Energy and Buildings 105 (2015) 285–293

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Energy and Buildings

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A new simplified model to calculate surface temperature and heat

transfer of radiant floor heating and cooling systems
Xiaozhou Wu a,b,∗ , Jianing Zhao b , Bjarne W. Olesen c , Lei Fang c , Fenghao Wang a
a
School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, PR China
b
School of Municipal and Environmental Engineering, Harbin Institute of Technology, PR China
c
International Centre for Indoor Environment and Energy, Department of Civil Engineering, Technical University of Denmark, Denmark

a r t i c l e i n f o a b s t r a c t

Article history: In this paper, a new simplified model to calculate surface temperature and heat transfer of radiant floor
Received 16 January 2015 heating and cooling system was proposed and established using the conduction shape factor. Measured
Received in revised form 9 July 2015 data from references were used to validate the proposed model. The results showed that the maximum
Accepted 20 July 2015
differences between the calculated surface temperature and heat transfer using the proposed model
Available online 29 July 2015
and the measured data were 0.8 ◦ C and 8.1 W/m2 for radiant floor heating system when average water
temperature between 40 ◦ C and 60 ◦ C. For the corresponding values were 0.3 ◦ C and 2.0 W/m2 for radiant
Keywords:
floor cooling systems when average water temperature between 10 ◦ C and 20 ◦ C. Numerically simulated
Radiant floor heating system
Radiant floor cooling system
data in this study were also used to validate the proposed model. The results showed that the surface
Surface temperature temperature and heat transfer of radiant floor calculated by the proposed model agreed very well with
Heat transfer the numerically simulated data when average water temperature changing from 25 ◦ C to 45 ◦ C for radiant
Conduction shape factor floor heating systems and from 10 ◦ C to 20 ◦ C for radiant floor cooling systems. Hence, the proposed model
was validated to be applicable and was believed to be potentially beneficial for the design and control of
radiant floor heating and cooling systems.
© 2015 Elsevier B.V. All rights reserved.

1. Introduction and cooling systems have been extensively applied in residential

and non-residential buildings all over the world [5,6].
Radiant floor heating and cooling systems, which are regarded Surface temperature and heat transfer of radiant floor are the
as an embedded surface heating and cooling systems, can use heat key parameters in the design and control of radiant floor heating
sources with lower temperature for heating and cool sources with and cooling systems. Along with the development of radiant floor
higher temperature for cooling compared to the traditional HVAC heating and cooling systems, many different models (or methods)
systems [1,2]. Due to the effect of warm floor surface in winter that calculate surface temperature and heat transfer of radiant floor
and that of cool floor surface in summer on indoor occupants, a have been developed. According to the description and assumption
radiant floor heating and cooling system can reach the same level of heat transfer process of radiant floor heating and cooling systems,
of thermal comfort (the same operative temperature) in a room at these models can be mainly classified as analysis model, numerical
a lower indoor air temperature in winter and a higher indoor air simulation model and simplified model.
temperature in summer [3,4]. Comparing to the traditional HVAC For an analysis model, a detailed mathematical description of
system, a smaller air temperature difference between indoor and heat transfer process of radiant floor is a prerequisite to the exist-
outdoor in buildings with radiant floor heating and cooling systems ence of analytical solutions, and generally the heat transfer process
may contribute to lower building energy demand and thus reduce is one-dimensional. The formulas for surface temperature and heat
energy consumption. In the last two decades, radiant floor heating transfer of radiant floor can then be obtained, such as Koschenz’s
model [7], Monte’s model [8], Lu’s model [9], Beck’s model [10] and
Laouadi’s model [11]. For a numerical simulation model, a more
detailed and multi-dimensional description of heat transfer pro-
cess of radiant floor will be made, such as two-dimensional and
∗ Corresponding author at: Department of Building Environment and Energy
three-dimensional. The surface temperature and heat transfer of
Engineering, School of Human Settlements and Civil Engineering, Xi’an Jiaotong
University, 28th West Xianning Road, Xi’an, Shaanxi 710049, PR China. radiant floor can be obtained by numerical simulation using finite
E-mail address: fonen519@mail.xjtu.edu.cn (X. Wu). difference method (FDM), finite volume method (FVM) or finite

http://dx.doi.org/10.1016/j.enbuild.2015.07.056
0378-7788/© 2015 Elsevier B.V. All rights reserved.
286 X. Wu et al. / Energy and Buildings 105 (2015) 285–293

Fig. 2. Round pipes in the infinity plane.

