EN ISO 11855-4:2015

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Building environment design - Design, dimensioning, installation and control of
embedded radiant heating and cooling systems - Part 4: Dimensioning and calculation of
the dynamic heating and cooling capacity of Thermo Active Building Systems (TABS)
(ISO 11855-4:2012)
Umweltgerechte Gebäudeplanung - Planung, Auslegung, Installation und Steuerung
flächenintegrierter Strahlheizungs- und -kühlsysteme - Teil 4: Auslegung und
Berechnung der dynamischen Wärme- und Kühlleistung für thermoaktive Bauteilsysteme
(TABS) (ISO 11855-4:2012)
Conception de l'environnement des bâtiments - Conception, construction et
fonctionnement des systèmes de chauffage et de refroidissement par rayonnement -
Partie 4: Dimensionnement et calculs relatifs au chauffage adiabatique et à la puissance
frigorifique pour systèmes thermoactifs (TABS) (ISO 11855-4:2012)
Ta slovenski standard je istoveten z: EN ISO 11855-4:2015
ICS:
91.140.10 Sistemi centralnega Central heating systems
ogrevanja
91.140.30 3UH]UDþHYDOQLLQNOLPDWVNL Ventilation and air-
VLVWHPL conditioning
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 11855-4
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2015
ICS 91.140.10; 91.140.30 Supersedes EN 15377-3:2007
English Version
Building environment design - Design, dimensioning, installation
and control of embedded radiant heating and cooling systems -
Part 4: Dimensioning and calculation of the dynamic heating and
cooling capacity of Thermo Active Building Systems (TABS)
(ISO 11855-4:2012)
Conception de l'environnement des bâtiments - Conception, Umweltgerechte Gebäudeplanung - Planung, Auslegung,
construction et fonctionnement des systèmes de chauffage Installation und Steuerung flächenintegrierter
et de refroidissement par rayonnement - Partie 4: Strahlheizungs- und -kühlsysteme - Teil 4: Auslegung und
Dimensionnement et calculs relatifs au chauffage Berechnung der dynamischen Wärme- und Kühlleistung für
adiabatique et à la puissance frigorifique pour systèmes thermoaktive Bauteilsysteme (TABS) (ISO 11855-4:2012)
thermoactifs (TABS) (ISO 11855-4:2012)
This European Standard was approved by CEN on 30 July 2015.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2015 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 11855-4:2015 E
worldwide for CEN national Members.

Contents Page
European foreword .3
European foreword
The text of ISO 11855-4:2012 has been prepared by Technical Committee ISO/TC 205 “Building environment
design” of the International Organization for Standardization (ISO) and has been taken over as EN ISO
11855-4:2015 by Technical Committee CEN/TC 228 “Heating systems and water based cooling systems in
buildings” the secretariat of which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by February 2016, and conflicting national standards shall be withdrawn
at the latest by February 2016.
This standard is applicable for design, construction and operation of radiant heating and cooling systems. The
methods defined in part 2 are intended to determine the design heating or cooling capacity used for the design
and evaluation of the performance of the system.
For identifying product characteristics by testing and proving the thermal output of heating and cooling
surfaces embedded in floors, ceilings and walls the standard series EN 1264 can be used.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN 15377-3:2007.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Endorsement notice
The text of ISO 11855-4:2012 has been approved by CEN as EN ISO 11855-4:2015 without any modification.
INTERNATIONAL ISO
STANDARD 11855-4
First edition
2012-08-01
Building environment design — Design,
dimensioning, installation and control of
embedded radiant heating and cooling
systems —
Part 4:
Dimensioning and calculation of the
dynamic heating and cooling capacity of
Thermo Active Building Systems (TABS)
Conception de l'environnement des bâtiments — Conception,
construction et fonctionnement des systèmes de chauffage et de
refroidissement par rayonnement —
Partie 4: Dimensionnement et calculs relatifs au chauffage adiabatique
et à la puissance frigorifique pour systèmes thermoactifs (TABS)

