358
1.2930
2.30 × 0.60
1.40 × 0.60
1.40 × 0.60
0.82
0.81
0.95
Fig. 8. Simulated old building.
3. convective to zone via backside of unit or via extra fins, possibly
enhanced by fans.
The radiators were modelled using the standard water radiator
model provided in the software [18]. On the waterside, the heat
transfer calculation uses the logarithmic mean temperature difference
between water and air. On the airside, heat transfer between the unit
and its environment is split into three components:
In our model, the effective heat transfer is described by a power law
expression in the temperature difference water to air, Eq. (13); the
corresponding coefficients are often supplied by manufacturers
(Table 5). It can be noted that, since both the overall power and the
transfers 1. and 2. above are specified in the model by separate equations, transfer 3. will have to take up the slack to reach the given power.
The surface temperature of the unit is used in the calculation of
transfers 1. and 2. above, and obtained from information on the relation
1. convective and radiative via front of unit,
2. exchange with envelope behind unit,
296
Journal of Building Engineering 23 (2019) 291–300
K.-V. Võsa, et al.
between surface and total thermal resistance of the water-air interface,
Eq. (18). The heat balance of waterside is
Table 6
Steady-state model results, windowless (EN 442-2), top = 20 °C .
(24)
Radiator
Model
ta ° C
W
tr ° C
where m is the water mass flow and Tin and Tout are entering and leaving
water temperatures, respectively. The total heat balance of the unit is
written as
11-type
Cconv
DNCA
IDA ICE
Cconv
DNCA
IDA ICE
Cconv
DNCA
IDA ICE
20.45
21.07
21.04
20.59
21.28
21.26
20.56
21.23
21.20
561.7
532.3
534.9
565.6
536.4
538.5
565.2
536.2
537.4
33.88
33.96
33.97
34.13
34.29
34.31
36.38
36.42
36.41
P = mcp (Tin
Tout ),
Qfront + Qconv + Q wall ,
22-par.
(25)
with Qfront the heat transferred on the front side of the radiator (longwave radiation and convection) modelled in the zone model, Qconv an
extra convective heat load, e.g. from back side and possible fins, and
Qwall the heat transferred between the back side of the unit and facing
zone surface. Q wall is modelled as long-wave radiation between the wall
and the unit. Alternatively, a constant heat transfer coefficient can be
provided.
The model assumes equal surface temperatures for both front and
rear surfaces of the radiator. For the 22-type serial panel radiator, these
temperatures are different, with the front panel having a higher surface
temperature than the rear panel, shown in Fig. 1. Consequently, the
model was modified to enable differing temperatures for the front and
rear panel surfaces. This will lower the heat loss from the rear of the
radiator.
The rear panel surface temperature t r was derived as a function of
the front panel surface temperature tr and heat output ,
t r = tr
(A 2 + B ),
22-ser.
Table 7
Steady-state model results, windowed (new building), top = 20 ° C.
Radiator
Model
ta ° C
W
tr ° C
11-type
Cconv
DNCA
IDA ICE
Cconv
DNCA
IDA ICE
Cconv
DNCA
IDA ICE
20.20
20.49
20.34
20.27
20.59
20.58
20.26
20.58
20.56
201.1
197.1
190.1
201.6
197.6
189.4
201.5
197.5
188.5
26.33
26.53
26.35
26.52
26.76
26.55
27.38
27.59
27.32
22-par.
22-ser.
(26)
where the coefficients A = 0.00001937 and B = 0.02307 were calculated from previous laboratory measurements performed in the EN 4422 test chamber, reported in [4] (see e.g. Fig. Fig. 10 there).
insufficient when considering buildings with heat recovery through the
ventilation system (“new building type” in this paper). The sum of radiator Erad and air heating coil Erad energy consumptions should be used
instead,
3. Results
(27)
Etot = Erad + Ecoil .
