EN ISO 13791:2012

SLOVENSKI STANDARD
01-julij-2012
1DGRPHãþD
SIST EN ISO 13791:2005
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Thermal performance of buildings - Calculation of internal temperatures of a room in
summer without mechanical cooling - General criteria and validation procedures (ISO
13791:2012)
Wärmetechnisches Verhalten von Gebäuden - Sommerliche Raumtemperaturen bei
Gebäuden ohne Anlagentechnik - Allgemeine Kriterien und Validierungsverfahren (ISO
13791:2012)
Performance thermique des bâtiments - Calcul des températures intérieures en été d'un
local sans dispositif de refroidissement - Critères généraux et procédures de validation
(ISO13791:2012)
Ta slovenski standard je istoveten z: EN ISO 13791:2012
ICS:
91.120.10 Toplotna izolacija stavb Thermal insulation
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 13791
NORME EUROPÉENNE
EUROPÄISCHE NORM
March 2012
ICS 91.120.10 Supersedes EN ISO 13791:2004
English Version
Thermal performance of buildings - Calculation of internal
temperatures of a room in summer without mechanical cooling -
General criteria and validation procedures (ISO 13791:2012)
Performance thermique des bâtiments - Calcul des Wärmetechnisches Verhalten von Gebäuden -
températures intérieures en été d'un local sans dispositif de Sommerliche Raumtemperaturen bei Gebäuden ohne
refroidissement - Critères généraux et procédures de Anlagentechnik - Allgemeine Kriterien und
validation (ISO 13791:2012) Validierungsverfahren (ISO 13791:2012)
This European Standard was approved by CEN on 14 March 2012.

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, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2012 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13791:2012: E
worldwide for CEN national Members.

Contents Page
Foreword .3

Foreword
This document (EN ISO 13791:2012) has been prepared by Technical Committee ISO/TC 163 "Thermal
performance and energy use in the built environment" in collaboration with Technical Committee CEN/TC 89
“Thermal performance of buildings and building components” the secretariat of which is held by SIS.
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 September 2012, and conflicting national standards shall be
withdrawn at the latest by September 2012.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 13791:2004.
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, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland, Turkey and the United Kingdom.
Endorsement notice
The text of ISO 13791:2012 has been approved by CEN as a EN ISO 13791:2012 without any modification.
INTERNATIONAL ISO
STANDARD 13791
Second edition
2012-03-15
Thermal performance of buildings —
Calculation of internal temperatures of
a room in summer without mechanical
cooling — General criteria and validation
procedures
Performance thermique des bâtiments — Calcul des températures
intérieures en été d'un local sans dispositif de refroidissement —
Critères généraux et procédures de validation

Reference number
ISO 13791:2012(E)
©
ISO 2012
ISO 13791:2012(E)
©  ISO 2012
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
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Published in Switzerland
ii © ISO 2012 – All rights reserved