Reference number
ISO 11855-4:2012(E)
©
ISO 2012
ISO 11855-4:2012(E)
©  ISO 2012
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
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Published in Switzerland
ii © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
Contents Page
Foreword . iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviations . 1
5 The concept of Thermally Active Surfaces (TAS) . 6
6 Calculation methods . 11
6.1 General . 11
6.2 Rough sizing method . 12
6.3 Simplified sizing by diagrams . 13
6.4 Simplified model based on finite difference method (FDM) . 19
6.4.1 Cooling system . 20
6.4.2 Hydraulic circuit and slab . 20
6.4.3 Room . 22
6.4.4 Limits of the method . 24
6.5 Dynamic building simulation programs . 25
7 Input for computer simulations of energy performance . 25
Annex A (informative) Simplified diagrams . 26
Annex B (normative) Calculation method . 31
B.1. Pipe level . 31
B.2. Thermal nodes composing the slab and room . 31
B.3. Calculations for the generic h-th hour . 35
B.4 Sizing of the system . 41
Annex C (informative) Tutorial guide for assessing the model . 42
Annex D (informative) Computer program . 44
Bibliography . 52

ISO 11855-4:2012(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 11855-4 was prepared by Technical Committee ISO/TC 205, Building environment design.
ISO 11855 consists of the following parts, under the general title Building environment design — Design,
dimensioning, installation and control of embedded radiant heating and cooling systems:
— Part 1: Definition, symbols, and comfort criteria
— Part 2: Determination of the design and heating and cooling capacity
— Part 3: Design and dimensioning
— Part 4: Dimensioning and calculation of the dynamic heating and cooling capacity of Thermo Active
Building Systems (TABS)
— Part 5: Installation
— Part 6: Control
Part 1 specifies the comfort criteria which should be considered in designing embedded radiant heating and
cooling systems, since the main objective of the radiant heating and cooling system is to satisfy thermal
comfort of the occupants. Part 2 provides steady-state calculation methods for determination of the heating
and cooling capacity. Part 3 specifies design and dimensioning methods of radiant heating and cooling
systems to ensure the heating and cooling capacity. Part 4 provides a dimensioning and calculation method to
design Thermo Active Building Systems (TABS) for energy-saving purposes, since radiant heating and cooling
systems can reduce energy consumption and heat source size by using renewable energy. Part 5 addresses
the installation process for the system to operate as intended. Part 6 shows a proper control method of the
radiant heating and cooling systems to ensure the maximum performance which was intended in the design
stage when the system is actually being operated in a building.
iv © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
Introduction
The radiant heating and cooling system consists of heat emitting/absorbing, heat supply, distribution, and
control systems. The ISO 11855 series deals with the embedded surface heating and cooling system that
directly controls heat exchange within the space. It does not include the system equipment itself, such as heat
source, distribution system and controller.
The ISO 11855 series addresses an embedded system that is integrated with the building structure.
Therefore, the panel system with open air gap, which is not integrated with the building structure, is not
covered by this series.
The ISO 11855 series shall be applied to systems using not only water but also other fluids or electricity as a
heating or cooling medium.
The object of the ISO 11855 series is to provide criteria to effectively design embedded systems. To do this, it
presents comfort criteria for the space served by embedded systems, heat output calculation, dimensioning,
dynamic analysis, installation, operation, and control method of embedded systems.
INTERNATIONAL STANDARD ISO 11855-4:2012(E)

