EN ISO 10211-1:1995

SLOVENSKI STANDARD
01-december-1997
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Thermal bridges in building construction - Heat flows and surface temperatures - Part 1:
General calculation methods (ISO 10211-1:1995)
Wärmebrücken im Hochbau - Wärmeströme und Oberflächentemperaturen - Teil 1:
Allgemeine Berechnungsverfahren (ISO 10211-1:1995)
Ponts thermiques dans le bâtiment - Calcul des températures superficielles et des flux
thermiques - Partie 1: Méthodes de calcul générales (ISO 10211-1:1995)
Ta slovenski standard je istoveten z: EN ISO 10211-1:1995
ICS:
91.120.10 Toplotna izolacija stavb Thermal insulation
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

ISO
INTERNATIONAL
10211-1
STANDARD
First edition
1995-08-15
Thermal bridges in building construction -
Heat flows and surface temperatures -
Part 1:
General calculation methods
Flux de chaleur et temperatures
Ponts thermiques dans Ie batiment -
superficielles -
Partie 7: Methodes g&Grales de calcul
Reference number
ISO 1021 l-l :1995(E)
--
ISO 10211-1:1995(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. Esch 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.
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.
International Standard ISO 1021 l-l was prepared by the European
Committee for Standardization (CEN) in collaboration with Technical
Committee lSO/TC 163, Thermal insulation, Subcommittee SC 2,
Cakulation methods, in accordance with the Agreement on technical
cooperation between ISO and CEN (Vienna Agreement).
ISO 10211 consists of the following Part, under the general title Thermal
Heat flows and surface temperatures:
bridges in building construction -
Part 7: General calculation methods
The following part is in preparation:
- Part 2: Calculation of linear thermal bridges
Annexes A, B and C form an integral part of this part of ISO 10211.
Annexes D, E, F and G are for information only.
0 ISO 1995
All rights reserved. Unless otherwise specified, no patt of this publication may be reproduced
or- utilized in any form or by any means, electrontc or mechanical, including protocopying and
mrcrofilm, without Permission in writing from the publisher.
International Orga nization for Standardization
CH-l 21 1 Geneve 20 l Switzerla nd
Case postale 56 l
Printed in Switzerland
ISO 10211=1:1995(E)
CONTENTS
iv
Foreword
iv
Introduction
1 Scope 1
2 Normat ive references
3 Definiti ons and Symbols 2
4 Principl
5 Modelling of the construction
5.1 Rules for modelling
5.2 Conditions for simplifying the geometrical model
6 Calculation values 19
6.1 Given calculation values
6.2 Methods of determining the calculation values
7 Calculation method
7.1 Calculation rules 22
7.2 Determination of the thermal coupling coefficients
and the heat flowrate 22
7.3 Determination of the temperature at the internal surface
8 Input and output data 26
8.1 Input data
8.2 Output data
Validation of calculation methods 28
Annex A(normative)
Annex B(normative) Equivalent thermal conductivity of air cavities 32
Determination of the linear and Point thermal
Annex C(normative)
transmittances
Annex D(informative) Examples of the use of quasi-homogeneous layers
Annex E(informative) lnternal surface resistances 44
Annex F(informative) Determination of L- and g-values for more than two
boundary temperatures 51
Annex G(informative) Assessment of surface condensation 54
0.0
Ill
ISO 10211=1:1995(E)
Fore word
The text of EN ISO 1021 1-l : 1995 has been prepared by Technical Committee CEN/TC 89
“Thermal Performance of buildings and building components” in collaboration with ISO/TC 163
“Thermal insulation” .
This European Standard shall be given the Status of a National Standard, either by publicatiori
of an identical text or by endorsement, at the latest by February 1996, and conflicting national
Standards shall be withdrawn at the latest by February 1996.
According to CEN/CENELEC Internal Regulations, the following countries are bound to implement
this European Standard: Austria, Belgium, Denmark, Finland, France, Germany, Greece, lceland,
Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the
United Kingdom.
Introduction
Thermal bridges, which in general occur at any junction between building components or
where the building structure changes composition, have two consequences:
a) a Change in heat flow rate
and
b) a Change in internal surface temperature
compared with those of the unbridged structure.