ISO 13791:2012(E)
Contents Page
Foreword . v
Introduction . vii
1  Scope . 1
2  Normative references . 1
3  Terms, definitions, symbols and units . 2
3.1  Terms and definitions . 2
3.2  Symbols and units . 3
3.3  Subscripts . 5
4  Determination of internal temperatures . 6
4.1  Assumptions . 6
4.2  Evaluation of the relevant temperatures . 6
4.2.1  Internal air temperature . 6
4.2.2  Internal surface temperature . 7
4.2.3  Surface delimiting two solid layers . 8
4.2.4  Surface of an air layer . 8
4.2.5  External surface of a room element . 9
4.2.6  Relevant temperatures for special construction elements . 9
4.3  Room thermal balance . 10
4.4  Boundary conditions . 11
4.4.1  Single room . 11
4.4.2  Similar rooms . 11
4.4.3  Adjacent room with defined value of the air temperature . 14
4.4.4  Floor on ground . 15
4.4.5  Cellar or crawl space . 15
4.4.6  Ceiling below attic . 15
4.5  Terms in the thermal balance equations . 15
4.5.1  Heat conduction through components . 15
4.5.2  Convective heat transfer . 16
4.5.3  Short-wave radiation heat transfers . 19
4.5.4  Long-wave radiation heat transfer . 23
4.5.5  Internal gains . 25
4.5.6  Heat flow due to ventilation . 26
5  Determination of internal humidity . 27
6  Procedure for carrying out calculations . 27
6.1  General . 27
6.2  Design climatic data . 27
6.2.1  General . 27
6.2.2  Long-period design climatic data . 28
6.2.3  Design warm sequence . 28
6.3  Geometrical and thermophysical characteristics of room elements . 28
6.4  Design internal gains . 28
6.5  Design occupant behaviour . 28
6.6  Calculation procedure . 29
6.6.1  General . 29
6.6.2  Definition of the starting conditions . 29
6.6.3  Prediction of the internal temperatures . 29
7  Report of the calculation . 29
ISO 13791:2012(E)
8  Validation procedures .30
8.1  Introduction .30
8.2  Validation of heat transfer processes .30
8.2.1  General .30
8.2.2  Heat conduction through opaque elements .30
8.2.3  Internal long-wave radiation exchanges .32
8.2.4  Sunlit area of a window due to external obstructions .34
8.3  Validation procedure for the whole calculation method.37
8.3.1  General .37
8.3.2  Geometry for the test rooms .38
8.3.3  Thermophysical properties of opaque walls .39
8.3.4  Properties of glazing .39
8.3.5  Solar parameters .41
8.3.6  Boundary conditions .42
8.3.7  Internal energy sources .45
8.3.8  Ventilation .46
8.3.9  Descriptions of the validation tests .46
Annex A (informative) Example of solution technique .49
Annex B (informative) Convective heat transfer through ventilated air layer.57
Annex C (informative) Shading due to overhangs and side fins .64
Annex D (informative) Design climatic data in the warm season .72
Annex E (informative) Calculation of the internal long-wave radiation exchanges in buildings .73
Annex F (informative) External radiative long-wave heat transfer coefficients .75
Annex G (informative) Solar factors .77
Annex H (informative) Internal gains .79
Annex I (informative) Air ventilation .81
Annex J (informative) Detailed results of the validation tests considered in the “whole validation
model” procedure .89
Annex K (informative) Calculation method for internal humidity without moisture absorption into
or desorption from walls and other structures .91
Annex L (informative) Normative references to international publications with their corresponding
European publications .94
Bibliography .96

iv © ISO 2012 – All rights reserved

ISO 13791:2012(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 13791 was prepared by Technical Committee ISO/TC 163, Thermal performance and energy use in the
built environment, Subcommittee SC 2, Calculation methods.
This second edition cancels and replaces the first edition (ISO 13791:2004), which has been technically
revised. The main changes compared to the previous edition are given in the following table:
ISO 13791:2012(E)
Clause/subclause Changes
2 Added ISO 9050, ISO 10292, ISO 15099, ISO 15927-2 and EN 673
3.2 Deleted q and v and added m
a m a
4.2.1 Amended Equation (1)
Deleted m and added the descriptions of  and v
a,i a ai
4.5.6.1 Replaced q by m
a a
8.3.9.1 Amended the values in Tables 22 and 23
8.3.9.2 Amended the values in Tables 24 and 25
I.2.2 Replaced m by m
a
Amended Equation (I.1) and added the descriptions of n and p
Amended Equation (I.4) and added the description of C
w
Amended the unit used in Table I.1
I.2.3 Replaced m, m and m by m , m and m , respectively
w T a a,w a,T
Amended Equations (I.5), (I.6), (I.9), (I.10), (I.11), (I.12), (I.13) and (I.14)
Replaced A by A in Equation (I.13)
T
Replaced c by C
p w
Added the descriptions of Equations (I.8) and (I.10)
I.2.3.3.3 Amended the description I.2.3.3.3
I.3.2 Replaced c by C
p w
Replaced m by m
w a,w
I.3.3 Replaced m by m
T a,T
Annex J Amended the values in Tables J.1 and J.2
Annex K Added as a new annex
vi © ISO 2012 – All rights reserved