3.1. Steady-state analytical model
This is evident as higher extracted air temperatures correspond to more
heat recovery and lower energy consumption of the heating coil, and
vice versa. The differences in energy consumption can be split into two
primary components - additional energy losses from behind the radiator
Erear and differences due to different thermal comfort provided by the
radiator front surface Efront ,
In our analytical calculation For the windowless room, we found
that the Cconv values returned 25–30 W higher heat outputs than the
DNCA module and IDA ICE, Table 6. This is expected, since when calculating the Cconv values, average cooling water temperatures were used
in place of measured surface temperatures, which led to artificially
higher heat transfer coefficients. Such approach was acceptable for
corrections inside the test chamber, however using these values in real
rooms with similar dimensions may not produce accurate results. The
analytical model using DNCA equations and the IDA ICE simulation
show instead differences of only 1–3 W. Moreover, among the radiator
types, the 11-type reached the same operative temperature emitting
3–4 W less than all the other models.
For the windowed room, the results between different models were
on a similar 5–6% scale, as illustrated in Table 7. The model using Cconv
still had the highest heat outputs by 11–13 W. The DNCA model shows
7–9 W higher heat outputs than the IDA ICE model. This can be explained by our simplified approach used in the analytical model - we
considered the wall and window as a single surface with a weighted
average R-value. In the IDA ICE model, a window was instead implemented, with convection and radiation calculated separately from
the wall.
To summarize, the differences between different models are within
reason and give us confidence that annual simulation results from IDA
ICE will be accurate enough to quantify the differences between radiator types.
(28)
E = Efront + Erear .
Erear was calculated by logging the heat fluxes from the external wall
and behind radiator.
Erear = Arad
(qrear
qwall ) t ,
(29)
where t corresponds to the simulation time-step and the summation is
done over the heating period (i.e. when the radiator is in use). Efront
can then be calculated from Eq. (28).
The set-point differences sp were calculated using additional simulations results, where the set-point was varied. For ± 0.25 °C, this
difference in energy consumption is proportional to that from the reference set-point of 20 °C, returning the plot in Fig. 15. Simulation results of the 22-type serial panel radiator with additional rear losses
deducted ( Erear = 0 ) were used as the relative benchmark in all the
following results (Tables 8 and 9), as an ideal reference case is not welldefined for systems controlled by operative temperature. As the ideal
convector has no physical location inside the room model and releases
heat directly into the air node inside the room, it will also not exhibit
any additional rear losses.
Annual energy consumption is up to 0.37% higher for the new
building type and 1.57% higher for the old building type compared to
the relative benchmark. The difference is greater in the old building due
to lack of heat recovery. This is evident from the Efront -values - for the
new building, the front-side losses are only 0.02–0.10% (compared to
0.73–1.08% in the old building).
3.2. Annual simulation
Duration graphs for the panel surface temperatures are shown in
Figs. 11, 12, 13 and 14.
Comparing annual energy consumption of the radiators is
297
Journal of Building Engineering 23 (2019) 291–300
K.-V. Võsa, et al.
Fig. 11. Duration graphs for Strasbourg, old building.
Fig. 14. Duration graphs for Tallinn, new building.
Fig. 12. Duration graphs for Strasbourg, new building.
higher due to the higher supply water T, causing a higher net radiative
heat exchange behind the rear wall and rear radiator panel. The size of
the radiator naturally corresponds to a proportionally higher additional
rear loss.
Qualitatively, we observe that the 22-type serial connected radiator
performs the best in all four cases. The higher front panel surface
temperature resulted in the best thermal comfort out of the considered
cases ( Efront =0 as it was used as the reference benchmark), while
lower rear panel temperature corresponds to a lower additional rear
heat loss (Fig. 1). For the new building, the differences between the
tested real radiators (11-type and both 22-types) were up to 0.14% and
0.06% in Strasbourg and Tallinn. This corresponds to a set-point difference of 0.01 °C only. For standardisation and practical purposes, this
difference is largely negligible. For the old building, the differences
were 1.38% and 1.11% for Strasbourg and Tallinn, corresponding to
set-point differences of 0.11 °C and 0.14 °C.
