Building environment design - 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 11855-4:2021)

This document 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 document defines a detailed method aimed at the calculation of heating and cooling capacity in
non-steady state conditions.

Umweltgerechte Gebäudeplanung - Flächenintegrierte Strahlheizungs- und -kühlsysteme - Teil 4: Auslegung und Berechnung der dynamischen Wärme- und Kühlleistung für thermoaktive Bauteilsysteme (TABS) (ISO 11855-4:2021)

Dieses Dokument ermöglicht die Berechnung der Spitzenkühlleistung thermoaktiver Bauteilsysteme (TABS) auf der Grundlage von Wärmeeinträgen, wie solaren Wärmeinträgen, internen Wärmeeinträgen und Lüftung, sowie in Hinblick auf Kühlergröße, Flüssigkeitsstrom usw. die Berechnung des wasserseitigen Bedarfs an Kühlleistung, die für das System vorgesehen ist.
In diesem Dokument wird ein detailliertes Verfahren für die Berechnung der Heiz- und Kühlleistung bei nichtstationären Bedingungen festgelegt.

Conception de l'environnement des bâtiments - Systèmes intégrés de chauffage et de refroidissement par rayonnement - Partie 4: Dimensionnement et calculs relatifs au chauffage adiabatique et à la puissance frigorifique pour systèmes d'éléments de construction thermoactifs (TABS) (ISO 11855-4:2021)

Načrtovanje notranjega okolja v stavbah - Vgrajeni sevalni ogrevalni in hladilni sistemi - 4. del: Dimenzioniranje in izračun zmogljivosti dinamičnega ogrevanja in hlajenja toplotno-aktivnih delov stavbe (TABS) (ISO 11855-4:2021)

General Information

Status
Published
Public Enquiry End Date
02-Jun-2020
Publication Date
04-Oct-2021
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
13-Sep-2021
Due Date
18-Nov-2021
Completion Date
05-Oct-2021

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Standards Content (sample)

SLOVENSKI STANDARD
SIST EN ISO 11855-4:2021
01-november-2021
Nadomešča:
SIST EN ISO 11855-4:2015
Načrtovanje notranjega okolja v stavbah - Vgrajeni sevalni ogrevalni in hladilni

sistemi - 4. del: Dimenzioniranje in izračun zmogljivosti dinamičnega ogrevanja in

hlajenja toplotno-aktivnih delov stavbe (TABS) (ISO 11855-4:2021)

Building environment design - 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 11855-4:2021)
Umweltgerechte Gebäudeplanung - Flächenintegrierte Strahlheizungs- und -
kühlsysteme - Teil 4: Auslegung und Berechnung der dynamischen Wärme- und
Kühlleistung für thermoaktive Bauteilsysteme (TABS) (ISO 11855-4:2021)

Conception de l'environnement des bâtiments - Systèmes intégrés de chauffage et de

refroidissement par rayonnement - Partie 4: Dimensionnement et calculs relatifs au

chauffage adiabatique et à la puissance frigorifique pour systèmes d'éléments de
construction thermoactifs (TABS) (ISO 11855-4:2021)
Ta slovenski standard je istoveten z: EN ISO 11855-4:2021
ICS:
91.140.10 Sistemi centralnega Central heating systems
ogrevanja
91.140.30 Prezračevalni in klimatski Ventilation and air-
sistemi conditioning systems
SIST EN ISO 11855-4:2021 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 11855-4:2021
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SIST EN ISO 11855-4:2021
EN ISO 11855-4
EUROPEAN STANDARD
NORME EUROPÉENNE
September 2021
EUROPÄISCHE NORM
ICS 91.040.01 Supersedes EN ISO 11855-4:2015
English Version
Building environment design - 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 11855-4:2021)

Conception de l'environnement des bâtiments - Umweltgerechte Gebäudeplanung - Flächenintegrierte

Systèmes intégrés de chauffage et de refroidissement Strahlheizungs- und -kühlsysteme - Teil 4: Auslegung

par rayonnement - Partie 4: Dimensionnement et und Berechnung der dynamischen Wärme- und

calculs relatifs au chauffage adiabatique et à la Kühlleistung für thermoaktive Bauteilsysteme (TABS)

puissance frigorifique pour systèmes d'éléments de (ISO 11855-4:2021)
construction thermoactifs (TABS) (ISO 11855-4:2021)
This European Standard was approved by CEN on 29 July 2021.