ISO 13791:2012(E)
Introduction
This International Standard is intended for use by specialists to develop and/or validate methods for the hourly
calculation of the internal temperatures of a single room.
Examples of application of such methods include:
a) assessing the risk of internal overheating;
b) optimizing aspects of building design (building thermal mass, solar protection, ventilation rate, etc.) to
provide thermal comfort conditions;
c) assessing whether a building requires mechanical cooling.
Criteria for building performance are not included. They can be considered at national level. This International
Standard can also be used as a reference to develop more simplified methods for the above and similar
applications.
INTERNATIONAL STANDARD ISO 13791:2012(E)

Thermal performance of buildings — Calculation of internal
temperatures of a room in summer without mechanical
cooling — General criteria and validation procedures
1 Scope
This International Standard specifies the assumptions, boundary conditions, equations and validation tests for
a calculation procedure, under transient hourly conditions, of the internal temperatures (air and operative)
during warm periods, of a single room without any cooling/heating equipment in operation. No specific
numerical techniques are imposed by this International Standard. Validation tests are included in Clause 8. An
example of a solution technique is given in Annex A.
This International Standard does not contain sufficient information for defining a procedure able to determine
the internal conditions of special zones such as attached sun spaces, atria, indirect passive solar components
(trombe walls, solar panels) and zones in which the solar radiation may pass through the room. For such
situations different assumptions and more detailed solution models are needed (see Bibliography).
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 6946, Building components and building elements — Thermal resistance and thermal transmittance —
Calculation method
ISO 7345, Thermal insulation — Physical quantities and definitions
ISO 9050, Glass in building — Determination of light transmittance, solar direct transmittance, total solar
energy transmittance, ultraviolet transmittance and related glazing factors
ISO 9251, Thermal insulation — Heat transfer conditions and properties of materials — Vocabulary
ISO 9288, Thermal insulation — Heat transfer by radiation — Physical quantities and definitions
ISO 9346, Hygrothermal performance of buildings and building materials — Physical quantities for mass
transfer — Vocabulary
ISO 10077-1, Thermal performance of windows, doors and shutters — Calculation of thermal transmittance —
Part 1: General
ISO 10077-2, Thermal performance of windows, doors and shutters — Calculation of thermal transmittance —
Part 2: Numerical method for frames
ISO 10292, Glass in building — Calculation of steady-state U values (thermal transmittance) of multiple
glazing
ISO 13370, Thermal performance of buildings — Heat transfer via the ground — Calculation methods
ISO 13791:2012(E)
ISO 15099, Thermal performance of windows, doors and shading devices — Detailed calculations
ISO 15927-2, Hygrothermal performance of buildings — Calculation and presentation of climatic data —
Part 2: Hourly data for design cooling load
EN 410, Glass in building — Determination of luminous and solar characteristics of glazing
EN 673, Glass in building — Determination of thermal transmittance (U value) — Calculation method
3 Terms, definitions, symbols and units
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 7345, ISO 9251, ISO 9288,
ISO 9346 and the following apply.
3.1.1
internal environment
closed space delimited from the external environment or adjacent spaces by the building fabric
3.1.2
room element
wall, roof, ceiling, floor, door or window that separates the internal environment from the external environment
or an adjacent space
3.1.3
room air
air of the internal environment
3.1.4
internal air temperature
temperature of the room air
3.1.5
internal surface temperature
temperature of the internal surface of a building element
3.1.6
mean radiant temperature
uniform surface temperature of an enclosure in which an occupant would exchange the same amount of
radiant heat as in the actual non-uniform enclosure
3.1.7
operative temperature
uniform temperature of an enclosure in which an occupant would exchange the same amount of heat by
radiation plus convection as in the actual non-uniform environment
2 © ISO 2012 – All rights reserved