Although similar calculation procedures are used, the procedures are not identical for the
calculation of heat flows and of surface temperatures.
Usuallv a thermal bridge gives rise to 3-dimensional or 2-dimensional heat flows, which
tan beprecisely determined using detailed numerical calculation methods as described in
this Standard. These are termed “Class A” methods. and Part 1 of this Standard lays down
criteria which have to be satisfied in Order that a method tan be described as being “Class
A ” .
In manv applications numerical calculations which are based on a 2-dimensional
representation of the heat flows provide results with an adequate accuracy. These are
termed “Class B” methods.
Part 2 of this Standard lavs down criteria for the calculation of linear thermal bridges
M
which have to be satisfied in Order that the calculation method tan be described as beirigg
“Class B”.
Other less precise but much simpler methods. which are not based on numerical calculation
may provide adequate assessment of the additional heat loss caused by thermal bridges.
Simplified methods are given in prEN ISO 14683. Thermal bridges in building
constructions - Linear thermal transmittance - Simplified methods and design values
(ISO/DIS 14683: 1995).
iv
0 ISO
ISO 10211=1:1995(E)
1 Scope
Part 1 of this Standard sets out the specifications on a 3-D and 2-D geometrical model of a
thermal bridge for the numerical calculation of:
- heat flows in Order to assess the Overall heat loss from a building;
minimum surface temperatures in Order to assess the risk of surface condensation.
These specifications include the geometrical boundaries and subdivisions of the model, the
thermal boundary conditions and the thermal values and relationships to be used.
The Standard is based upon the following assumptions:
- steady-state conditions apply;
- all physical properties are independent of temperature;
- there are no heat sources within the building element.
It may also be used for the derivation of linear and Point thermal transmittances and of
surface temperature factors.
2 Normative references
This Standard incorporates by dated and undated reference, provisions from other
publications. These normative references are cited at the appropriate places in the text and
the publications are listed hereafter. For dated references, subsequent amendments to or
revisions of any of these publications apply to this Standard only when incorporated in it
by amendment or revision. For undated references the latest edition of the publication
referred to applies.
ISO 7345 Thermal insulation - Physical quantities and definitions
prEN 673 Thermal insulation of glazing - Calculation rules for determining the
steady state thermal transmittance of glazing
prEN ISO 6946-1 Building components and building elements - Thermal resistance and
thermal transmittance - Calculation method
prEN ISO 10456 Thermal insulation -
Building materials and products - Determination of
declared and design values
prEN ISO 13789 Thermal Performance of buildings
- Specific transmission heat loss -
Calculation method
ISO 10211=1:1995(E)
3 Definitions and Symbols
3.1 Def initions
For the purposes of this Standard, the definitions of ISO 7345 and the following
definitions apply:
3.1.1 thermal bridge: Part of the building envelope where the otherwise uniform
thermal resistance is significantly changed by:
a) full or partial Penetration of the building envelope by materials with a
different thermal conductivity
and/or
b) a Change in thickness of the fabric
and/or
c) a differente between internal and external areas, such as occur at
wall/floor/ceiling junctions.
3.1.2 3-D geometrical modei: Geometrical model, deduced from building Plans,
such that for each of the orthogonal axes, the Cross section perpendicular to that
axis changes within the boundary of the model (see figure 1).
3.1.3 3-D flanking element: Part of the 3-D geometrical model which, when
considered in isolation, tan be represented by a 2-D geometrical model (see
figure 1 and 2).
3.1.4 3-D central element: Part of the 3-D geometrical model which is not a 3-D
flanking element (see figure 1).
3.1.5 2-D geometrical model: Geometrical model deduced from building Plans,
such that for one of the orthogonal axes, the Cross-section perpendicular to that
axis does not Change within the boundaries of the model (see figure 2).
NOTE: A 2-D geometrical model is used for two-dimensional calculations.
3.1.6 construction planes: Planes in the 3-D or 2-D model which separate:
- different materials;
- the geometrical model from the remainder of the construction;
- the flanking elements from the central element.
(see figure 3).
3.1.7 tut-off planes: Those construction planes that are boundaries to the 3-D
model or 2-D model by separating the model from the remainder of the
construction (see figure 3).