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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, 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: Rue de la Science 23, B-1040 Brussels

© 2021 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 11855-4:2021 E

worldwide for CEN national Members.
---------------------- Page: 3 ----------------------
SIST EN ISO 11855-4:2021
EN ISO 11855-4:2021 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

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SIST EN ISO 11855-4:2021
EN ISO 11855-4:2021 (E)
European foreword

This document (EN ISO 11855-4:2021) has been prepared by Technical Committee ISO/TC 205

"Building environment design" in collaboration with 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 March 2022, and conflicting national standards shall

be withdrawn at the latest by March 2022.

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 11855-4:2015.

Any feedback and questions on this document should be directed to the users’ national standards

body/national committee. A complete listing of these bodies can be found on the CEN websites.

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, France, Germany, Greece, Hungary, Iceland,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the

United Kingdom.
Endorsement notice

The text of ISO 11855-4:2021 has been approved by CEN as EN ISO 11855-4:2021 without any

modification.
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SIST EN ISO 11855-4:2021
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SIST EN ISO 11855-4:2021
INTERNATIONAL ISO
STANDARD 11855-4
Second edition
2021-08
Building environment design —
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 — Systèmes intégrés de
chauffage et de refroidissement par rayonnement —
Partie 4: Dimensionnement et calculs relatifs au chauffage
adiabatique et à la puissance frigorifique pour systèmes d'éléments de
construction thermoactifs (TABS)
Reference number
ISO 11855-4:2021(E)
ISO 2021
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols ......................................................................................................................................................................................................................... 1

5 The concept of thermally active building surfaces (TABS) ....................................................................................... 4

6 Calculation methods ......................................................................................................................................................................................10

6.1 General ........................................................................................................................................................................................................10

6.2 Rough sizing method ......................................................................................................................................................................13

6.3 Simplified sizing by diagrams .................................................................................................................................................13

6.4 Simplified model based on 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 Effects of acoustic ceiling units on the cooling performance of TABS ........................................................25

8 Input for computer simulations of energy performance.........................................................................................25

Annex A (informative) Simplified diagrams ..............................................................................................................................................27

Annex B (normative) Calculation method ...................................................................................................................................................33

Annex C (informative) Tutorial guide for assessing the model..............................................................................................44

Annex D (informative) Computer program .................................................................................................................................................47

Bibliography .............................................................................................................................................................................................................................58

© ISO 2021 – All rights reserved iii
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(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.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

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. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/

iso/ foreword .html.

This document was prepared by Technical Committee ISO/TC 205, Building environment design, in

collaboration with the European Committee for Standardization (CEN) Technical Committee CEN/TC

228, Heating systems and water based cooling systems in buildings, in accordance with the Agreement on

technical cooperation between ISO and CEN (Vienna Agreement).

This second edition cancels and replaces the first edition (ISO 11855-4:2012), which has been

technically revised.
The main changes compared to the previous edition are as follows:
— editorial corrections;
— picture redraws;
— updated Bibliography;
— improved wording.
A list of all parts in the ISO 11855 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2021 – All rights reserved
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(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 is applicable to water-based embedded surface heating and cooling systems

in buildings. The ISO 11855 series is applied to systems using not only water but also other fluids or

electricity 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.

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, control method of embedded systems, and input

parameters for the energy calculations.

The ISO 11855 series consists of the following parts, under the general title Building environment

design — Embedded radiant heating and cooling systems:
— Part 1: Definitions, symbols, and comfort criteria
— Part 2: Determination of the design 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 7: Input parameters for the energy calculation

ISO 11855-1 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. ISO 11855-2 provides steady-state calculation methods for

determination of the heating and cooling capacity. ISO 11855-3 specifies design and dimensioning

methods of radiant heating and cooling systems to ensure the heating and cooling capacity.