ISO 13791:2012(E)
3.2 Symbols and units
For the purposes of this document, the following symbols and units apply.
Symbol Definition Unit
A area m
A area of the surface in contact with the air layer m
c
A floor area m
f
A area of room element j m
j
A projected area of the considered system m
p
A sunlit area m
s
A shaded area m
sh
a thermal diffusivity m /s
C heat capacity J/K
.
c specific heat capacity J/(kg K)
.
c specific heat capacity of air J/(kg K)
a
c coefficient of discharge —
d
.
c specific heat capacity of the medium J/(kg K)
me
c velocity coefficient —
v
d thickness m
E ventilation parameter —
r
F view factor —
F view factor from the element with the sky —
sk
f solar distribution factor —
d
f internal convective factor —
ic
f sunlit factor —
s
f solar to air factor —
sa
f solar loss factor —
sl
G moisture production kg/s
i
G moisture influx by ventilation kg/s
v
g heat flow rate per volume W/m
s
g acceleration due to gravity m/s
H height of the element m
2.
h surface coefficient of heat transfer W/(m K)
2.
h convective heat transfer coefficient for ventilated layers W/(m K)
a
2.
h convective heat transfer coefficient of the surface W/(m K)
c
2.
h convective heat transfer coefficient for closed spaces W/(m K)
g
2.
h long-wave radiative heat transfer coefficient W/(m K)
lr
ISO 13791:2012(E)
I intensity of solar radiation W/m
I diffuse component of the solar radiation reaching the surface W/m
d
I direct component of the solar radiation reaching the surface W/m
D
J long-wave radiosity W/m
lr,j
k crack coefficient —
l length m
m mass air flow rate kg/s
a
m mass forced air flow rate by mechanical ventilation kg/s
a,m
m mass air flow rate by natural ventilation kg/s
a,n
m mass flow rate due to temperature kg/s
a,T
m mass flow rate due to wind kg/s
a,w
n flow exponent —
p pressure Pa
q density of heat flow rate W/m
q density of heat flow rate by convection W/m
c
q density of heat flow rate by conduction W/m
cd
q density of heat flow rate by conduction at the internal surface W/m
c,i
q density of heat flow rate due to long-wave radiation exchanged with W/m
lr
other internal surfaces
q correction for the long-wave radiation exchanges from the wall to W/m
sk
the sky
q density of heat flow rate due to the absorbed short-wave radiation W/m
sr
R thermal resistance mK/W
T thermodynamic temperature K
T temperature of the environment K
e
T temperature of the air entering the air layer K
in
T temperature of the air leaving the layer K
out
t time s
2.
U thermal transmittance W/(m K)
V volume m
v velocity m/s
x,y,z co-ordinates m
2
  thermal conductance W/(m K)
  heat flow rate W
 heat flow rate due to internal sources W
i
  solar to air heat flow rate W
sa
  heat flow rate of solar radiation entering the room W
sr
4 © ISO 2012 – All rights reserved

ISO 13791:2012(E)
 heat flow rate by ventilation W
v
  heat flow rate due to the air entering the room through air layers W
va
within the elements bounding the room
 solar absorptance —
 long-wave emissivity of the surface
  celsius temperature °C
  defined air temperature of the adjacent room °C
a,d
  air temperature of the adjacent room °C
a,e
  temperature of the internal air °C
a,i
 temperature of the mechanically supplied air °C
v
 thermal conductivity W/(mK)
viscosity kg/(ms)
 humidity by volume of internal air kg/m
i
  humidity by volume of inflowing air kg/m
in
  solar reflectance —
 density of air kg/m
a
  average solar reflection coefficient of room surfaces —
m
  density of the medium kg/m
me
  density of the air at the temperature T kg/m
a,o 0
2 4
 Stefan-Boltzmann constant W/(m K )

