EN ISO 11855-2:2021

SLOVENSKI STANDARD
01-december-2021
Nadomešča:
SIST EN ISO 11855-2:2015
Načrtovanje notranjega okolja v stavbah - Vgrajeni sevalni ogrevalni in hladilni
sistemi - 2. del: Določanje načrtovane grelne in hladilne moči (ISO 11855-2:2021)
Building environment design - Embedded radiant heating and cooling systems - Part 2:
Determination of the design heating and cooling capacity (ISO 11855-2:2021)
Umweltgerechte Gebäudeplanung - Flächenintegrierte Strahlheizungs- und -
kühlsysteme - Teil 2: Bestimmung der Auslegungs-Heiz- bzw. Kühlleistung (ISO 11855-
2:2021)
Conception de l'environnement des bâtiments - Systèmes intégrés de chauffage et de
refroidissement par rayonnement - Partie 2: Détermination de la puissance calorifique et
frigorifique à la conception (ISO 11855-2:2021)
Ta slovenski standard je istoveten z: EN ISO 11855-2:2021
ICS:
91.140.10 Sistemi centralnega Central heating systems
ogrevanja
91.140.30 Prezračevalni in klimatski Ventilation and air-
sistemi conditioning systems
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 11855-2
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2021
EUROPÄISCHE NORM
ICS 91.040.01 Supersedes EN ISO 11855-2:2015
English Version
Building environment design - Embedded radiant heating
and cooling systems - Part 2: Determination of the design
heating and cooling capacity (ISO 11855-2:2021)
Conception de l'environnement des bâtiments - Umweltgerechte Gebäudeplanung - Flächenintegrierte
Systèmes intégrés de chauffage et de refroidissement Strahlheizungs- und -kühlsysteme - Teil 2: Bestimmung
par rayonnement - Partie 2: Détermination de la der Auslegungs-Heiz- bzw. Kühlleistung (ISO 11855-
puissance calorifique et frigorifique à la conception 2:2021)
(ISO 11855-2:2021)
This European Standard was approved by CEN on 10 September 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 11855-2:2021 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 11855-2:2021) 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 April 2022, and conflicting national standards shall be
withdrawn at the latest by April 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 11855-2:2015.
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 website.
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 11855-2:2021 has been approved by CEN as EN ISO 11855-2:2021 without any
modification.
INTERNATIONAL ISO
STANDARD 11855-2
Second edition
2021-09
Building environment design —
Embedded radiant heating and cooling
systems —
Part 2:
Determination of the design heating
and cooling capacity
Conception de l'environnement des bâtiments — Systèmes intégrés de
chauffage et de refroidissement par rayonnement —
Partie 2: Détermination de la puissance calorifique et frigorifique à la
conception
Reference number
ISO 11855-2:2021(E)
©
ISO 2021
ISO 11855-2:2021(E)
© ISO 2021
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Phone: +41 22 749 01 11
Email: copyright@iso.org
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Published in Switzerland
ii © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 Concept of the method to determine the heating and cooling capacity .3
6 Heat exchange coefficient between surface and space . 4
7 Simplified calculation methods for determining heating and cooling capacity or
surface temperature . 6
7.1 Universal single power function . 7
7.2 Thermal resistance methods . 9
8 Use of basic calculation programmes .12
8.1 Basic calculation programmes .12
8.2 Items to be included in a complete computation documentation .13
9 Calculation of the heating and cooling capacity .13
Annex A (normative) Calculation of the heat flux .14
Annex B (informative) General resistance method .36
Annex C (informative) Pipes embedded in wooden construction .42
Annex D (normative) Method for verification of FEM and FDM calculation programmes .50
Annex E (normative) Values for heat conductivity of materials and air layers .53
Annex F (informative) Maximal surface temperatures for floor heating systems .55
Bibliography .56
ISO 11855-2:2021(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 11855-2:2012), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— update of the figures for type A and C,
— update of the thermal, relevant material characteristics,
— editorial corrections.