ISO 10211=1:1995(E)
F2
F3
Figure 1: 3-D model with five 3-D flanking elements and one 3-D
central element- Fl to F5 have constant Cross-sections
perpendicular to at least one axis. C is the remaining part
F2 F4
F3
Figure 2: The cross sections of the flanking elements in a 3-D
model tan be treated as 2-D models. F2 to F5 refer to figure 1.

ISO 10211=1:1995(E)
Figure 3: Example of a 3-D model showing construction planes.
C, are construction planes perpendicular to the x-axis
C, are construction planes perpendicular to the y-axis
C, are construction planes perpendicular to the z-axis
Cut-Off planes are indicated with enlarged arrows. Planes that
separate flanking elements from the central element are encircled.
3.1.8 auxiliary planes: Planes which, in addition to the construction planes,
divide the geometrical model into a number of cells.
3.1.9 quasi-homogeneous layer: Layer which consists of two or more materials
with different thermal conductivities, but which tan be considered as a
homogeneous layer with an effective thermal conductivity (see figure 4).
Figure 4: Example of a minor Point thermal bridge giving rise to
3-dimensional heat flow, which is incorporated into a
quasi-homogeneous layer
-
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ISO 10211=1:1995(E)
Differente between the internal air
3.1.10 temperature differente ratio, cRSi:
temperature and the temperature of the internal surface, divided by the
differente between the internal air temperature and the external air temperature,
calculated with a surface resistance Rsi at the internal surface.
3.1 .l 1 temperature factor at the internal surface, fRsi: Differente between the
temperature of the internal surface and the external air temperature, divided by
the differente between the internal air temperature and the external air
temperature, calculated with a surface resistance Rsi at the internal surface.
NOTE: fRsi = 1 - 3.1.12 temperature weighting factor, g: Factor which states the relative
influence of the air temperatures of the thermal environments upon the surface
temperature at the Point under consideration.
3.1.13 external reference temperature: External air temperature, assuming that
the sky is completely overcast.
3.1.14 internal reference temperature:
(a) Dry resultant temperature in the room under consideration.
(b) Mean value of the internal air temperature in the room under
consideration.
NOTE 1: (a) is used when calculating heat flows in Order to assess the
Overall heat loss and (b) is used when calculating surface temperatures in
Order to assess the risk of surface condensation.
NOTE 2: For calculation purposes the reference temperature is considered to
be uniform throughout the internal environment.
3.1 .15 dry resultant temperature: The arithmetic mean value of the internal air
temperature and the mean radiant temperature of all surfaces surrounding the
internal environment.
3.1.16 thermal coupling coefficient, Lij: Heat flow per unit temperature
I
differente between two environments i,j which are thermally con iected by the
construction under consideration.
3.1 .17 linear thermal transmittance, W Correction term for the
inear influence
coeffic
of a thermal bridge when calculating the thermal coupling ent L from 1-D
calculations.
3.1 .18 Point thermal transmittance, x: Correction term for the Point influence
of a thermal bridge when calculating the thermal coupling coefficient L from 1-D
calculations.
OS0 10211=1:1995(E)
3.2 Symbols and units
Symbol Physical quantity Unit
A area m2
H height m
L thermal coupling coefficient WK
R thermal resistance m2-KIW
R external surface resistance m2-KIW
Sb
R internal surface resistance m2aK/W
sr’
T thermodynamic temperature K
lJ thermal transmittance W/(m2-K)
V volume
m3
b width
m
d thickness m
f temperature factor at the internal surface
Rd
temperature weighting factor
h heat transfer coefficient
W/(m2*K)
I length m
density of heat flow rate W/m2
8 Celsius temperature
C
fm temperature differente
K
A thermal conductivity
W/(maK)
temperature differente ratio
c
Rsi
heat flow rate W
@
Point thermal transmittance
WIK
X
w linear thermal transmittance
Wl(m-K)
List of subscripts
cav cavity
dewpoint
dP
e exterior
i
interior
I Linear
min minimum
S surface
@ ISO
ISO 10211=1:1995(E)
4 Principles
The temperature distribution in and the heat flow through a construction tan be
calculated if the boundary conditions and constructional details are known. For
this purpose, the geometrical model is divided into a number of adjacent material
cells, each with a homogeneous thermal conductivity. The criteria which shall be
met when constructing the model are given in clause 5.