The whole heat transfer process of radiant floor heating and

cooling systems can be divided into five processes: (1) heat
exchange between indoor environment and the upwards partial
surface of radiant floor, (2) heat conduction from the upwards
partial surface of radiant floor to screed layer surface, (3) heat
conduction from screed layer surface to outside surface of water
pipe, (4) heat conduction from outside surface of water pipe to the
downwards partial surface of radiant floor and (5) heat exchange
Fig. 1. Structure element of radiant floor heating and cooling systems. between the downwards partial surface of radiant floor and indoor
environment.
Due to the complicated shape and two-dimensional temper-
element method (FEM), such as Holopainen’s model [12],
ature field of the screed layer, it is difficult to calculate heat
Koschenz’s model [13], Larsen’s model [14], Jin’s model [15] and
conduction from screed layer surface to outside surface of water
Hogan’s model [16]. For a simplified model, some assumptions
pipe. In a radiant floor heating and cooling system which uses
of description of heat transfer process of radiant floor should be
low temperature heat sources for heating and high temperature
made firstly, and then formulas for surface temperature and heat
cool sources for cooling, the average water temperature is close to
transfer of radiant floor will be obtained by strict derivation based
indoor temperature which results in nearly uniform distribution of
on the principle of energy balance, such as Hulbert’s model [17],
surface temperature of both screed layer and water pipe [22]. The
Schutrum’s model [18], Kilkis’s model [19], Timothy’s model [20],
heat exchange between outside surface of water pipe and screed
Liu’s model [21], Zhang’s model [22] and Li’s model [23].
layer surface can be calculated using the conduction shape factor, as
Numerical simulation model can only obtain discrete values of
shown in Fig. 2, where tsc is the surface temperature of the infinity
surface temperature and heat transfer of radiant floor as the water
plane and td is the outside surface temperature of water pipe.
temperature, pipe space and thickness of screed layer are changed,
According to reference [27], the conduction shape factor for
and it is not convenient for diverse design using numerical sim-
thermal calculation between outside surface of water pipe and sur-
ulation model as this would involve too much time. In addition,
face of the infinity plane can be calculated by Eq. (1).
formulas for surface temperature and heat transfer of radiant floor
obtained by analytical solution were a bit complicated and difficult 2l Do
So =   , d1 > (1)
to understand for designers and engineers. Compared to analysis 2M (d +D /2) 2
ln Do
sh 1 M o
models and numerical simulation models, the simplified models
are more convenient for diverse design and easier to understand for
where So is the conduction shape factor, l is the length of water pipe
designers and engineers. Hence, the simplified models have been
and d1 is the difference between outside surface of water pipe and
adopted in many international and national design standards and
surface of the infinity plane.
handbooks [24–26].
In this study, a new simplified model using the conduction shape d1 = ıscr − Do (2)
factor was proposed to calculate surface temperature and heat
transfer of radiant floor heating and cooling systems. Measured As shown in Fig. 2, the upper and lower surface temperatures
data and numerically simulated data were then used to validate the of the floor are the same, which is one of the limited conditions
proposed model. The proposed model will be beneficial for design for using the conduction shape factor in the reference [27]. It is
and control of radiant floor heating and cooling systems. not suitable for any case in practice due to the different thermal
resistance above and below the water pipe, which will result in rel-
atively large temperature difference between the upper and lower
2. A new simplified model for radiant floor heating and
surface.
cooling systems
In order to solve this problem, we firstly made an assumption
of symmetrical structure above and below the water pipe, which
Radiant floor heating and cooling systems normally consist of
means that the thermal resistance (including the thermal conduc-
floor covering layer, screed layer, thermal insulation layer, con-
tivity and thickness) below the water pipe is equal to that above the
crete layer and pipe, as shown in Fig. 1, where M is the pipe space,
water pipe, and the upper and lower surface temperatures of the
Di /Do is the inner/outer diameter of water pipe, co is the thermal
floor should be the same, then the conduction shape factor between
conductivity of floor covering layer, ıco is the thickness of floor cov-
the water pipe and the upper surface of floor can be regarded as
ering layer, scr is the thermal conductivity of screed layer, ıscr is the
a half of that in the reference according to the definition of the
thickness of screed layer, ins is the thermal conductivity of thermal
conduction shape factor, as shown in Fig. 3 and Eq. (3).
insulation layer, ıins is the thickness of thermal insulation layer, con
is the thermal conductivity of concrete layer, ıcon is the thickness 1
S= So (3)
of concrete layer and p is the thermal conductivity of water pipe. 2
 X. Wu et al. / Energy and Buildings 105 (2015) 285–293 287