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

ISO 11855-2:2021(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, this document, 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 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.
INTERNATIONAL STANDARD ISO 11855-2:2021(E)
Building environment design — Embedded radiant heating
and cooling systems —
Part 2:
Determination of the design heating and cooling capacity
1 Scope
This document specifies procedures and conditions to enable the heat flux in water-based surface
heating and cooling systems to be determined relative to the medium differential temperature for
systems. The determination of thermal performance of water-based surface heating and cooling
systems and their conformity to this document is carried out by calculation in accordance with design
documents and a model. This enables a uniform assessment and calculation of water-based surface
heating and cooling systems.
The surface temperature and the temperature uniformity of the heated/cooled surface, nominal heat
flux between water and space, the associated nominal medium differential temperature, and the field
of characteristic curves for the relationship between heat flux and the determining variables are given
as the result.
This document includes a general method based on finite difference or finite element Methods and
simplified calculation methods depending on position of pipes and type of building structure.
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
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 Surface of the occupied area
A
A m Surface of the heating or cooling surface area
F
ISO 11855-2:2021(E)
Table 1 (continued)
Symbol Unit Quantity
A m Surface of the peripheral area
R
b — Calculation factor depending on the pipe spacing
u
B, B , B W/( m ⋅K) Coefficients depending on the system
G 0
D m External diameter of the pipe, including sheathing where used
d m External diameter of the pipe
a
d m Internal diameter of the pipe
i
d m External diameter of sheathing
M
c kJ/(kg⋅K) Specific heat capacity of water
Wa
h W/(m ⋅K) Total heat transfer coefficient (convection + radiation) between surface and space
t
h W/(m ⋅K) Total heat transfer coefficient (convection + radiation) between surface and space
A-F
(floor)
h W/(m ⋅K) Total heat transfer coefficient (convection + radiation) between surface and space
A-W
(wall)
h W/(m ⋅K) Total heat transfer coefficient (convection + radiation) between surface and space
A-C
(ceiling)
K W/(m ⋅K) Equivalent heat transmission coefficient
H
K — Parameter for heat conducting devices
WL
k — Parameter for heat conducting layer
CL
L m Width of heat conducting devices
WL
L m Width of fin (horizontal part of heat conducting device seen as a heating fin)
fin
L m Length of installed pipes
R
m — Exponents for determination of characteristic curves
m — Exponents for determination of characteristic curves
D
m — Exponents for determination of characteristic curves
u
m — Exponents for determination of characteristic curves
T
m kg/s Design heating or cooling medium flow rate
H
n, n — Exponents
G
q W/m Heat flux at the surface
q W/m Heat flux in the occupied area
A
q W/m Design heat flux
des
q W/m Limit heat flux
G
q W/m Nominal heat flux
N
q W/m Heat flux in the peripheral area
R
q W/m Outward heat flux
u
R m ⋅K/W Partial inwards heat transmission resistance of surface structure
o
R m ⋅K/W Partial outwards heat transmission resistance of surface structure
u
R m ⋅K/W Thermal resistance of surface covering
λ,B
R m ⋅K/W Thermal resistance of thermal insulation
λ,ins
s m In type B systems, thickness of thermal insulation from the outward edge of the
h
insulation to the inward edge of the pipes (see Figure 2)
s m In type B systems, thickness of thermal insulation from the outward edge of the
l
insulation to the outward edge of the pipes (see Figure 2)
s m Thickness of thermal insulation
ins
s m Pipe wall thickness
R
s m Thickness of the layer above the pipe
u
2 © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
Table 1 (continued)
Symbol Unit Quantity
s m Thickness of heat conducting device
WL
S m Thickness of the screed (excluding the pipes in type A systems)
W m Pipe spacing
h W/(m ⋅K) Heat exchange coefficient
α — Parameter factors for calculation of characteristic curves
i
λ W/(m⋅K) Heat conductivity of the heat diffusion device material
WL
θ °C Maximum surface temperature
s,max
θ °C Minimum surface temperature
s,min
θ °C Design indoor temperature