ISO 11855-4, this document, 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. ISO 11855-5 addresses the

installation process for the system to operate as intended. ISO 11855-6 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. ISO 11855-7 presents a

calculation method for input parameters to ISO 52031.
© ISO 2021 – All rights reserved v
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SIST EN ISO 11855-4:2021
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SIST EN ISO 11855-4:2021
INTERNATIONAL STANDARD ISO 11855-4:2021(E)
Building environment design — 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 document 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 document defines a detailed method aimed at the calculation of heating and cooling capacity in

non-steady state conditions.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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 — Embedded radiant heating and cooling systems — Part 1:

Definitions, symbols, and comfort criteria

ISO 11855-2, Building environment design — Embedded radiant heating and cooling systems — Part 2:

Determination of the design heating and cooling capacity
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 11855-1 apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Symbols
For the purposes of this document, the symbols in Table 1 apply.
Table 1 — Symbols
Symbol Unit Quantity
A m Area of the heating/cooling surface area

m Total area of internal vertical walls (i.e. vertical walls, external façades excluded)

C J/(m ·K) Specific thermal capacity of the thermal node under consideration
© ISO 2021 – All rights reserved 1
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
Table 1 (continued)
Symbol Unit Quantity
C J/(m ·K) Average specific thermal capacity of the internal walls
c J/(kg·K) Specific heat of the material constituting the j-th layer of the slab
c J/(kg·K) Specific heat of water
d m External diameter of the pipe
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-th hour
f - Design safety factor
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
thermal node (“A”)

Heat transfer coefficient between the thermal node under consideration and the ceiling

H W/K
surface thermal node (“C”)

H W/K Heat transfer coefficient between the thermal node under consideration and the circuit

Cct

H W/K Heat transfer coefficient between the thermal node under consideration and the next one

CondDn
Heat transfer coefficient between the thermal node under consideration and the
H W/K
CondUp
previous 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
surface thermal node (“F”)

H W/K Coefficient connected to the inertia contribution at the thermal node under consideration

Heat transfer coefficient between the thermal node under consideration and the
H W/K
IWS
internal 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

J - Number of layers constituting the slab as a whole
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

m kg/(m ·s) Specific water flow in the circuit, calculated on the area covered by the circuit

H,sp
- Number of partitions of the j-th layer of the slab
n - Actual number of iteration in iterative calculations
n h Number of operation hours of the circuit
n - Maximum number of iterations allowed in iterative calculations
Max
2 © ISO 2021 – All rights reserved
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
Table 1 (continued)
Symbol Unit Quantity
Max,h

W Maximum cooling power reserved to the circuit under consideration in the h-th hour

Cct
Max
W/m Maximum specific cooling power (per floor square metre)
Cct,Spec
q W/m Inward specific heat flux
q W/m Outward specific heat flux
W Heat flux impinging on the ceiling surface (“C”) in the h-th hour
W Heat flux extracted by the circuit in the h-th hour
Cct
W Total convective heat gains in the h-th hour
Conv
W Heat flux impinging on the floor surface (“F”) in the h-th hour
W Internal convective heat gains in the h-th hour
IntConv
W Internal radiant heat gains in the h-th hour
IntRad
W Heat flux impinging on the internal wall surface (“IWS”) in the h-th hour
IWS
W Primary air convective heat gains in the h-th hour
PrimAir
W Total radiant heat gains in the h-th hour
Rad
W Solar heat gains in the room in the h-th hour
Sun
W Transmission heat gains in the h-th hour
Transm
Q W/m Average specific cooling power
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
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
R (m ·K)/W
L,p
of the (p+1)-th thermal node
R (m ·K)/W Pipe thickness thermal resistance
R (m ·K)/W Circuit total thermal resistance
Conduction thermal resistance connecting the p-th thermal node with the boundary
R (m ·K)/W
U,p
of the (p-1)-th thermal node
R (m ·K)/W Wall surface thermal resistance
R (m ·K)/W Water flow thermal resistance
R (m ·K)/W Pipe level thermal resistance
R (m ·K)/W Convection thermal resistance at the pipe inner side
s m Pipe wall thickness
s M Thickness of the upper part of the slab
s m Thickness of the lower part of the slab
m Pipe spacing
m Thickness of the j-th layer of the slab
Δθ K Generic temperature difference
© ISO 2021 – All rights reserved 3
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
Table 1 (continued)
Symbol Unit Quantity
Max
K Maximum operative temperature drift allowed for comfort conditions
Comfort
s Calculation time step
°C Temperature of the air thermal node (“A”) in the h-th hour
°C Temperature of the ceiling surface thermal node (“C”) in the h-th hour
Max
°C Maximum operative temperature allowed for comfort conditions
Comf