where qd is the heat exchange rate between the downwards partial

surface of radiant floor and indoor environment and Ru /Rd is the
upwards/downwards partial heat transmission resistance of the
radiant floor, as shown in Eqs. (12) and (13).
1 ıco ıscr − Do /2
Ru = + + (12)
˛u co scr
Do /2 ı ıcon 1
Rd = + ins + + (13)
scr ins con ˛d

7.67(top − td )0.1 td < top
Fig. 3. Round pipes in the screed layer in the radiant floor. ˛d = (14)
5.7 td > top
According to the definition of the conduction shape factor [27],
where td is the downwards partial surface temperature of radi-
the equivalent thermal resistance between outside surface of water
ant floor and ˛d is the total heat exchange coefficient between the
pipe and screed layer surface in the radiant floor can be obtained
downwards partial surface of radiant floor and indoor environment
through Eq. (4).
and can be calculated by Eq. (14) [28].
M·l According to the calculation equation of heat exchange rate
Req = (4) between the downwards partial surface of radiant floor and indoor
Scr
environment, the formula for the downwards partial surface tem-
The heat exchange rate between the upwards partial surface of
perature of radiant floor (td ) can be obtained, as follows
radiant floor and indoor environment can be seen in Eq. (5).
qd
tw − top td = + top (15)
qu = (5) ˛d
R
1 ıco M ln (Do /Di ) M 3. Validation of the proposed model using the measured
R= + + + + Req (6) data
˛u co 2p ˛w Di

where qu is the heat exchange rate between the upwards partial The inputs for the proposed model include the pipe space,
surface of radiant floor and indoor environment, tw is the aver- inner/outer diameter of water pipe, thermal conductivity of floor
age water temperature, top is the indoor operative temperature, ˛u covering layer, thickness of floor covering layer, thermal conductiv-
is the total heat exchange coefficient between the upwards par- ity of screed layer, thickness of screed layer, thermal conductivity
tial surface of radiant floor and indoor environment and can be of thermal insulation layer, thickness of thermal insulation layer,
calculated by Eq. (7) [28] and ˛w is the convective heat exchange thermal conductivity of concrete layer, thickness of concrete layer
coefficient between inside surface of pipe and water and can be and thermal conductivity of water pipe as well as average water
calculated by Eq. (8) [29]. flow rate and temperature. When these motioned parameters are
 known, we can calculate the surface temperature and heat trans-
7.67(tu − top )0.1 tu > top
˛u = (7) fer of radiant floor heating and cooling system using the proposed
5.7 tu < top model.

where tu is the upwards partial surface temperature of radiant floor. 3.1. Parameters of radiant floor heating and cooling systems