i
θ °C Temperature of the heating or cooling medium
m
θ °C Average surface temperature
s,m
θ °C Return temperature of heating or cooling medium
R
θ °C Supply temperature of heating or cooling medium
V
θ °C Indoor temperature in an adjacent space
u
Δθ K Heating or cooling medium differential temperature
H
Δθ K Design heating or cooling medium differential temperature
H,des
Δθ K Limit of heating or cooling medium differential temperature
H,G
Δθ K Nominal heating or cooling medium differential temperature
N
Δθ K Heating or cooling medium differential supply temperature
V
Δθ K Design heating or cooling medium differential supply temperature
V,des
λ W/(m⋅K) Thermal conductivity
σ K Temperature drop θ −θ
V R
φ — Conversion factor for temperatures
ψ — Volume ratio of the attachment studs in the screed
5 Concept of the method to determine the heating and cooling capacity
A given type of surface (floor, wall, ceiling) delivers, at a given average surface temperature and indoor
temperature (operative temperature θ ), the same heat flux in any space independent of the type of
i
embedded system. It is, therefore, possible to establish a basic formula or characteristic curve for
cooling and a basic formula or characteristic curve for heating, for each of the type of surfaces (floor,
wall, ceiling), independent of the type of embedded system, which is applicable to all heating and
cooling surfaces (see Clause 6).
Two methods are included in this document:
— simplified calculation methods depending on the type of system (see Clause 7);
— finite element method and finite difference method (see Clause 8).
Different simplified calculation methods are included in Clause 7 for calculation of the surface
temperature (average, maximum and minimum temperature) depending on the system construction
(type of pipe, pipe diameter, pipe distance, mounting of pipe, heat conducting devices, distribution
layer) and construction of the floor/wall/ceiling [covering, insulation layer, trapped air layer (Annex E),
etc.]. The simplified calculation methods are specific for the given type of system, and the boundary
conditions listed in Clause 7 shall be met. In the calculation report, it shall be clearly stated which
calculation method has been applied.
ISO 11855-2:2021(E)
In case a simplified calculation method is not available for a given type of system, either a basic
calculation using two or three dimensional finite element or finite difference method can be applied
(see Clause 8 and Annex D).
NOTE In addition, laboratory testing (for example, EN 1264) can be applied.
Based on the calculated average surface temperature at given combinations of medium (water)
temperature and space temperature, it is possible to determine the steady state heating and cooling
capacity (see Clause 9).
6 Heat exchange coefficient between surface and space
The relationship between the heat flux and mean differential surface temperature [see Figure 1 and
Formulae (1) to (4)] depends on the type of surface (floor, wall, ceiling) and whether the temperature of
the surface is lower (cooling) or higher (heating) than the space temperature.
Key
X mean differential surface temperature (θ − θ ) in K
s,m i
Y heat flux q (W/m )
Figure 1 — Basic characteristic curve for floor heating and ceiling cooling
4 © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
For floor heating and ceiling cooling in Figure 1, the heat flux q is given by:
1,1
q = 8,92 (θ − θ ) (1)
S,m i
where
θ is the average surface temperature, in °C;
S,m
θ is the nominal indoor operative temperature, in °C.
i
For other types of surface heating and cooling systems, the heat flux q is given by:
Wall heating and wall cooling:
q = 8 (|θ − θ |) (2)
s,m i
Ceiling heating:
q = 6 (|θ − θ |) (3)
s,m i
Floor cooling:
q = 7 (|θ − θ |) (4)
s,m i
NOTE 1 Heat flux, q, is expressed in in W/m .
The heat transfer coefficient is combined convection and radiation.
NOTE 2 In many building system simulations using dynamic computer models, the heat transfer is often split
up in a convective part (between heated/cooled surface and space air) and a radiant part (between heated/
cooled surface and the surrounding surfaces or sources). The radiant heat transfer coefficient in the normal
temperature range (15-30) °C can be fixed to 5,5 W/m ·K. The convective heat transfer coefficient depends on
type of surface, heating or cooling, air velocity (forced convection) or temperature difference between surface
and air (natural convection).