Interestingly, an ideal convector outperforms the real radiators in
the new building. This is likely due to heat recovery and absence of
additional rear losses. Relative differences between the annual energy
consumption were higher in Strasbourg. The heating period is shorter
and the average temperature differential between the indoor and outdoor air temperatures is smaller, as illustrated in Figs. 15 and 16. Separate steady-state simulations with the same model showed a similar
trend - a lower temperature differential leads to a higher relative
emission difference. This can be explained with the differences in the
supply temperatures - radiator surface temperatures are a few degrees
higher in Strasbourg at equal outdoor air temperatures.
4. Conclusions
In this paper we have considered annual emission efficiencies at
equal operative temperature set-point of serial and parallel connected
panel radiators.
We formulated for the first time a combined analytical model that
solves the heat balance for both room and radiator in a real enclosure,
either with or without a window; we thus established a direct connection between heat output and a specific operative temperature, then
calculated the corresponding radiator surface and return temperatures.
As a consistent extension of an existing, experimentally grounded
analytical model for steady-state conditions in a test chamber, this
provided a validation for numerical computations in the same room.
Differences between the simulated and analytically calculated results
were sufficiently small to give us confidence that annual simulations
would be able to quantify the differences, if any, between the different
radiator types. Interestingly, in the steady-state calculations with windowless model corresponding to the EN442 test chamber, the 11-type
radiator performed the best; however, this was not valid any more for
the model with a window.
Fig. 13. Duration graphs for Tallinn, old building.
Although the operative temperatures are maintained at the same
level, indoor air temperatures are different due to the differences in
tMRT . Extra energy used to heat the air up is lost in the old building. In
the new structure, however, this energy can be recouped to a large
extent via heat recovery (limited only by its efficiency and by the
temperature of the air that can leave the enclosure). Additionally, the
radiators in the new building are smaller, and the surface temperatures
are lower due to a lower supply temperature. This results in a smaller
effect on tMRT and, therefore, on operative temperature and thermal
comfort. The differences in performance are thus considerably smaller
for the new building.
Additional rear losses were higher in the old building type, up to
0.62% for the 11-type radiator. This was to be expected, as the lower
level of thermal insulation results in a more intense heat transfer from
behind the radiator. Additionally, the rear panel surface temperature is
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Journal of Building Engineering 23 (2019) 291–300
K.-V. Võsa, et al.
Table 8
Annual simulation results for new building in Tallinn and Strasbourg.
Loc.
Type
Strasbourg
11
22-Par
22-Ser
100% convector
22-Ser, Erear = 0
11
22-Par
22-Ser
100% convector
22-Ser, Erear = 0
Tallinn
Size
Etot
900 × 300
500 × 300
500 × 300
–
500 × 300
1000 × 300
600 × 300
600 × 300
–
600 × 300
102.86
102.68
102.65
102.57
102.48
356.40
355.90
355.80
355.60
355.53
Etot
mm ×mm
kW h
0.38
0.20
0.17
0.09
0.00
0.87
0.37
0.27
0.07
0.00
Erear
Efront
Etot
Erear
Efront
0.31
0.18
0.17
0.00
0.00
0.49
0.29
0.27
0.00
0.00
0.07
0.02
0.00
0.09
0.00
0.37
0.08
0.00
0.07
0.00
0.37%
0.19%
0.16%
0.09%
0.00%
0.24%
0.10%
0.08%
0.02%
0.00%
0.30%
0.17%
0.16%
0.00%
0.00%
0.14%
0.08%
0.08%
0.00%
0.00%
0.07%
0.02%
0.00%
0.09%
0.00%
0.10%
0.02%
0.00%
0.02%
0.00%
Erear
Efront
Etot
Erear
Efront
8.14
5.00
2.53
0.00
0.00
11.77
7.17
4.42
0.00
0.00
12.39
11.53
0.00
14.13
0.00
19.05
17.35
0.00
21.52
0.00
1.57%
1.26%
0.19%
1.08%
0.00%
1.29%
1.02%
0.18%
0.90%
0.00%
0.62%
0.38%
0.19%
0.00%
0.00%
0.49%
0.30%
0.18%
0.00%
0.00%
0.95%
0.88%
0.00%
1.08%
0.00%
0.80%
0.73%
0.00%
0.90%
0.00%
-
sp
°C
0.02
0.01
0.01
0.00
0.00
0.02
0.01
0.01
0.00
0.00
Table 9
Annual simulation results for old building in Tallinn and Strasbourg.