  D 2/3   Measured data from references [12,15,21,23,30] regarding to

2/3 1/3 o p
˛w = 0.116(Re − 125)Pr 1+ , surface temperature and heat transfer of radiant floor heating and
L Do
cooling systems were used to validate the proposed model. Parame-
2200 ≤ Re ≤ 10000 (8) ters of radiant floor heating and cooling systems in these references
can be seen in Tables 1 and 2, where measured systems include typ-
ical embedded surface heating and cooling systems and thermally
ṁDo activated building systems (TABS).
Re = (9)
A As shown in Tables 1 and 2, the thicknesses of both screed layer
and thermal insulation in radiant floor cooling systems are less than
where ṁ is the water flow rate in pipe and A is the cross-sectional
those in radiant floor heating systems.
area of the pipe.
According to the calculation equation of heat exchange rate
3.2. Comparison of the calculated data with the measured data
between the upwards partial surface of radiant floor and indoor
environment, formula for the upwards partial surface of radiant
The average water temperature is determined by the heat trans-
floor temperature (tu ) can be obtained, as follows
fer rate when the other parameters (as shown in Tables 1 and 2)
qu are known. Meanwhile, the heat transfer rate is also determined
tu = + top (10)
˛u by the average water temperature. Hence, we can use two meth-
Since the temperature difference between water side and indoor ods to validate the proposed model. For one method, the average
temperature in upwards room is equal to that between water side temperature is determined from the measurement as the input for
and indoor temperature in downwards room, the heat exchange the model, and then the calculated heat transfer rate is used to
rate between the downwards partial surface of radiant floor and compare with the measured data. For the other method, the heat
indoor environment can be obtained as follows, transfer rate is determined from the measurement as the input for
the model, and then the calculated average water temperature is
Ru used to compare with the measured data. The first method was
qd = qu (11)
Rd relatively convenient and was adopted in most of the references.
288 X. Wu et al. / Energy and Buildings 105 (2015) 285–293

Table 1
Parameters of the radiant floor heating systems in literatures [12,21,30].

Cases co (W/(mk)) ıco (mm) scr (W/(mk)) ıscr (mm) ins (W/(mk)) ıins (mm) con (W/(mk)) ıcon (mm) M (mm) Do (mm)

1a – – 1.30 50 0.04 30 – – 150 16

2a – – 1.30 50 0.04 30 – – 300 16
3a – – 1.30 60 0.04 30 – – 150 16
4a – – 1.30 60 0.04 30 – – 300 16
5a – – 1.30 80 0.04 30 – – 150 16
6a – – 1.30 80 0.04 30 – – 300 16
7a – – 1.30 80 0.04 30 – – 100 20
8a – – 1.30 80 0.04 30 – – 125 20
9a – – 1.30 80 0.04 30 – – 150 20
10a – – 1.30 80 0.04 30 – – 200 20
11a – – 1.30 80 0.04 30 – – 200 20
12a – – 1.30 80 0.04 30 – – 250 20
13a – – 1.30 80 0.04 30 – – 300 20
14b 0.14 15 1.70 80 0.05 150 1.00 200 320 20
15c – – – – – – 0.62 43.7 16
a
Liu et al. [21].
b
Hol et al. [12].
c
Ho [30].

Table 2
Parameters of the radiant floor cooling systems in literatures [15,23].

Cases co (W/(mk)) ıco (mm) scr (W/(mk)) ıscr (mm) ins (W/(mk)) ıins (mm) con (W/(mk)) ıcon (mm) M (mm) Do (mm)

1a 1.10 9 1.51 50 0.03 25 – – 100 20

2a 1.10 9 1.51 50 0.03 25 – – 150 20
3a 1.10 9 1.51 50 0.03 25 – – 200 20
4a 0.15 10 1.51 50 0.03 25 – – 150 20
5b 0.14 10 1.28 40 0.04 20 – – 150 20
a
Li et al. [23].
b
Jin et al. [15].

In this study, we used the first method to validate the proposed As shown in Table 3, the maximum differences between the
model and the average water temperature was determined from calculated surface temperature and heat transfer of radiant
the measurement, as shown in Tables 3 and 4. floor heating systems using the proposed model and the cor-
Substituting the parameters of radiant floor (as shown in responding measured values are 0.8 ◦ C and 8.1 W/m2 when
Tables 1 and 2) as well as indoor operative temperature and aver- average water temperature changing from 40 ◦ C to 60 ◦ C. The
age water flow rate and temperature (as shown in Tables 3 and 4) difference between the calculated surface temperature and
into the proposed model, the surface temperature and heat transfer heat transfer of radiant floor heating systems and the corre-
of radian floor can be obtained, as shown in Tables 3 and 4. sponding measured data in references [12,21,30] is slightly
large. The reason for this may be due to the measured aver-
age water temperature in references [12,21,30] were greatly
(1) Radiant floor heating systems larger than the indoor operative temperature (see Table 3). This
Comparison of the calculated surface temperature and heat would contribute to a non-uniform distribution of surface tem-
transfer of radiant floor heating systems with the measured perature of screed layer and differ from the assumption in the
data can be seen in Table 3. proposed model.