By using the simplified calculation method in Annex A, the characteristic curves present the heat flux
as a function of the difference between the heating or cooling medium temperature and the indoor
temperature. For the user of Annex A, this means not to do any calculations by directly using values
of heat transfer coefficients. Consequently, Annex A does not include values for such an application or
special details or formulae concerning heat transfer coefficients on heating or cooling surfaces.
Thus, the values α of Table A.20 are not intended to calculate the heat flux directly. In fact, they are
provided exclusively for the conversion of characteristic curves in accordance with Formula (A.33). For
simplifications these calculations are based on the same heat transfer coefficient for floor cooling and
ceiling heating, 6,5 W/(m ·K).
For every surface heating and cooling system, there is a maximum allowable heat flux, the limit heat flux
q . This is determined for a selected design indoor room temperature of θ (for heating, often 20 °C and
G i
for cooling, often 26 °C) at the maximum or minimum surface temperature θ and a temperature
F,max
drop σ = 0 K.
For the calculations, the centre of the heating or cooling surface area, regardless of the type of system,
is used as a reference point for θ .
S,max
The average surface temperature, θ , which determines the heat flux (refer to the basic characteristic
S,m
curve) is linked with the maximum or minimum surface temperature: θ < θ and θ > θ
S,m S,max S,m S,min
always applies. (See Annex F for the maximal surface temperature for floor heating systems.)
The attainable value, θ , depends not only on the type of system, but also on the operating conditions
S,m
(temperature drop σ = θ −θ , outward heat flux q and heat resistance of the covering R ).
V R u λ,B
ISO 11855-2:2021(E)
The following assumptions form the basis for the calculation of the heat flux:
— the heat transfer between the heated or cooled surface and the space occurs in accordance with the
basic characteristic curve;
— the temperature drop is σ = 0 K. The dependence of the characteristic curve on the temperature
drop is determined by using the logarithmically determined mean differential heating medium
temperature Δθ [see Formula (1)];
H
m kg
H
— the turbulent pipe flow is: > 4 000 ;
d h×m
i
— there is no lateral heat flux;
— the heat-conducting layer of the floor heating system is thermally decoupled by thermal insulation
from the structural base of the building. The thermal insulation does not need to be directly below
the system.
7 Simplified calculation methods for determining heating and cooling capacity
or surface temperature
Two types of simplified calculation methods can be applied according to this document:
— one method is based on a single power function product of all relevant parameters developed from
the finite element method (FEM);
— another method is based on calculation of equivalent thermal resistance between the temperature
of the heating or cooling medium and the surface temperature (or room temperature).
A given system construction can only be calculated with one of the simplified methods. The correct
method to apply depends on the type of system, A to G (position of pipes, concrete or wooden
construction) and the boundary conditions listed in Table 2.
NOTE Type A is a system with pipes embedded in the thermal diffusion layer . Type C is a system with pipes
embedded in the adjustment layer.
Table 2 — Criteria for selection of simplified calculation method
Type of Reference to
Pipe position Figure Boundary conditions
system method
In screed A, C, H, I, J 2 a) W ≥ 0,050 m s ≥ 0,01 m 7.1
u
Thermally decoupled from the structural 0,008 m ≤ d ≤ 0,03 m A.2.2
base of the building by thermal insulation
s /λ ≥ 0,01
u e
In insulation, conductive devices B 2 b) 0,05 m ≤ W ≤ 0,45 m 7.1
Not wooden constructions except for 0,014 m ≤ d ≤ 0,022 m A.2.3
weight bearing and thermal diffusion layer
0,01 m ≤ s /λ ≤ 0,18 m
u e
Plane section system D 2 c) 7.1,
A.2.4
In concrete slab E 4 S /W ≥ 0,3 7.2,
T
B.1
Capillary tubes in concrete surface F 5 d /W ≤ 0,2 7.2, B.2
a
Wooden constructions, pipes in sub floor G 6 λ ≥ 10 λ 7.2, Annex C
wl
or under sub floor, conductive devices
S ≥ 0,01
WL λ
6 © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
7.1 Universal single power function
The heat flux between embedded pipes (temperature of heating or cooling medium) and the space is
calculated by Formula (5):
m
i
qB=⋅ ()a ⋅Δθ (5)
H
∏ i
i
where
B is a system-dependent coefficient in W/(m ⋅K), this depends on the type of system;
m
i is the power product, which links the parameters of the structure (surface covering, pipe
()a
∏ i
spacing, pipe diameter and pipe covering).