Building environment design — Design, dimensioning,
installation and control of embedded radiant heating and
cooling systems —
Part 4:
Dimensioning and calculation of the dynamic heating and
cooling capacity of Thermo Active Building Systems (TABS)
1 Scope
This part of ISO 11855 allows the calculation of peak cooling capacity of Thermo Active Building Systems
(TABS), based on heat gains, such as solar gains, internal heat gains, and ventilation, and the calculation of
the cooling power demand on the water side, to be used to size the cooling system, as regards the chiller size,
fluid flow rate, etc.
This part of ISO 11855 defines a detailed method aimed at the calculation of heating and cooling capacity in
non-steady state conditions.
The ISO 11855 series is applicable to water based embedded surface heating and cooling systems in
residential, commercial and industrial buildings. The methods apply to systems integrated into the wall, floor or
ceiling construction without any open air gaps. It does not apply to panel systems with open air gaps which
are not integrated into the building structure.
The ISO 11855 series also applies, as appropriate, to the use of fluids other than water as a heating or cooling
medium. The ISO 11855 series is not applicable for testing of systems. The methods do not apply to heated or
chilled ceiling panels or beams.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 11855-1, Building environment design — Design, dimensioning, installation and control of embedded
radiant heating and cooling systems — Part 1: Definition, symbols, and comfort criteria
3 Terms and definitions
For the purposes of this document, the terms and definitions in ISO 11855-1 apply.
4 Symbols and abbreviations
For the purposes of this part of ISO 11855, the symbols and abbreviations in Table 1 apply:
ISO 11855-4:2012(E)
Table 1 — Symbols and abbreviations
Symbol Unit Quantity
A
m Area of the heating/cooling surface area
F
A m Total area of internal vertical walls (i.e. vertical walls, external façades excluded)
W
C J/(m ·K) Specific thermal capacity of the thermal node under consideration
C J/(m ·K) Average specific thermal capacity of the internal walls
W
c
J/(kg·K) Specific heat of the material constituting the j-th layer of the slab
j
c
J/(kg·K) Specific heat of water
w
d
m External diameter of the pipe
a
E kWh/m Specific daily energy gains
Day
Running mode (1 when the system is running; 0 when the system is switched off) in the
h
f
-
rm
h-th hour
f - Design safety factor
s
F
- View factor between the floor and the ceiling
v F-C
F
- View factor between the floor and the external walls
v F-EW
F
- View factor between the floor and the internal walls
v F-W
h W/(m ·K) Convective heat transfer coefficient between the air and the ceiling
A-C
h
W/(m ·K) Convective heat transfer coefficient between the air and the floor
A-F
h
W/(m ·K) Convective heat transfer coefficient between the air and the internal walls
A-W
h
W/(m ·K) Radiant heat transfer coefficient between the floor and the ceiling
F-C
h W/(m ·K) Radiant heat transfer coefficient between the floor and the internal walls
F-W
Heat transfer coefficient between the thermal node under consideration and the air
H W/K
A
thermal node (“A”)
Heat transfer coefficient between the thermal node under consideration and the ceiling
H W/K
C
surface thermal node (“C”)
H W/K Heat transfer coefficient between the thermal node under consideration and the circuit
Circuit
H W/K Heat transfer coefficient between the thermal node under consideration and the next one
CondDown
Heat transfer coefficient between the thermal node under consideration and the previous
H W/K
CondUp
one
H - Fraction of internal convective heat gains acting on the thermal node under consideration
Conv
Heat transfer coefficient between the thermal node under consideration and the floor
H W/K
F
surface thermal node (“F”)
H W/K Coefficient connected to the inertia contribution at the thermal node under consideration
Inertia
Heat transfer coefficient between the thermal node under consideration and the internal
H W/K
IWS
wall surface thermal node (“IWS”)
H - Fraction of total radiant heat gains impinging on the thermal node under consideration
Rad
h
W/(m ·K) Total heat transfer coefficient (convection + radiation) between surface and space
t
J - Number of layers constituting the slab as a whole
2 © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
Symbol Unit Quantity
J
- Number of layers constituting the upper part of the slab
J
- Number of layers constituting the lower part of the slab
L
m Length of installed pipes
R