θ °C Maximum operative temperature allowed for comfort conditions in the reference case

Comf,Ref
°C Temperature of the floor surface thermal node (“F”) in the h-th hour

°C Temperature of the core of the internal walls thermal node (“IW”) in the h-th hour

°C Temperature of the internal wall surface thermal node (“IWS”) in the h-th hour

IWS
°C Room mean radiant temperature in the h-th hour
°C Room operative temperature in the h-th hour
°C Temperature of the p-th thermal node in the h-th hour
°C Temperature of the pipe level thermal node (“PL”) in the h-th hour
°C Daily average temperature of the conductive region of the slab
Slab
°C Water inlet actual temperature in the h-th hour
Wa,In
Setp,h
°C Water inlet set-point temperature in the h-th hour
Wa,In
Setp
°C Water inlet set-point temperature in the reference case
Wa,In,Ref
°C Water outlet temperature in the h-th hour
Wa,Out
λ W/(m·K) Thermal conductivity of the material of the pipe embedded layer

λ W/(m·K) Thermal conductivity of the material constituting the j-th layer of the slab

λ W/(m·K) Thermal conductivity of the material constituting the pipe
ξ K Actual tolerance in iterative calculations
ξ K Maximum tolerance allowed in iterative calculations
Max
ρ kg/m Density of the material constituting the j-th layer of the slab
various Slope of correlation curves
5 The concept of thermally active building surfaces (TABS)

A thermally active building surface (TABS) 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).
4 © ISO 2021 – All rights reserved
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
Key
1 concrete
2 floor
3 pipes
4 room
5 reinforcement
6 window
Figure 1 — Example of position of pipes in TABS

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 thermally active building surfaces (TABS), 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.
© ISO 2021 – All rights reserved 5
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
Key
1 heating and 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
6 pipe level
Figure 2 — Simple scheme of a TABS

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 and

cooling system components (including the chiller) is possible.
6 © ISO 2021 – All rights reserved
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SIST EN ISO 11855-4:2021
ISO 11855-4:2021(E)
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 ca
...

SLOVENSKI STANDARD
oSIST prEN ISO 11855-4:2020
01-maj-2020
Načrtovanje okolja v stavbah - Vgrajeni hladilni in ogrevalni sistemi - 4. del:
Dimenzioniranje in izračun zmogljivosti dinamičnega ogrevanja in hlajenja
termoaktivnega gradbenega sistema (TAGS) (ISO/DIS 11855-4:2020)

Building environment design - 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/DIS 11855-4:2020)
Umweltgerechte Gebäudeplanung - Flächenintegrierte Strahlheizungs- und -
kühlsysteme - Teil 4: Auslegung und Berechnung der dynamischen Wärme- und
Kühlleistung für thermoaktive Bauteilsysteme (TABS) (ISO/DIS 11855-4:2020)

Conception de l'environnement des bâtiments - Systèmes intégrés 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/DIS 11855-4:2020)
Ta slovenski standard je istoveten z: prEN ISO 11855-4
ICS:
91.140.10 Sistemi centralnega Central heating systems
ogrevanja
91.140.30 Prezračevalni in klimatski Ventilation and air-
sistemi conditioning systems
oSIST prEN ISO 11855-4:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN ISO 11855-4:2020
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oSIST prEN ISO 11855-4:2020
DRAFT INTERNATIONAL STANDARD
ISO/DIS 11855-4
ISO/TC 205 Secretariat: ANSI
Voting begins on: Voting terminates on:
2020-03-16 2020-06-08
Building environment design — 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 — Systèmes intégrés 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)
ICS: 91.040.01
THIS DOCUMENT IS A DRAFT CIRCULATED
This document is circulated as received from the committee secretariat.
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
ISO/CEN PARALLEL PROCESSING
BEING ACCEPTABLE FOR INDUSTRIAL,
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
Reference number
NATIONAL REGULATIONS.
ISO/DIS 11855-4:2020(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
PROVIDE SUPPORTING DOCUMENTATION. ISO 2020
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested 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 2020 – All rights reserved
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(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 Building Active Surfaces (TABS) .................................................................................... 4