Table 3
Comparison of the calculated surface temperature and heat transfer of radiant floor heating systems with the measured data in literatures [12,21,30].

Cases tw (◦ C) top (◦ C) Measured td (◦ C) Calculated td (◦ C) Error td (◦ C) Measured qd (W/m2 ) Calculated qd (W/m2 ) Error qd (W/m2 )
a
1 56.0 18.0 38.0 38.1 0.0 192.0 192.5 0.5
2a 57.0 22.1 35.3 34.9 −0.4 126.7 122.5 −4.2
3a 57.0 19.0 39.1 38.3 −0.8 193.0 184.9 −8.1
4a 59.0 18.0 33.2 32.5 −0.7 145.9 139.5 −6.4
5a 58.0 25.2 40.3 40.6 0.3 145.0 147.8 2.9
6a 56.0 24.0 34.8 34.7 −0.1 103.7 102.7 −1.0
7a 57.0 25.2 44.0 44.8 0.8 180.5 188.1 7.6
8a 57.0 22.4 42.6 42.6 0.0 193.9 194.2 0.3
9a 59.0 26.2 44.8 44.4 −0.4 178.6 174.5 −4.0
10a 50.5 23.3 35.5 35.0 −0.5 117.1 112.3 −4.8
11a 59.5 26.0 40.6 40.8 0.2 140.2 141.7 1.5
12a 58.0 24.2 38.4 39.0 0.6 136.3 142.0 5.7
13a 59.9 23.2 37.7 38.3 0.6 139.2 144.8 5.6
14b 40.0 21.0 26.1 26.1 0.1 55.2 54.6 0.5

15c 43.0 25.8 28.5 29.0 0.5 29.2 34.1 5.0

43.6 28.4 30.3 30.3 0.0 20.5 20.6 0.1
a
Liu et al. [21].
b
Hol et al. [12].
c
Ho et al. [30].
 X. Wu et al. / Energy and Buildings 105 (2015) 285–293 289

Table 4
Comparison of the calculated surface temperature and heat transfer of radiant floor cooling systems with the measured data in literatures [15,23].

Cases tw (◦ C) top (◦ C) Measured td (◦ C) Calculated td (◦ C) Error td (◦ C) Measured qd (W/m2 ) Calculated qd (W/m2 ) Error qd (W/m2 )

17.8 24.2 19.3 19.4 0.1 31.9 31.3 0.6

1a 18.5 23.2 19.6 19.7 0.1 23.4 23.0 0.4
19.8 24.3 20.8 20.9 0.1 22.8 22.0 0.7

17.5 24.1 19.8 19.5 0.3 28.0 29.9 2.0

2a 18.4 23.8 20.3 20.0 0.3 22.8 24.4 1.7
20.0 24.7 21.2 21.4 0.2 22.8 21.3 1.5

17.5 24.4 20.1 19.9 0.2 28.0 29.0 1.0

3a 18.4 24.3 20.5 20.5 0.0 24.7 24.8 0.1
20.0 25.3 21.8 21.9 0.1 22.8 22.2 0.5

17.8 25.1 21.3 21.1 0.2 24.7 26.1 1.4

4a 18.5 24.7 21.1 21.3 0.2 23.4 22.2 1.2
19.8 24.9 21.9 22.1 0.2 19.5 18.3 1.2

10.8 28.1 20.7 20.4 0.3 48.3 50.3 2.0

11.9 28.4 21.2 21.0 0.2 47.0 48.0 1.0
13.8 28.3 21.9 21.8 0.1 41.8 42.2 0.4
13.8 26.5 21.1 20.8 0.3 35.4 37.1 1.7
5b
15.8 27.3 22.4 22.2 0.2 32.1 33.5 1.5
16.8 25.5 21.8 21.6 0.2 24.4 25.5 1.2
18.2 26.1 22.7 22.6 0.1 21.9 22.6 0.8
20.2 26.6 23.8 23.8 0.1 18.0 18.3 0.3
a
Li et al. [23].
b
Jin et al. [15].