In clause 6 instructions are given for the determination of the values of thermal
conductivity and boundary conditions.
The temperature distribution is determined either by means of an iterative
calculation or by a direct Solution technique, after which the temperature
distribution within the material cells is determined by interpolation.
The calculation rules and the method of determining the temperature distribution
are described in clause 7.
NOTE: Some of the following clauses contain differentes between the
calculation of surface temperatures and the calculation of heat flows; the
differentes are given in tables 1, 3 and 4.
Modelling of the construction
5.1 Rules for modelling
lt is not usually feasible to model a complete building using a Single geometrical
model. In most cases the building may be partitioned into several Parts (including
the subsoil where appropriate) by using tut-off planes. This partitioning shall be
performed in such a way that any differentes in calculation result between the
partitioned building and the building when treated as a whole is avoided.
This partitioning into several geometrical models is achieved by choosing suitable
tut-off planes.
5.1 .l Cut-Off planes of the geometrical model
The geometrical model includes the central element(s), the flanking elements and
where appropriate the subsoil. The geometrical model is delimited by tut-off
planes.
ISO 10211=1:1995(E)
@ ISO
Cut-Off planes shall be positioned as follows:
- at a symmetry plane if this is less than 1 m from the central element (see
figure 5);
- at least 1 m from the central element if there is no nearer symmetry plane;
- in the subsoi I according to table 1.
NOTE: If the re is more than one thermal bridge present in the geometrical
model, the calculated surface temperature at the central element of the
second thermal bridge is only correct if the second thermal bridge is at a
distance of at least 1 m from the nearest tut-off plane (see figure 6), unless
the tut-off plane is a symmetry plane.
Dimensions in mm
Figure 5: Symmetry planes which tan be used as tut-off planes

0 ISO
ISO 10211=1:1995(E)
Dimensions in mm
Figure 6: Two thermal bridges A and B in the Same modeLThe thermal
bridge nearest to the tut-off planes does not fulfil the condition of
being at least 1 m from a tut-off plane (left). This difficulty is
avoided by extending the model in two directions (right)
Table 1: Location of tut-off planes in the subsoil
(foundations, ground floors, basements)
Distance to centrai element in metres
Direction Purpose of the calculation
Surface temperatures, heat flow, see
see figure 7a figure 7b
/
i
I
11 at least 1 m
1 Horizontal inside the building 0,5 b
Horizontal outside the building Same distance as
2,5 b
inside the building
Il
Vertical below ground level 3m
2,5 b
I ll I I
Vertical below floor level (see Note) 1 m
I ll I I
where:
b is the width (the smaller dimension) of the ground floor in
metres.
NOTE: This value applies only if the level of the floor under consideration is
more than 2 m below the ground level.
ISO 10211=1:1995(E)
0 ISO
Dimensions in mm
2 sb
I
I
/
/
/
/
/
/
I
/
/
/
/
Figure 7b: Soil dimensions -
Figure 7a: Soil dimensions -
calculation of heat flow
calculation of surface temperatures
5.1.2 Adjustments to dimensions
Adjustments to the dimensions of the geometrical model with respect to the
actual geometry are allowed if they have no significant influence on the result of
the calculation; this tan be assumed if the conditions in 5.2.1 are satisfied.
5.1.3 Auxiliary planes
The number of auxiliary planes in the model shall be such that adding more
auxiliary planes does not Change the temperature differente ratios cRsi by more
than 0,005 (sec also A.2).
@ ISO
ISO 10211=1:1995(E)
NOTE: A guideline for fulfilling this requirement in many cases is (see figure
.
.
The distances between adjacent parallel planes should not exceed the
following values:
- within the central element 25 mm
- within the flanking elements, measured from the construction plane which
separates the central element from the flanking element:
2000 and 4000 mm.
25, 25, 50, 50, 50, 100, 200, 500, 1000,
I dimensions (e.g. window
For constructions with indentations of sma
profiles) a finer subdivision will be needed see figure 8b).
Dimensions in mm
/
\
*.