m
kg/(m ·s) Specific water flow in the circuit, calculated on the area covered by the circuit
H,sp
m
- Number of partitions of the j-th layer of the slab
j
n - Actual number of iteration in iterative calculations
n h Number of operation hours of the circuit
h
Max
n - Maximum number of iterations allowed in iterative calculations
Max,h
P W Maximum cooling power reserved to the circuit under consideration in the h-th hour
Circuit
Max 2
P W/m Maximum specific cooling power (per floor square metre)
Circuit,Spec
q W/m Inward specific heat flow
i
q W/m Outward specific heat flow
u
h
Q W Heat flow impinging on the ceiling surface (“C”) in the h-th hour
C
h
Q W Heat flow extracted by the circuit in the h-th hour
Circuit
h
Q
W Total convective heat gains in the h-th hour
Conv
h
Q W Heat flow impinging on the floor surface (“F”) in the h-th hour
F
h
Q W Internal convective heat gains in the h-th hour
IntConv
h
Q W Internal radiant heat gains in the h-th hour
IntRad
h
Q
W Heat flow impinging on the internal wall surface (“IWS”) in the h-th hour
IWS
h
Q W Primary air convective heat gains in the h-th hour
PrimAir
h
Q W Total radiant heat gains in the h-th hour
Rad
h
Q W Solar heat gains in the room in the h-th hour
Sun
h
Q
W Transmission heat gains in the h-th hour
Transm
Q
W/m Average specific cooling power
W
R (m ·K)/W Generic thermal resistance
R
(m ·K)/W Additional thermal resistance covering the lower side of the slab
Add C
R
(m ·K)/W Additional thermal resistance covering the upper side of the slab
Add F
Convection thermal resistance connecting the air thermal node (“A”) with the ceiling
RCAC K/W
surface thermal node (“C”)
Convection thermal resistance connecting the air thermal node (“A”) with the floor surface
RCAF K/W
thermal node (“F”)
Convection thermal resistance connecting the air thermal node (“A”) with the internal wall
RCAW K/W
surface thermal node (“IWS”)
ISO 11855-4:2012(E)
Symbol Unit Quantity
R (m ·K)/W Internal thermal resistance of the slab conductive region
int
Conduction thermal resistance connecting the p-th thermal node with the boundary of the
R (m ·K)/W
L,p
(p+1)-th thermal node
R
(m ·K)/W Pipe thickness thermal resistance
r
Radiation thermal resistance connecting the floor surface thermal node (“F”) with the
RRFC K/W
ceiling surface thermal node (“C”)
Radiation thermal resistance connecting the internal wall surface thermal node (“IWS”)
RRWC K/W
with the ceiling surface thermal node (“C”)
Radiation thermal resistance connecting the internal wall surface thermal node (“IWS”)
RRWF K/W
with the floor surface thermal node (“F”)
R (m ·K)/W Circuit total thermal resistance
t
Conduction thermal resistance connecting the p-th thermal node with the boundary of the
R (m ·K)/W
U,p
(p-1)-th thermal node
R
(m ·K)/W Wall surface thermal resistance
Walls
R
(m ·K)/W Water flow thermal resistance
w
R
(m ·K)/W Pipe level thermal resistance
x
R (m ·K)/W Convection thermal resistance at the pipe inner side
z
s
m Pipe wall thickness
r
s
m Thickness of the upper part of the slab
s
m Thickness of the lower part of the slab
W m Pipe spacing
δ
m Thickness of the j-th layer of the slab
j
 K Generic temperature difference
Max
 K Maximum operative temperature drift allowed for comfort conditions
Comfort
t s Calculation time step
h

°C Temperature of the air thermal node (“A”) in the h-th hour
A
h
 °C Temperature of the ceiling surface thermal node (“C”) in the h-th hour
C
Max
 °C Maximum operative temperature allowed for comfort conditions
Comfort
 °C Maximum operative temperature allowed for comfort conditions in the reference case
Comfort,Ref
h

°C Temperature of the floor surface thermal node (“F”) in the h-th hour
F
h
 °C Temperature of the core of the internal walls thermal node (“IW”) in the h-th hour
IW
h
 °C Temperature of the internal wall surface thermal node (“IWS”) in the h-th hour
IWS
h
 °C Room mean radiant temperature in the h-th hour
MR
h

°C Room operative temperature in the h-th hour
Op
4 © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
Symbol Unit Quantity
h