Nowadays, many energy efficient building technologies such (2) The average temperature of supply and return water is consid-
as increased thermal insulation and air tightness have been ered as a typical reference temperature for calculation due to
extensively applied in the modern buildings. Theses energy the small water temperature change.
efficient building technologies will contribute to small build- (3) Resistance between water and inner pipe can be ignored when
ing heat loss and low energy demand in winter and also small the thermal conductivity of pipes is more than 100 W/(mK) [15].
average water temperature in the radiant floor heating systems. Otherwise, the resistance must be considered.
Hence, taking account of the practical conditions for the mod-
ern buildings, small average water temperature for radiant floor
heating systems should be used to validate the proposed model
and this work will be done in the next section.
(2) Radiant floor cooling systems
Comparison of the calculated surface temperature and heat
transfer of radiant floor cooling systems with the measured data
can be seen in Table 4.
As shown in Table 4, the maximum differences between the
calculated surface temperature and heat transfer of radiant
floor cooling systems using the proposed model and the cor-
responding measured values are 0.3 ◦ C and 2.0 W/m2 when
average water temperature changing from 10 ◦ C to 20 ◦ C. The
difference between the calculated surface temperature and
heat transfer of radiant floor cooling systems and the mea-
sured data in references [15,23] is small. This may be due to
that the measured average water temperatures in references
[15,23] were close to the indoor operative temperature, which
contribute to a uniform distribution of surface temperature of
screed layer and coincide with the assumption in the proposed
model.

4. Validation of the proposed model using the numerically

simulated data

4.1. Numerical simulation model and boundary conditions

In order to simplify the numerical simulation model of radiant

floor, the following assumptions are made:

(1) Homogeneous materials of each layer and negligible contact

resistance between any two layers in the radiant floor. Fig. 4. Numerical simulation model of radiant floor.
290 X. Wu et al. / Energy and Buildings 105 (2015) 285–293

Fig. 5. Relation between surface temperature and heat transfer of radiant floor and pipe space when ıscr = 65 mm, tw = 35 ◦ C.

(4) Heat conduction along pipe axis is ignored and the heat con- by using the finite difference method (FDM). The program is vali-
duction inside floor is two-dimensional steady state. dated against the standard EN ISO 10211 and EN ISO 10077-2 and
(5) Symmetric distribution of water pipelines. adopted as the test program for thermal performance calculation
of radiant floor in the standard ISO 11855 [25].
Based on the above assumptions, the numerical simulation In the HEAT2 program, there is an integrated pre-processor
model of radiant floor can be seen in Fig. 4. which is a CAD-like drawing program that makes it even simpler
Two-dimensional heat conduction differential equation which to generate input for a wide range of heat transfer problems. The
describes the heat transfer of radiant floor can be expressed as geometry is built using rectangles of different materials that may
following, overlap each other, and then a suitable input mesh will automat-
ically be generated when the pre-processor is used [31]. It is also
∂2 t ∂2 t
+ 2 =0 (16) possible to give the input for a problem numerically without using
∂2 x ∂ y the pre-processor [31]. In this study, since the shape of radiant
Four boundary conditions are needed to solve the above differ- floor is rectangle, the pre-processor was used and input mesh will
ential equation. automatically be generated.

∂t
=0 (17)
∂x 4.2. Comparison of the calculated data with the numerically
x=± M
2
simulated data
∂t
−scr = ˛u (tu − top ) (18)
∂y D Since the changes of parameters for the radiant floor except
y=ıco +ıscr − 2o
the pipe space, thickness of screed layer and average water tem-
∂t perature were relatively small in practice, typical parameters of
−con = ˛d (tds − top ) (19) the radiant floor heating and cooling systems in the standard ISO
∂y D
y= 2o +ıins +ıcon
11855 [25] were used as the inputs for the proposed model and the
The temperature fields of radiant floor are calculated by solving numerically simulated model, as shown in Table 5. Indoor opera-
the partial differential equation (as shown in Eq. (16)) using HEAT2 tive temperature was set as 20 ◦ C for the heating case and 26 ◦ C for
program [31], and then the heat transfer of radiant floor can be cal- the cooling case. When the pipe space, average water temperature
culated. HEAT2 is a PC-program for two-dimensional transient and and thickness of screed layer are given, the surface temperature
steady-state heat conduction within objects that can be described and heat transfer of radiant floor can be calculated by using the
in a rectangular grid. HEAT2 solves the heat conduction equation proposed model and the numerically simulated model.