‘.
‘l
. .
-\
.
Figure 8a: Example of construction planes supplemented with auxiliary planes
ISO 10211=1:1995(E)
@ ISO
indicates construction planes
indicates auxiliary planes
Figure 8b: Example of construction planes and auxiliary planes
in the 2-D geometrical model of a window frame
5.1.4 Quasi-homogeneous layers and materials
In a geometrical model materials with different thermal conductivities may be
replaced by a material with a Single thermal conductivity if the conditions in
5.2.2 are satisfied.
NOTE: Examples are joints in masonry, wall-ties in thermally insulated
cavities, screws in wooden laths, roof tiles and the associated air cavity and
tile battens.
5.2 Conditions for simplif ying the geome trical model
Calculation results obtained from a geometrical model with no simplifications
shall have precedence over those obtained from a geometrical model with
simplifications.
The following adjustments tan be made.
NOTE: This is important when the results of a calculation are close to any
required value.
*1
:’
lit
$i
‘>i
f
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ISO 10211=1~1995(E)
5.2.1 Conditions for adjusting dimensions to simplify the geometrical model
Adjustment to the dimensions may be made only to materials with thermal
conductivity less than 3 W/(m*K).
a) Change in the location of the surface of a block of material adjacent to the
internal or external surface of the geometrical model (see figure 9):
the local adjustment d,,,, to the location of surfaces which are not flat,
relative to the mean location of the surface, shall not exceed:
d
corr = 40, A
where:
d corr is the local adjustment perpendicular to the mean location of the
internal or external surface;
R cOrr is equal to 0,03 m2 l K/W;
A is the thermal conductivity of the material in question.
NOTE: Examples are inclined surfaces, rounded edges and profiled surfaces,
such as roof tiles.
v LA~II sockel
d
l\
Figure 9: Change in the location of the internai or externai surface
ISO 10211=1:1995(E)
b) Change in the interface of two regions of different material:
- the relocation of the interface shall take place in a direction perpendicular to
the internal surface;
- the relocation of the interface shall be such that the material with the lower
thermal conductivity is replaced by the material with the higher thermal
conductivity (see figure 10).
NOTE: Examples are recesses for sealing Strips, kit joints, adjusting blocks,
wall sockets, inclined surfaces and other connecting details.
b d
a
simplifications
com bination
Thermal Simplification
Material
block conductivity
b C d
a
,
I
x1 > x,
XI ’ x3 XI < x, XI < x2
1 XI
L
x3 ’ x2 x3 ’ x2 x3 < x2
Jh
*
Figure 10: Four possibilities for relocating the interface between three
material blocks, depending on the ratio of their thermal conductivities
ISO 1021 l-1:1995(E)
c) Neglecting thin Ia yers:
- layers with a thickness of not more than 1 mm may be ignored;
NOTE: Examples are non-metal membranes which resist the passage of
moisture or water vapour.
d) Neg/ecting appendages attached to the outside surface:
- components of the building which have been attached to the outside surface
(i.e. attached at discrete points).
NOTE: Examples are rainwater gutters and discharge pipes.
5.2.2 Conditions for using quasi-homogeneous material layers to simplify the
geometrical model
The following conditions for incorporating minor linear and Point thermal bridges
into a quasi-homogeneous layer apply in all cases:
- the layers of material in question are located in a part of the construction
which, after simplification, becomes a flanking element;
- the thermal conductivity of the quasi-homogeneous layer after simplification
is not more than IJ5 times the lowest thermal conductivity of the materials
present in the layer before simplification.
a) Calcula tion of the thermal coupling coefficient L
The thermal conductivity of the quasi-homogeneous layer shall be calculated
according to equation (1):
d
h/ -
(1)
Cl;
A
-- -i
R R c
si - se -
A.