i
NOTE Heat flux, q, is expressed in W/m .
This calculation method is given in Annex A for the following four types of systems:
— type A with pipes embedded in the screed or concrete (see Figure 2 and A.2.2);
— type B with pipes embedded outside the screed (see Figure 2 and A.2.3);
— type C with pipes embedded in the screed (see Figure 2 and A.2.2);
— type D plane section systems (see A.2.4).
Figure 2 shows the types as embedded in the floor, but the methods can also be applied for wall and
ceiling systems with a corresponding position of the pipes.
This method shall only be used for system configurations meeting the boundary conditions listed for
the different types of systems in Annex A.
a) Type A and C
ISO 11855-2:2021(E)
b) Type B
c) Type D
d) Type H
8 © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
d) Type I
f) Type J
Key
1 floor covering
2a weight bearing and thermal diffusion layer (cement screed, anhydrite screed, asphalt screed)
2b weight bearing and thermal diffusion layer (cement screed, anhydrite screed, asphalt screed, wood)
2c weight bearing and thermal diffusion layer (cement screed, anhydrite screed, asphalt screed, timber)
2d weight bearing and thermal diffusion layer
3 adjustment layer (cement screed, anhydrite screed, asphalt screed)
4 profile
5 heating and cooling pipe
6a protection layer (plastic foil)
6b protection layer
7 pipe anchorage
8 heat diffusion devices
9a insulation layer
9b thermal insulation
10 adjustment layer
11a structural bearing
11b structural bearing / existing floor
Figure 2 — System types A, B, C, D, H, I and J covered by the method in Annex A
7.2 Thermal resistance methods
The heat flux between embedded pipes (temperature of heating or cooling medium) and the space or
surface is calculated using thermal resistances.
The concept is shown in Figure 3.
ISO 11855-2:2021(E)
An equivalent resistance, R , between the heating or cooling medium to a fictive core (or heat
HC
conduction layer) at the position of the pipes is determined. This resistance includes the influence of
the pipe type, pipe distance and method of pipe installation (in concrete, wooden construction, etc.).
This is how a fictive core temperature is calculated. The heat transfer between this fictive layer and
the surfaces, R and R (or space and neighbour space) is calculated using linear resistances (adding of
i e
resistance of the layers above and below the heat conductive layer).
The equivalent resistance of the heat conductive layer is calculated in different ways depending on the
type of system.
This calculation method, using the general resistance concept, is given in Annex B for the following two
types of systems:
— type E with pipes embedded in massive concrete slabs (see Figure 4 and B.1);
— type F with capillary pipes embedded in a layer at the inside surface (see Figure 5 and B.2).
Figure 3 — Basic network of thermal resistance
Key
1 space 1
2 space 2
a
Conductive layer.
Figure 4 — Pipes embedded in a massive concrete layer, type E
10 © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
Key
1 rib
Figure 5 — Capillary pipes embedded in a layer at the inner surface, type F
This calculation method, using the general resistance concept, is shown in Annex C for pipes embedded
in wooden floor constructions using heat conducting plates (Figure 6).