6 Calculation methods ......................................................................................................................................................................................... 9

6.1 General ........................................................................................................................................................................................................... 9

6.2 Rough sizing method ......................................................................................................................................................................11

6.3 Simplified sizing by diagrams .................................................................................................................................................12

6.4 Simplified model based on FDM ...........................................................................................................................................18

6.4.1 Cooling system ................................................................................................................................................................19

6.4.2 Hydraulic circuit and slab .....................................................................................................................................19

6.4.3 Room .......................................................................................................................................................................................22

6.4.4 Limits of the method .................................................................................................................................................23

6.5 Dynamic building simulation programs.........................................................................................................................24

7 Effects of Acoustic Ceiling Units on the Cooling Performance of TABS ......................................................24

8 Input for computer simulations of energy performance.........................................................................................24

Annex A (informative) Simplified diagrams ..............................................................................................................................................26

Annex B (normative) Calculation method ...................................................................................................................................................33

Annex C (informative) Tutorial guide for assessing the model..............................................................................................43

Annex D (informative) Computer program .................................................................................................................................................46

Bibliography .............................................................................................................................................................................................................................59

© ISO 2020 – All rights reserved iii
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(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 7: Input parameters for the energy calculation

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. Part 7 presents a calculation method for input parameters to ISO 52031.

iv © ISO 2020 – All rights reserved
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(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, control method of embedded systems, and input

parameters for the energy calculations.
© ISO 2020 – All rights reserved v
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oSIST prEN ISO 11855-4:2020
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oSIST prEN ISO 11855-4:2020
DRAFT INTERNATIONAL STANDARD ISO/DIS 11855-4:2020(E)
Building environment design — 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 — 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:

Table 1 — Symbols and abbreviations
Symbol Unit Quantity
A m Area of the heating/cooling surface area

A m Total area of internal vertical walls (i.e. vertical walls, external façades excluded)

C J/(m ·K) Specific thermal capacity of the thermal node under consideration
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
Table 1 (continued)
Symbol Unit Quantity
C J/(m ·K) Average specific thermal capacity of the internal walls
J/(kg·K) Specific heat of the material constituting the j-th layer of the slab
c J/(kg·K) Specific heat of water
d m External diameter of the pipe
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-th hour
- Design safety factor
F - View factor between the floor and the ceiling
v F-C
- 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
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
thermal node (“A”)

Heat transfer coefficient between the thermal node under consideration and the ceiling

H W/K
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
H W/K
CondUp
previous 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
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
H W/K
IWS
internal 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

J - Number of layers constituting the slab as a whole
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

kg/(m ·s) Specific water flow in the circuit, calculated on the area covered by the circuit

H,sp
- Number of partitions of the j-th layer of the slab
n - Actual number of iteration in iterative calculations
n h Number of operation hours of the circuit
2 © ISO 2020 – All rights reserved
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
Table 1 (continued)
Symbol Unit Quantity
Max
n - Maximum number of iterations allowed in iterative calculations
Max,h

W Maximum cooling power reserved to the circuit under consideration in the h-th hour

