FprEN ISO 11855-4
(Main)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/FDIS 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/FDIS 11855-4:2021)
Umweltgerechte Gebäudeplanung - Flächenintegrierte Strahlheizungs- und -kühlsysteme - Teil 4: Auslegung und Berechnung der dynamischen Wärme- und Kühlleistung für thermoaktive Bauteilsysteme (TABS) (ISO/FDIS 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/FDIS 11855-4:2021)
Načrtovanje okolja v stavbah - Vgrajeni hladilni in ogrevalni sistemi - 4. del: Dimenzioniranje in izračun zmogljivosti dinamičnega ogrevanja in hlajenja termoaktivnega gradbenega sistema (TAGS) (ISO/FDIS 11855-4:2021)
General Information
RELATIONS
Standards Content (sample)
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
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
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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
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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.
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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 criteria3 Terms and definitions
For the purposes of this document, the terms and definitions in ISO 11855-1 apply.
4 Symbols and abbreviationsFor the purposes of this part of ISO 11855, the symbols and abbreviations in Table 1 apply:
Table 1 — Symbols and abbreviationsSymbol 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© ISO 2020 – All rights reserved 1
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oSIST prEN ISO 11855-4:2020
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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-Wh 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-WHeat transfer coefficient between the thermal node under consideration and the air
H W/Kthermal node (“A”)
Heat transfer coefficient between the thermal node under consideration and the ceiling
H W/Ksurface thermal node (“C”)
H W/K Heat transfer coefficient between the thermal node under consideration and the circuit
CircuitH W/K Heat transfer coefficient between the thermal node under consideration and the next one
CondDownHeat 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
ConvHeat transfer coefficient between the thermal node under consideration and the floor
H W/Ksurface thermal node (“F”)
H W/K Coefficient connected to the inertia contribution at the thermal node under consideration
InertiaHeat 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
Radh W/(m ·K) Total heat transfer coefficient (convection + radiation) between surface and space
J - Number of layers constituting the slab as a wholeJ - 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
CircuitMax
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
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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 pipeξ 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.
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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
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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.
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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.
Key1 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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