ISO 11855-2:2021(E)
Tube in subfloor
Tube under subfloor
Key
1 heat emission plates increase heat transfer where necessary
2 floor covering
3 flooring board
4 wood joist or truss
5 tube
6 insulation decreases downward heat flow
7 finished floor
8 fiberglass batt insulation with reflective surface up
Figure 6 — Pipes in wooden constructions, type G
The equivalent resistance of the conductive layer may also be determined either by calculation using
finite element analysis (FEA) or finite difference methods (FDM) (see Clause 8) or by laboratory testing.
8 Use of basic calculation programmes
8.1 Basic calculation programmes
A numerical analysis by finite element method or by finite difference method shall be conducted in
accordance with the state-of-the-art practice and the applicable codes and standards, in such a way that
they can readily be verified. The calculation programme used shall be verified according to Annex D.
The numerical analysis may be used to calculate the heating and cooling capacity or the equivalent
resistances. On basis of the equivalent resistances, the heating and cooling capacity is calculated for
different temperature differences between the surface and the room.
12 © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
8.2 Items to be included in a complete computation documentation
The following items shall be included in a complete computation documentation:
— representation and documentation of the structure to be analysed, by means of the technical
drawings, diagrams and sketches;
— indication of the material data used as a basis and the requisite data sources;
— description of load cases used as a basis, including substantiation by codes and standards;
— description and representation of the numerical model applied, indicating the mathematical and
physical basis, for example, the element type, the shape functions, number of elements, nodes and
degrees of freedom;
— name, verification, if available, and origin of the computation programme;
— description of the technical assumptions, simplifications and restrictions underlying the model.
9 Calculation of the heating and cooling capacity
In some of the described calculation methods, the heating and cooling capacity are determined directly
(see Annex A).
In other described calculation methods, the average surface temperature is determined and the heating
and cooling capacity is calculated according to Formula (6):
q = h (|θ − θ |) (6)
des t s,m i
NOTE Design heat flux, q , is expressed in in W/m .
des
For evaluation of the performance of the system – and when calculating the total heating and cooling
power needed from the energy generation system (boiler, heat exchanger, chiller, etc.) – the heat
transfer at the outward (back) side shall also be considered. This heat transfer shall be regarded as a
loss if the outward side is facing the outside, an un-conditioned space or another building entity, and it
depends on the temperature difference between the pipe layer as well as the heat transfer resistance to
and the temperature in the neighbour space or outside.
ISO 11855-2:2021(E)
Annex A
(normative)
Calculation of the heat flux
A.1 General
The basic calculation is done for reference heating systems (see A.2).
For floor heating systems these results apply directly.
The method described in A.3 enables the conversion of these results into results for other surfaces in
the room (ceiling and wall heating). The method is also applicable for all the cooling surfaces (floor,
[13]
ceiling, wall cooling). This calculation method is based on the results obtained in A.2.2/A.2.3 and
A.2.4. The change in the surface thermal resistance ΔR =Δ(1/α) influences the temperature field within
α
[13]
the system in the same way as a change in the thermal resistance of the surface covering ΔR .
λ,B
A.2 Reference heating systems
A.2.1 General
The heat flux q at a surface is determined by the following parameters:
— pipe spacing W;
— thickness s and thermal conductivity λ of the layer above the pipe;
u E
— thermal conduction resistance R of covering;
λ,B
— pipe external diameter D = d , including sheathing (D = d ) if necessary and the thermal conductivity
a M
of the pipe λ and/or the sheathing λ . In the case of non-circular pipes, the equivalent diameter of
R M
circular pipes having the same circumference is to be calculated (the screed covering shall be used
unchanged). The thickness and the thermal conduction resistance of firmly deposited barrier layers
up to a thickness of 0,3 mm shall not be taken into consideration. In this case, D = d shall be used;
a
— heat conducting devices, characterized by the value K in accordance with A.3;
WL
— contact between the pipes and the heat conducting devices or screed, characterized by the factor
a ;
K
— the heat-conducting layer of the heating system is thermally decoupled by the thermal insulation
from the structural base of the building.