Circuit
Max
P W/m Maximum specific cooling power (per floor square metre)
Circuit,Spec
q W/m Inward specific heat flow
q W/m Outward specific heat flow
W Heat flow impinging on the ceiling surface (“C”) in the h-th hour
Q W Heat flow extracted by the circuit in the h-th hour
Circuit
W Total convective heat gains in the h-th hour
Conv
W Heat flow impinging on the floor surface (“F”) in the h-th hour
W Internal convective heat gains in the h-th hour
IntConv
Q W Internal radiant heat gains in the h-th hour
IntRad
W Heat flow impinging on the internal wall surface (“IWS”) in the h-th hour
IWS
W Primary air convective heat gains in the h-th hour
PrimAir
W Total radiant heat gains in the h-th hour
Rad
Q W Solar heat gains in the room in the h-th hour
Sun
W Transmission heat gains in the h-th hour
Transm
Q W/m Average specific cooling power
R (m ·K)/W Generic thermal resistance
R (m ·K)/W Additional thermal resistance covering the lower side of the slab
Add C
(m ·K)/W Additional thermal resistance covering the upper side of the slab
Add F
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
R (m ·K)/W
L,p
of the (p+1)-th thermal node
R (m ·K)/W Pipe thickness thermal resistance
R (m ·K)/W Circuit total thermal resistance
Conduction thermal resistance connecting the p-th thermal node with the boundary
R (m ·K)/W
U,p
of the (p-1)-th thermal node
R (m ·K)/W Wall surface thermal resistance
Walls
R (m ·K)/W Water flow thermal resistance
R (m ·K)/W Pipe level thermal resistance
R (m ·K)/W Convection thermal resistance at the pipe inner side
s m Pipe wall thickness
s m Thickness of the upper part of the slab
s m Thickness of the lower part of the slab
W m Pipe spacing
m Thickness of the j-th layer of the slab
© ISO 2020 – All rights reserved 3
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
Table 1 (continued)
Symbol Unit Quantity
Δθ K Generic temperature difference
Max
K Maximum operative temperature drift allowed for comfort conditions
Comfort
Δt s Calculation time step
°C Temperature of the air thermal node (“A”) in the h-th hour
°C Temperature of the ceiling surface thermal node (“C”) in the h-th hour
Max
θ °C Maximum operative temperature allowed for comfort conditions
Comfort

θ °C Maximum operative temperature allowed for comfort conditions in the reference case

Comfort,Ref
°C Temperature of the floor surface thermal node (“F”) in the h-th hour

°C Temperature of the core of the internal walls thermal node (“IW”) in the h-th hour

θ °C Temperature of the internal wall surface thermal node (“IWS”) in the h-th hour

IWS
°C Room mean radiant temperature in the h-th hour
θ °C Room operative temperature in the h-th hour
θ °C Temperature of the p-th thermal node in the h-th hour
°C Temperature of the pipe level thermal node (“PL”) in the h-th hour
°C Daily average temperature of the conductive region of the slab
Slab
θ °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
θ °C Water inlet set-point temperature in the reference case
Water,In,Ref
θ °C Water outlet temperature in the h-th hour
Water,Out
W/(m·K) Thermal conductivity of the material of the pipe embedded layer

W/(m·K) Thermal conductivity of the material constituting the j-th layer of the slab

λ W/(m·K) Thermal conductivity of the material constituting the pipe
ξ K Actual tolerance in iterative calculations
ξ K Maximum tolerance allowed in iterative calculations
Max
kg/m Density of the material constituting the j-th layer of the slab
various Slope of correlation curves
5 The concept of Thermally Building Active Surfaces (TABS)

A Thermally Active Building Surface (TABS) 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).
4 © ISO 2020 – All rights reserved
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
Key
C concrete
F floor
P pipes
R room
RI reinforcement
W window
Figure 1 — Example of position of pipes in TABS

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.

© ISO 2020 – All rights reserved 5
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(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.
6 © ISO 2020 – All rights reserved
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
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).
© ISO 2020 – All rights reserved 7
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
Key
X time, h
Y temperature, °C
PMV Predicted Mean Vote
θ air temperature
air
θ ceiling temperature
θ mean radiant temperature
θ floor temperature
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 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

8 © ISO 2020 – All rights reserved
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)
2 2

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.
Key
X (upper diagram) supply 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
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.

© ISO 2020 – All rights reserved 9
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oSIST prEN ISO 11855-4:2020
ISO/DIS 11855-4:2020(E)

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.

Key
1 upper surface
2 pipe surface
3 lower surface
Figure 6 — Heat transfer through structures containing pipes
Figure 7 — Transfer functions for building elements containing pipes
Another poss
...

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