°C Temperature of the p-th thermal node in the h-th hour
p
h
 °C Temperature of the pipe level thermal node (“PL”) in the h-th hour
PL
Av
 °C Daily average temperature of the conductive region of the slab
Slab
h
 °C Water inlet actual temperature in the h-th hour
Water,In
Setp,h

°C Water inlet set-point temperature in the h-th hour
Water,In
Setp

°C Water inlet set-point temperature in the reference case
Water,In,Ref
h

°C Water outlet temperature in the h-th hour
Water,Out
 W/(m·K) Thermal conductivity of the material of the pipe embedded layer
b
λ
W/(m·K) Thermal conductivity of the material constituting the j-th layer of the slab
j

W/(m·K) Thermal conductivity of the material constituting the pipe
r

K Actual tolerance in iterative calculations
 K Maximum tolerance allowed in iterative calculations
Max

kg/m Density of the material constituting the j-th layer of the slab
j

various Slope of correlation curves

ISO 11855-4:2012(E)
5 The concept of Thermally Active Surfaces (TAS)
A Thermally Active Surface (TAS) is an embedded water based surface heating and cooling system, where
the pipe is embedded in the central concrete core of a building construction (see Figure 1).

Key
C concrete
F floor
P pipes
R room
RI reinforcement
W window
Figure 1 — Example of position of pipes in TAS
The building constructions embedding the pipe are usually the horizontal ones. As a consequence, in the
following sections, floors and ceilings are usually referred to as active surfaces. Looking at a typical structure
of a TAS, heat is removed by a cooling system (for instance, a chiller), connected to pipes embedded in the
slab. The system can be divided into the elements shown in Figure 2.
6 © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
Key
1 heating/cooling equipment
2 hydraulic circuit
3 slab including core layer with pipes
4 possible additional resistances (floor covering or suspended ceiling)
5 room below and room above
PL pipe level
Figure 2 — Simple scheme of a TAS
Thermally active surfaces exploit the high thermal inertia of the slab in order to perform the peak-shaving. The
peak-shaving consists in reducing the peak in the required cooling power (see Figure 3), so that it is possible
to cool the structures of the building during a period in which the occupants are absent (during night time, in
office premises). This way the energy consumption can be reduced and a lower night time electricity rate can
be used. At the same time a reduction in the size of heating/cooling system components (including the chiller)
is possible.
ISO 11855-4:2012(E)
Y
X
Key
X time, h
Y cooling power, W
1 heat gain
2 cooling power needed for conditioning the ventilation air
3 cooling power needed on the water side
4 reduction of the required peak power
Figure 3 — Example of peak-shaving effect
TABS may be used both with natural and mechanical ventilation (depending on weather conditions).
Mechanical ventilation with dehumidifying may be required depending on external climate and indoor humidity
production. In the example in Figure 3, the required peak cooling power needed for dehumidifying the air
during day time is sufficient to cool the slab during night time.
As regards the design of TABS, the planner needs to know if the capacity at a given water temperature is
sufficient to keep the room temperature within a given comfort range. Moreover, the planner needs also to
know the heat flow on the water side to be able to dimension the heat distribution system and the chiller/boiler.
This part of ISO 11855 provides methods for both purposes.
When using TABS, the indoor temperature changes moderately during the day and the aim of a good TABS
design is to maintain internal conditions within the range of comfort, i.e. –0,5 < PMV < 0,5, during the day,
according to ISO 7730 (see Figure 4).
8 © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
Y
X
Key
X  time, h
Y  temperature, °C
PMV Predicted Mean Vote
θ  air temperature
air
θ  ceiling temperature
c
θ  mean radiant temperature
mr
θ  floor temperature
f
θ water return temperature
w exit
Figure 4 — Example of temperature profiles and PMV values vs. time
Some detailed building system calculation models have been developed to determine the heat exchanges
under unsteady state conditions in a single room, the thermal and hygrometric balance of the room air,
prediction of comfort conditions, check of condensation on surfaces, availability of control strategies and
calculation of the incoming solar radiation. The use of such detailed calculation models is, however, limited
due to the high amount of time needed for the simulations. The development of a more user friendly tool is
required. Such a tool is provided in this part of ISO 11855, and allows the simulation of TAS.