Loc.
Type
Strasbourg
11
22-Par
22-Ser
100% convector
22-Ser, Erear = 0
11
22-Par
22-Ser
100% convector
22-Ser, Erear = 0
Tallinn
Size
Erad
Etot
2300 × 600
1400 × 600
1400 × 600
–
1400 × 600
2300 × 600
1400 × 600
1400 × 600
–
1400 × 600
1329.30
1325.30
1311.30
1322.90
1308.77
2423.70
2417.40
2397.30
2414.40
2392.88
20.53
16.53
2.53
14.13
0.00
30.82
24.52
4.42
21.52
0.00
mm ×mm
kW h
-
sp
°C
0.13
0.10
0.02
0.09
0.00
0.16
0.13
0.02
0.11
0.00
Fig. 16. Operative temperature duration graphs for 22-type serial radiator
during annual simulation. Breaks in the graphs mark the length of the heating
period, and operative temperatures over 20.0 °C correspond to the non-heating
period.
Fig. 15. Percentage of additional annual heating energy needed when increasing the set-point by 0.1 K.
Annual simulations run with IDA ICE then showed that 22-type
serial-connected panel radiators performed best both in new and old
buildings. A higher front panel surface temperature results in the best
thermal comfort out of the considered cases, while lower rear panel
temperature corresponds to a lower additional rear heat loss.
Since a large proportion of heat from exhaust air was recouped by
means of heat recovery, the annual energy consumption differences in
the new building were only up to 0.14%. This corresponded to a setpoint difference of barely 0.01 °C, too small for standardisation or
practical calculation purposes. For the old building, the differences
were higher, up to 1.38%, leading to a set-point difference of up to
0.14 °C. Additional rear losses had a larger impact on the old building,
as expected.
All things considered, it seems that the formalism developed in this
paper, which extends to ordinary rooms the analytical model introduced in [4] and further developed in [23] for a specific test
chamber, constitutes a reliable analytical counterpart of numerical
calculations.
We should stress that our analytical room heat balance model implementation was directly compared to a corresponding room model in
IDA ICE, which is well known to be experimentally validated [18,28].
Rather than seeking a direct experimental validation of a customary
heat balance formulation, we validated the generic radiator model in
IDA ICE with experimental data of heat emitters against our analytical
room and radiator model. This validation exercise revealed that with
experimentally measured values, IDA ICE was capable to simulate the
performance differences of the radiators studied. This made it possible
for the first time to run annual simulations of the heat emission efficiency for the different radiators, which was experimentally measured.
One should also notice how, when comparing the annual consumption for different radiator types, no device could be set as our
299
Journal of Building Engineering 23 (2019) 291–300
K.-V. Võsa, et al.
baseline, i.e. as an ideal reference case. For systems where the air
temperature is controlled, this could be modelled as a purely convective
radiator. However, the operative temperature also considers surface
temperatures, which in turn are determined by radiation. This poses
two questions - where is the heat emitter located and how much of its
heat is emitted via radiation. To our knowledge, no common agreement
about such ideal emitter exists yet, either it be a radiator, underfloor
heating, ceiling heater etc. [29]. The definition of such a benchmark
would be thus interesting not only for improving our analytical model,
but also in more general investigations for systems with operative
temperature control. Some efforts in this sense have been started recently, see e.g. [30].
Lastly, we should remark that in this study we addressed applications only to radiators. The model we developed can however be applied also to other heat emitters, for comparable heat emission efficiency analyses. In other words, as discussed in the introduction, the
present formulation constitutes an extension of previous literature results as well.
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Acknowledgements
The authors are grateful for support by the European Regional
Development Fund via the Estonian Centre of Excellence in Zero Energy
and Resource Efficient Smart Buildings and Districts ZEBE, grant 20142020.4.01.15-0016. Funding by the Estonian Research Council through
grant IUT1-15 is also acknowledged. We also wish to warmly thank the
Rettig ICC Research Centre for the measurements performed in the
EN442 test chamber.
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