L -i
where:
/
A is the effective thermal conductivity of the quasi-homogeneous layer;
d is the thickness of the thermally inhomogeneous layer;
A is the area of the building component;
L is the thermal coupling coefficient of the building component
determined by a 2-D or 3-D calculation;
d are the thicknesses of the homogeneous layers which are part of the
i
construction;
A are the thermal conductivities of these homogeneous layers.
i
ISO 10211=1:1995(E)
@ ISO
NOTE: The use of equation (1) is appropriate if a number of identical minor
thermal bridges are present (wall-ties, joints in masonry, hollow blocks
etc.). The calculation of L tan be restricted to a basic area which is
representative of the inhomogeneous layer. For instance a cavity wall with 4
wall-ties per Square metre tan be represented by a basic area of 0,25 m2
with one wall-tie.
b) Calculation of the internal surface temperature and the linear thermal
transmittance W or the Point thermal transmittance x (see annex C)
The thermal conductivity of the quasi-homogeneous layer may be taken as:
(AA + . . . . . + An/&)
=
/1/
+ . . . . . . +
(A, 42)
where:
A’ is the effective thermal conductivity of the quasi-homogeneous
layer;
A l . A are the thermal conductivities of the constituent materials;
0 n
A . . A are the areas of the constituent materials measured in the plane of
0 fl
the layer;
provided that:
- the thermal bridges in the layer under consideration are at or nearly at right
angles to the internal or external surface of the constructions and penetrate
the layer over its entire thickness;
- the thermal resistance (surface to surface) of the construction after
simplification is at least 1 ,5 (m2 l K)/W;
- the conditions of at least one of the groups stated in table 2 are met (see
figure 11).
ISO 10211=1:1995(E)
Table 2: Specific conditions for incorporating linear or Point
thermal bridges in a quasi-homogeneous layer
A R
Group (sec
tb At, Rcl t,i Ai di
m2 m2-K/W m2-KIW W/tm*K) m
figure 11) W/(m*K)
< 0,05.1,, 2 0,5
1 5 1,5
2 >3 5 30 x 10-6 5 0,5
2 30 x 1 o-6 > 0,5 2 0,5
3 >3
< 0,5
4 >3 5 30 x 10-6 > 0,5 2 0,5 2 0,l
where:
Atb is the thermal conductivity of the thermal bridge to be incorporated
in the quasi-homogeneous layer;
is the area of the Cross section of the thermal bridge;
A
tb
/tb is the length of a linear thermal bridge;
R is the thermal resistance of the layer without the presence of the
Point thermal bridge;
R is the total thermal resistance of the layers between the quasi-
t,i
homogeneous layer considered and the internal surface;
A is the thermal conductivity of the material layer between the
i
quasi-homogeneous layer considered and the internal surface with
the highest value of Ai times di;
d is the thickness of the Same layer.
i
NOTE: Group 1 includes linear thermal bridges. Examples are joints in
masonry, wooden battens in air cavities or in insulated cavities of
minor thickness.
Group 2 includes such items as wall-ties insofar as they are fitted in
masonry or concrete or are located in an air cavity, as weil as nails and
screws in layers of material or Strips with the indicated maximum
thermal resistance.
Groups 3 and 4 include such items as cavity ties insofar as they
penetrate an insulation layer which has a higher thermal resistance
than that indicated for group 2. The inner leaf must then have thermal
properties which sufficiently Iimit the influence of the thermal bridge
on the internal surface temperature. This may be the case if the inner
leaf has a sufficient thermal resistance (group 3) or the thermal
conductivity of the inner leaf is such that the heat flow through the
cavity ties is adequately distributed over the internal surface; most
masonry or concrete inner leaves are examples of group 4.
Calculation examples are given in annex D.
ISO 10211=1:1995(E)
@ ISO
R,, OS
R,, 0s
1 ( 1 <
Group 1
Group 2
.
f
,dr,i ,&,i ,
s
1 1
Group 3
Group 4
Figure 11 : Specific conditions for incorporating linear and Point thermal
bridges in a quasi-homogeneous layer for the groups given in table 2
l
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ISO 10211=1:1995(E)
6 Calculation values
6.1 Given calcula tion values
Use the values given in this subclause unless non-Standard values are justified
for a particular Situation.
NOTE: Non-Standard values may be justified by local conditions (e.g.
established temperature distributions in the ground) or by specific material
properties (e.g. the effect of a low emissivity coating on the surface
resistance).
6.1.1 Thermal conductivities of materials
The design values of thermal conductivities of building materials and products
should either be calculated according to prEN 30456 or taken from tabulated
values.