The diagrams in Figure 5 show an example of the relation between internal heat gains, water supply
temperature, heat transfer on the room side, hours of operation and heat transfer on the water side. The
diagrams refer to a concrete slab with raised floor (R = 0,45 (m ·K)/W) and an allowed room temperature
range of 21°C to 26°C.
The upper diagram shows on the Y-axis the maximum permissible total heat gain in space (internal heat gains
plus solar gains) [W/m ], and on the X-axis the required water supply temperature. The lines in the diagram
correspond to different operation periods (8 h, 12 h, 16 h, and 24 h) and different maximum amounts of
energy supplied per day [Wh/(m ·d)].
The lower diagram shows the cooling power [W/m ] required on the water side (to dimension the chiller) for
TAS as a function of supply water temperature and operation time. Further, the amount of energy rejected per
day is indicated [Wh/(m ·d)].
The example shows that, for a maximum internal heat gain of 38 W/m and 8 h operation, a supply water
temperature of 18,2 °C is required. If, instead, the system is in operation for 12 h, a supply water temperature
ISO 11855-4:2012(E)
of 19,3 °C is required. In total, the amount of energy rejected from the room is approximately 335 Wh/m per
day. In the same conditions, the required cooling power on the water side is 37 W/m (for 8 h operation) and
25 W/m (for 12 h operation) respectively. Thus, by 12 h operation, the chiller can be much smaller.
Y
X
Y
Key
X (upper diagram) inlet temperature tabs, °C
Y (upper diagram) maximum total heat gain in space (W/m , floor area)
Y (lower diagram) mean cooling power tabs (W/m , floor area)
Figure 5 — Working principle of TABS
10 © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
6 Calculation methods
6.1 General
TABS are systems with high thermal inertia. Therefore, for sizing chillers coupled with them, dynamic
simulations have to be carried out. In principle, the solution of heat transfer inside structures with embedded
pipes has to deal with 2-D calculations (see Figure 6). The calculation time required to consider the 2-D
thermal field and the overall balance with the rest of the room is usually too high. Therefore, mathematical
models in literature are usually based on a link between the pipe surface and the upper and lower surfaces
(i.e. floor and ceiling).
One possibility to model radiant systems is to apply response factors to the pipe surface, upper surface and
lower surface of the slab (see Figure 7). This way, the conduction heat transfer is defined via nine response
factor series, that can be reduced to six response factor series, because of reciprocity rules.
Hp: T = T = T
1 2 3
T T T
q = 0 q = 0
1 2 1
Key
1 upper surface
2 pipe surface
3 lower surface
Figure 6 — Heat transfer through structures containing pipes
z
z
z
z
z
z
z z z
Figure 7 — Transfer functions for building elements containing pipes
ISO 11855-4:2012(E)
Another possibility is to consider a resistance between the external pipe surface and an equivalent core
temperature at pipe level, which represents the average temperature along the axial plane of the pipes (see
Figure 8). From the core level to upward and downward levels, a 1-D resistance-capacity network or 1-D
response factor series (or transfer function) can be applied.
R
θ
t
Key
LS  lower part of the slab
LST  lower surface temperature (ceiling)
R  circuit total thermal resistance
t
US  upper part of the slab
UST upper surface temperature (floor)
θ  mean temperature at the pipe level
PL
θ water supply temperature
Water,In
Figure 8 — Simplified model for the conductive heat transfer in a structure containing pipes
In this part of ISO 11885, the following calculation methods are presented:
 Rough sizing method, based on a standard calculation of the cooling load (error: 20÷30%). To be used
starting from the knowledge of the daily heat gains in the room (see 6.2).
 Simplified method using diagrams for sizing, based on the knowledge of the total energy to be extracted
daily to ensure comfort conditions (error: 15÷20%). For details, see 6.3.
 Simplified model based on finite difference method (FDM) (error: 10÷15%). It consists in detailed dynamic
simulations predicting the heat transfers in the slab and even in the room via FDM. Based on the
knowledge of the values of the variable cooling loads of the room during each hour of the day. For further
details, see 6.4.
 Detailed simulation models (error: 6÷10%). It implies the overall dynamic simulation model for the radiant
system and the room via detailed building-system simulation software (see 6.5).
6.2 Rough sizing method
The cooling system shall be sized via the following equation:
12 © ISO 2012 – All rights reserved