The calculation method is limited to the boundary conditions listed in Table A.1.
Table A.1 — Criteria for selection of the simplified calculation method
Type of Figure Boundary conditions Reference to meth-
system od
A, C, H, I, J Figure A.1 T ≥ 0,050 m A.2.2
s ≥ 0,01 m
u
0,008 m ≤ D ≤ 0,03 m
s /λ ≥ 0,01
u e
14 © ISO 2021 – All rights reserved

ISO 11855-2:2021(E)
Table A.1 (continued)
Type of Figure Boundary conditions Reference to meth-
system od
B Figure A.2 0,05 m ≤ T ≤ 0,45 m A.2.3
0,014 m ≤ D ≤ 0,022 m
0,01 m ≤ s /λ ≤ 0,18 m
u e
D Figure A.3 A.2.4
n
The heat flux is proportional to ()Δθ , where the temperature difference between the heating
H
medium and the room temperature is calculated according to Formula (A.1) and expressed in K:
θθ−
VR
Δθ (A.1)
H
θθ−
Vi
In
θθ−
Ri
and where experimental and theoretical investigations of the exponent n have shown that:
1,0 < n < 1,05
Within the limits of the achievable accuracy, n = 1 is used.
The heat flux q is calculated by:
m
i
qB=⋅ a ⋅Δθ (A.2)
∏ H
i
i
where
B is a system-dependent coefficient in W/(m ⋅K), this depends on the type of system;
m
i
is a power product which links the parameters of the structure together (see A.2.2, A.2.3
Π()a
i
i
and A.2.4).
NOTE The heat flux, q, is expressed in W/m .
A distinction shall be made between systems with pipes inside the screed, systems with pipes below
the screed and plane section systems. Formula (A.2) applies directly for usual constructions.
A.2.2 Systems with pipes inside the screed (type A, C, H, I, J)
For these systems (see Figure A.1), the characteristic curves are calculated by:
m m m
W U D
qB=⋅aa⋅⋅aa⋅⋅Δθ (A.3)
B H
WU D
where B = B = 6,7 in W/m ⋅K.
NOTE 1 The heat flux, q, is expressed in W/m .
The B-values are valid for a thermal conductivity λ = λ = 0,35 W/(m⋅K) of the pipe and pipe wall
R R,0
thickness s = s = (d −d )/2 = 0,002 m.
R R,0 a i
For other materials with different heat conductivity or pipe wall thickness or for sheathed pipes, B shall
be calculated in accordance with A.2.6.
For a heating screed, a value for λ of Table D.1 shall be used. If a different value is used, its validity shall
E
be checked.
ISO 11855-2:2021(E)
The surface covering factor, a , is in accordance with the Formula (A.4):
B
s
1 u,0
+
αλ
u,0
a = (A.4)
B
s
u,0
++R
»,B
αλ
E
where
h = 10,8 W/(m ⋅K);
A-F
λ = 1 W/(m⋅K);
u, 0
s = 0,045 m;
u, 0
R is the thermal conduction resistance of the floor covering, in (m ⋅K)/W;
λ, B
λ is the thermal conductivity of the screed, in W/(m⋅K);
E
a is the pipe spacing factor in accordance with Table A.2; a = f(R );
w w λ,B
a is the covering factor in accordance with Table A.3; a = f(W, R );
U U λ,B
a is the pipe external diameter factor in accordance with Table A.4; a = f(W, R ).
D D λ,B
W
m =−1 (A.5)
W
0,075
where 0,050 m ≤ W ≤ 0,375 m (where W is the pipe spacing).
m = 100(0,045 – s ) (A.6)
u u
where s ≥ 0,010 m (where s is the thickness of the layer above the pipe).
u u
m = 250(D – 0,020) (A.7)
D
applies where 0,008 m ≤ D ≤ 0,030 m (where D is the external diameter of the pipe, including sheathing
where used).
Formulae (A.4) to (A.7) are valid for a thickness of layer above the pipe (inward) of 0,065 m < s
...