Fig. 6. Relation between surface temperature and heat transfer of radiant floor and average water temperature when M = 150 mm, ıscr = 65 mm.
 X. Wu et al. / Energy and Buildings 105 (2015) 285–293 291

Fig. 7. Relation between surface temperature and heat transfer of radiant floor and thickness of the screed layer when M = 150 mm, tw = 35 ◦ C.

Table 5
Parameters of the radiant floor heating and cooling systems in ISO 11855.

co (W/(mk)) ıco (mm) scr (W/(mk)) ins (W/(mk)) ıins (mm) con (W/(mk)) ıcon (mm) Di (mm) Do (mm)

0.23 15 1.2 0.04 30 2.1 180 17.7 20

(1) Radiant floor heating systems (2) Radiant floor cooling systems
Comparison of the calculated surface temperature and heat Comparison of the calculated surface temperature and heat
transfer of radiant floor heating systems with the numerically transfer of radiant floor cooling systems with the numerically
simulated data can be seen in Figs. 5–7. simulated data can be seen in Figs. 10–12.
Figs. 5–7 show that the surface temperature and heat transfer Figs. 10–12 show that the surface temperature and heat
of radiant floor calculated using the proposed model agree very transfer of radiant floor calculated using the proposed model
well with the numerically simulated data when the pipe space agree very well with the numerically simulated data when the
varied from 50 mm to 300 mm, the average water temperature pipe space varied from 50 mm to 200 mm, the average water
was from 25 ◦ C to 45 ◦ C and the thickness of screed layer was temperature was from 10 ◦ C to 20 ◦ C and the thickness of screed
from 35 mm to 95 mm. layer was from 35 mm to 95 mm.
As shown in Figs. 5–7, both the pipe space and average water As shown in Figs. 10–12, both the pipe space and average
temperature have large impact on the surface temperature and water temperature have large impact on the surface temper-
heat transfer of radiant floor heating systems, while the thick- ature and heat transfer of radiant floor cooling systems, while
ness of the screed layer seems has nearly no influence on the the thickness of the screed layer has nearly no influence on the
surface temperature and heat transfer of radiant floor heating surface temperature and heat transfer of radiant floor cooling
systems. This is mainly due to that the pipe space has rela- systems. This is mainly due to that the pipe space has rela-
tively large impact on the thermal resistance of radiant floor, tively large impact on the thermal resistance of radiant floor,
while the thickness of the screed layer has relatively no influ- while the thickness of the screed layer has relatively no influ-
ence on the thermal resistance of radiant floor, as shown in ence on the thermal resistance of radiant floor, as shown in
Figs. 8 and 9. Besides, average water temperature has no impact Figs. 8 and 9.
on the thermal resistance of radiant floor but large impact on
the temperature difference, as shown in Eq. (6).

Fig. 9. Relation between thermal resistance of radiant floor and thickness of the
Fig. 8. Relation between thermal resistance of radiant floor and pipe space. screed layer.
292 X. Wu et al. / Energy and Buildings 105 (2015) 285–293

Fig. 10. Relation between surface temperature and heat transfer of radiant floor and pipe space when ıscr = 65 mm, tw = 15 ◦ C.

Fig. 11. Relation between surface temperature and heat transfer of radiant floor and average water temperature when M = 100 mm, ıscr = 65 mm.

Fig. 12. Relation between surface temperature and heat transfer of radiant floor and thickness of the screed layer when M = 100 mm, tw = 15 ◦ C.

5. Conclusions the surface temperature and heat transfer of radiant floor, while
the thickness of screed layer had nearly no impact on the surface
A valid simplified model to calculate surface temperature and temperature and heat transfer of radiant floor.
heat transfer of radiant floor heating and cooling system was devel-
oped using the conduction shape factor. The effect of average water Acknowledgments
temperature, pipe space and thickness of screed layer on the surface
temperature and heat transfer of radiant floor were quantitatively This study was funded by National Natural Science Foundation
analyzed using the proposed model. The results showed that both of China (Grant number 51408482) and China Postdoctoral Sci-
pipe space and average water temperature had a large impact on ence Foundation (Grant number 2014M550496) and supported by
 X. Wu et al. / Energy and Buildings 105 (2015) 285–293 293

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