ISO 11855-4:2012(E)
E
Day
Max 2
P 1000f     [W/m] (1)
Circuit,Spec s
n
h
where
Max
P is the maximum specific cooling power (per floor square metre) [W/m ];
Circuit,Spec
E  is the specific daily energy gains [kWh/m ];
Day
n  is the number of operation hours of the circuit [h];
h
f  is the safe design factor (greater than one, usually 1,15) [-].
s
For this purpose, E shall be calculated in the following way:
Day
 The hourly values of heat gains are calculated for the room under the design conditions and occupancy
schedules, via an energy simulation tool or a proper method for the calculation of heat gains.
 E is the sum of the 24 values of heat gains.
Day
The heat gains calculation has to be carried out using an operative temperature 0,5°C lower than the average
operative temperature during occupancy hours, for the sake of safe design. As a consequence, if the room
operative temperature drift during occupancy hours is 21,0°C to 26,0°C, then the room average operative
temperature during occupancy hours is 23,5°C, and the reference room operative temperature for the
calculation of heat gains is 23,0°C.
6.3 Simplified sizing by diagrams
In this case, the calculation of the heat gains has to be carried out by means of the value of the total cooling
energy to be provided during the day in order to ensure comfort conditions at the average operative
temperature (for instance, 23,0°C). This method is based on the assumption that the entire thermally
conductive part of the slab is maintained at an almost constant temperature during the whole day, due to its
own thermal inertia and the thermal resistance dividing it from the rooms over and below. This average
temperature of the slab is calculated by the method itself and is used to calculate the water supply
temperature depending on the running time of the circuit.
The following magnitudes are involved in this method:
 E : specific daily energy gains in the room during the design day: it consists of the sum of heat gains
Day
values acting during the whole design day, divided by the floor area [kWh/m ].
Max
 θ : maximum operative room temperature allowed for comfort conditions [°C].
Comfort
 Orientation of the room: used to determine when the peak load in heat gains happens: east (morning),
south (noon) or west (afternoon).
 Number of active surfaces: distinguishes whether the slab works transferring heat both through the floor
side and through the ceiling side or just through the ceiling side (see Figure 9).
 n : number of operation hours of the circuit [h].
h
 R : internal thermal resistance of the slab conductive region [(m ·K)/W]. It is the average thermal
Int
resistance that connects the conductive parts of the slab placed near the pipe level to the pipe level itself
(see Figure 12).
ISO 11855-4:2012(E)
Av
 θ : daily average temperature of the conductive region of the slab [°C]. It is a result of the present
Slab
method and depends on the number of active surfaces (ceiling only, or ceiling and floor), the running
mode (24 h or 8 h) and the shape of the internal load profile (lunch break or not) and room orientation.
The average temperature of the slab is achieved through coefficients included in the method by the
equation.
Av Max
θθ E     [°C] (2)
Slab Comfort Day
where ω is a coefficient, whose values are given in Tables 1 and 2.
 R : circuit total thermal resistance, obtained via the Resistance Method (for further details, see
t
ISO 11855-2) [(m ·K)/W]. This thermal resistance depends on the characteristics of the circuit, pipe, and
conductive slab (see Figure 14).
Setp
  : water supply temperature required for ensuring comfort conditions [°C].
Water,In
It is obtained through the following equation:
E 1000
Setp Av Day
θθ RR     [°C] (3)
 