The thermal conductivity of soil tan be taken as 2,0 W/(mK)
NOTE: Other values for the thermal conductivity of the soil may be used if
information on the local seit condition is avaitable. See prEN 1190.
6.1 .2 Surface resistances
The values according to table 3 shall be apptied.
For heat flow calculations the value of ßsi is related to the internal mean dry
resultant temperature.
For the calcutation of surface temperatures the value of ß,i is related to the mean
internal air temperature, but shall take account of the non-uniform air
temperature due to thermal stratification and the non-uniform radiant
temperature that exists in edges and corners.
NOTE: When calculating the surface temperature, the following values for
the internal surface resistance are recommended:
Glazing: 0,13 m2mK/W
Upper half of the room: 0,25 m2aK/W
Lower half of the room: 0,35 m2mK/W
The value of R,i = 0,50 m2eK/W is recommended if significant thermal
shielding by objects such as furniture may occur. See annex E.
ISO 10211=1:1995(E)
@ ISO
Table 3: Surface resistances (m2mK/W)
Purpose of calculation
Surface temperatures Heat flow rate
l
I
External surf acc resistance &
Internal surface resistance R,i
1 ‘1 See Annex E
6.1 .3 Boundary temperatures
Table 4 gives the boundary temperatures which shall be used.
Table 4: Boundary temperatures
Purpose of calculation
Heat flow rate
Surface temperature
t
air temperature dry resultant temperature
lnternal
see 6.2.3 see 6.2.3
Internal in unheated rooms
air temperature, assuming that air temperature,
External
the sky is completely overcast assuming that the sky is
completely overcast
at the distance below ground at the distance below
Soil (horizontal tut-off plane)
level given in table 1: yearly ground level given in
average external air table 1: adiabatic
temperature boundary condition
6.2 Methods of determining the calcula tion values
6.2.1 Thermal conductivity of quasi-homogeneous layers
The thermal conductivity of quasi-homogeneous layers shall be calculated
according to equations (1) and (2).
6.2.2 Equivalent thermal conductivity of air cavities
An air cavity shall be considered as a homogeneous conductive material with a
thermal conductivity AC.
lf the thermal resistance of an air layer or cavity is known, the thermal
conductivity is obtained from:

0 ISO
ISO 10211=1:1995(E)
d
cav
A
(3)
cav =
R
cav
where:
A is the thermal conductivity of the air layer or cavity;
cav
d is the thickness of the air layer;
cav
R Cav is the thermal resistance in the main direction of heat flow.
Thermal resistances and thermal conductivities of air layers and cavities bounded
by opaque materials are given in annex B.
For the thermal resistance of air layers in multiple glazing see prEN 673.
NOTE: Air cavities with dimensions of more than 0,5 m along each one of
the orthogonal axis shall be treated as rooms (see 6.2.3).
6.2.3 Determining the temperature in an adjacent unheated room
If sufficient information is available, the temperature in an adjacent unheated
room may be calculated according to prEN 33789.
If the temperature in an adjacent unheated room is unknown and cannot be
calculated according prEN 33789, because the necessary information is not
available, the heat flows and internal surface temperatures tan not be
calculated. However all required coupling coefficients and temperature weighting
factors tan be calculated and presented according to annex F.
NOTE: When assessing the thermal behaviour of thermal bridges, the
available information is usually restricted to a specific part of the
construction (e.g. junctions) and little or no information is available on
dimensions or on the total coupling coefficients of the adjacent room.
7 Calcuiation method
The geometrical model is divided into a number of cells, each with a
characteristic Point (called a node). By applying the laws of energy conservation
(div q = 0) and Fourier (a = -Agrad 0) and taking into account the boundary
conditions, a System of equations is obtained which is a function of the
temperatures at the nodes. The Solution of this System, either by a direct
Solution technique or by an iterative method, provides the node temperatures
from which the temperature field tan be determined. From the temperature
distribution, the heat flows tan be calculated by applying Fourier’s law.
60 IOZW1:1995(E)
Calculation programs shall be verified according to the require
annex A.