Slab int t
Water,In

h

0,15m
Key
1 concrete
2 reinforced concrete
Conductive region: Material 1 and Material 2
Number of active surfaces: 2
Figure 9 — Example 1 — Conductive regions and numbers of active surfaces
14 © ISO 2012 – All rights reserved

0,20m 0,07m
ISO 11855-4:2012(E)
0,15m
Key
1 wood
2 air
3 reinforced concrete
Conductive region: Material 3
Number of active surfaces: 1
Figure 10 — Example 2 — Conductive regions and numbers of active surfaces
0,20m 0,15m 0,04m
ISO 11855-4:2012(E)
0,15m
0,03m
Key
1 wood
2 concrete
3 fibreglass
4 reinforced concrete
Conductive region: Material 4
Number of active surfaces: 1
Figure 11 — Example 3 — Conductive regions and numbers of active surfaces
16 © ISO 2012 – All rights reserved

0,20m 0,06m 0,02m
ISO 11855-4:2012(E)
ROS
R /2•R /2
Up Down
θ
Slab
R
R
Up int
R /2+R /2
Up Down
R /2
Up
θ
θ
PL
Slab
R /2
Down
θ
θ
PL
Down
θ
Slab
Key
CR  conductive region
LCR lower part of the slab conductive region
PL  pipe level
R total thermal resistance of the lower part of the slab conductive region
Down
R  internal thermal resistance of the slab conductive region
int
R  total thermal resistance of the upper part of the slab conductive region
Up
ROS rest of the slab
UCR upper part of the slab conductive region
θ  average daily temperature at the pipe level
PL
θ  average daily temperature of the conductive region of the slab
slab
Figure 12 — Thermal resistance network equivalent to the slab conductive region in simplified sizing
by diagrams
The coefficients suggested for the calculation of the average temperature of the conductive region of the slab
are given in Tables 2 and 3, depending on the shape of the internal heat gain profile. For intermediate
duration (e.g. a lunch break), a correspondent interpolation between coefficients of Table 2 and Table 3 is
recommended.
Table 2 — Constant internal heat gains from 8:00 to 18:00
Orientation of the room
Number of active
Circuit running mode East (E) South (S) West (W)
surfaces
ω
Floor and ceiling (C2) -4,6 816 -5,3 696 -5,935
Continuous (24 h)
Only ceiling (C1) -6,3 022 -7,2 237 -7,7 982
Floor and ceiling (I2) -5,5 273 -6,1 701 -6,7 323
Intermittent (8 h)
Only ceiling (I1) -7,2 853 -7,8 562 -8,5 791
ISO 11855-4:2012(E)
Table 3 — Constant internal heat gains from 8:00 to 12:00 and from 14:00 to 18:00
Orientation of the room
Number of active
Circuit running mode East (E) South (S) West (W)
surfaces
ω
Floor and ceiling (C2) -6,279 -7,1 094 -7,3 681
Continuous (24 h)
Only ceiling (C1) -7,9 663 -8,7 989 -8,7 455
Floor and ceiling (I2) -8,1 474 -8,758 -9,3 264
Intermittent (8 h)
Only ceiling (I1) -10,029 -10,685 -10,967

Max
By the choice of θ , it is possible to adapt the method to different maximum room operative
Comfort
temperatures, if the same maximum operative temperature drift allowed for comfort conditions is kept. Once
Max Max
θ is defined, the tables can be summarized by diagrams. For example, if θ = 26°C, the diagram
Comfort Comfort
for constant internal heat gains from 8:00 to 18:00 is as given in Figure 13.
Y
0 0,2 0,4 0,6 0,8
X
Key
X E °C
Day,
Y θ kWh/m
slab,
Figure 13 — Diagram for determining θ as a function of the specific daily energy, exposure of the
slab
room (E = east, S = south, W = west), running mode of the circuit (C = continuous - 24 h, I =
intermittent - 8 h), and number of active surfaces (1 or 2), in the case of constant internal heat gains
during the day
18 © ISO 2012 – All rights reserved
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