7.1 Calcula tion rußes
7.1 .1 Heat flows between material cells and adjacent environment
The density of heat flow rate, perpendicular to the interface between a material
cell and the adjacent environment shall satisfy:
- - -
(0 0)
s
=
(4
R
S
where:
is the density of heat flow rate;
is the internal or external reference temperature;
0 is the temperature at the internal or external surface;
S
R is the internal or external surface resistance.
S
7.1 .2 Heat flows at tut-off planes
The tut-off planes shall be adiabatic (i.e. Zero heat flow) with the exception
given in 6.1 .3.
NOTE: In the case of calculating surface temperatures, the horizontal cut-
off plane in the soil is not adiabatic, but has a fixed temperature.
7.1 .3 Solution of the equations
The equations shall be solved according to the requirements given in A.2.
7.1 .4 Calculation of the temperature distribution
ure distribution wi thin each mat erial cell shall be calculated by
The temperat
between the node tem perat ures
inte rpolation
NOTE: Linear interpolation suffices.
Determha tion of the therma/ csup4inry coefficients and the heat flo w rate
7.2
More than two boundary temperatures
7.2.1
The heat flow rate Qii from environment i to a thermally connected environmentj
I
is given by:
~ = Lji(O. - 0’)
(5)
, I
/
@ ISO
ISO 1021%1:1995(E)
The total heat flow rate from a room or buiiding tan be calculated using the
principles as stated in clause 4. For more than two environments with different
temperatures (e.g. different internal temperatures or different external
temperatures), the total heat flow rate @ of the room or the building tan be
calculated from:
cp = 1 { Lii(O. - 0.) }
(6)
, I
i
where L,j are the total coupling coefficients between each pair of environments.
NOTE: F.1 gives a method to calculate the thermal coupling coefficients.
7.2.2 Two boundary temperatures, unpartitioned model
If there are on ly two environments with two different temperatures (e.g. one
Ie external temperature), and if the total room or building is
internal and or
calculated 3-dimensionally from a Single model, then the total thermal coupling
coefficient L, , 2 tan be obtained from the total heat flow rate Q of the room or
building:
4) - f, 2 (0, - 0,)
(7)
I
7.2.3 Two boundary temperatures, partitioned model
If the room or building has been partitioned (see figure 12), the total L,,j-value is
calculated from (8):
N M
30 20
L
(8)
i,j = i, + i, ’
CL n(n c
LNn
n-l m-l k-l
where:
D
2 is the thermal coupling coefficient obtained from a 3-D calculation
n fi, j!
for part n of the room or building;
D
f is the linear thermal cou pling coeff ic ient
obtained from a 2-D
m (i, j!
calculation for part m of the r oom or buil ding;
ISO 10211=1:1995(E)
@ ISO
l is the length over which the value Lmff,yapplies;
m
u is the thermal transmittance obtained from a 1-D calculation for part k
k(i,j)
of the
room or building;
A is the
area over which the value U, applies;
k
N is the total number of 3-D Parts;
M is the total number of 2-D Parts;
K is the total number of 1-D Parts.
NOTE: In formula (8) Z A, is less than the total surface area of the envelope.
---
?
i
L’5” I
t
e- w- m--
--+
I
L
I
I
-t-
p” I
4 1
b
Figure 12: Building envelope partitioned into 3-D, 2-D and
1 -D geometrical modeis
7.3 Determination of the tempera ture at the infernal surface
7.3.1 More than two boundary temperatures
If there are more than two boundary temperatures, the temperature weighting
factor g shall be used. The temperature weighting factors provide the means to
calculate the temperature at any location at the inner surface with coordinates
(x,y,z) as a linear function of any set of boundary temperatures.
NOTE 1: At least three boundary temperatures are involved if the
geometrical model includes internal environments with different
temperatures and also if the subsoil is part of the geometrical model (see
6.1 .3).
@ ISO
ISO 10211~1:1995(E)
Using the temperature weighting factors, the surface temperature at location
(x,y,z) is given by:
(9)
= gl(xfylz) @l + g2tx,ylz) @* l *‘* + g,(X,y,z) 0,
x, Y,X
with:
(10)
Sl(XfYJ) + g,ky,z) + . . . . + g,(x,y,z) = 1
NOTE 2: F.3 gives a method for calculating the weighting factors.
Calculate the internal surface temp
...