3.3 Subscripts
a air cd conduction
b building ec external ceiling
c convection ef external floor
D direct solar radiation eq equivalent
d diffuse solar radiation ic internal ceiling
e external if internal floor
g ground il inlet section
i internal lr long-wave radiation
l leaving the section mr mean radiant
n normal to surface op operative
r radiation sa solar to air
s surface sk sky
sl solar loss t time
sr short-wave radiation v ventilation
va ventilation through air cavity
ISO 13791:2012(E)
4 Determination of internal temperatures
4.1 Assumptions
The evaluation of the internal temperature of a room involves the solution of a system of equations of the
transient heat and mass transfers between the external and internal environment through the opaque and
transparent elements bounding the room envelope. The procedures given in this International Standard allow
the user to determine the time-dependent temperature of each component, including the internal air. Accepted
assumptions for the calculation of the internal temperatures of a single room under transient conditions in
absence of any cooling plant are:
 the air temperature is uniform throughout the room;
 the various surfaces of the room elements are isothermal;
 the thermophysical properties of the materials composing the room elements are time-independent;
 the heat conduction through the room elements (excluding to the ground) is assumed to be one-
dimensional;
 the heat conduction to the ground through room elements is treated by an equivalent one-dimensional
heat flow rate according to ISO 13370;
 the effect of thermal bridges is generally neglected, but if it is considered the heat storage contribution of
the thermal bridges is neglected;
 air spaces are treated as air layers bounded by two isothermal and parallel surfaces;
 convective heat transfer coefficients: at the external surface they depend on the wind velocity and
direction, at the internal surface they depend on the direction of the heat flow;
 the long-wave radiative heat flow rate at the external surfaces of the room elements is related to a time-
independent heat transfer coefficient;
 the external radiant environment (sky excluded) is at the external air temperature (see 4.5.4.1);
 the distribution of solar radiation within the room is time-independent;
 the dimensions of each element are measured inside the room;
 the mean radiant temperature is calculated by weighting the various internal surface temperatures
according to the relevant areas;
 the operative temperature is the average between the internal air temperature and the mean surface
temperature.
4.2 Evaluation of the relevant temperatures
4.2.1 Internal air temperature
The air temperature of a room, at any given time, is obtained by solving Equation (1), where heat flow rates to
room air are taken as positive:
N

a,i
()Aq ΦΦΦΦcV (1)
 c,i j v i,c sa va a a a,i
 t
j1
6 © ISO 2012 – All rights reserved

ISO 13791:2012(E)
where
N is the number of internal surfaces delimiting the internal air;
A is the area of each building element;
q is the density of the heat flow rate by convection at the internal surface (see 4.5.2.2);
c,i
 is the heat flow rate by ventilation (see 4.5.6);
v
 is the convective part of heat flow rate due to internal sources (see 4.5.5);
i,c
 is the solar to air heat flow rate (see 4.5.3.4);
sa
 is the heat flow rate due to the air entering the room through air layers within the elements
va
bounding the room;
c is the specific heat capacity of air;
a
 is the density of the internal air;
a
V is the volume of the internal air;
a,i
 is the temperature of the internal air;
a,i
t is the time.
NOTE Because of the very small value of the term ( V ) the right-hand side of Equation (1) can be assumed to

a a,i
be zero.
4.2.2 Internal surface temperature
The internal surface temperature at element j is obtained by solving Equation (2), where heat flow rates to the
internal surface, except q , are taken as positive:
c,j
Φ
i,r
qqqq   0 (2)
lr,jjsr, c,j cd,j
N
A
 j
j1
where
q is the density of heat flow rate due to long-wave radiation exchanged with other internal surfaces
lr
(see 4.5.4.2);
q is the density of heat flow rate due to the absorbed short-wave radiation (see 4.5.3.2);
sr
q is the density of heat flow rate released to room air by convection (see 4.5.2.2);
c
q is the density of heat flow rate by conduction (see 4.5.1);
cd
 is the heat flow rate due to the radiative component of internal gains (see 4.5.5);
i,r
N is the number of surfaces delimiting the internal air;
A is the area of room element j.
j
ISO 13791:2012(E)
4.2.3 Surface delimiting two solid layers
j-1 jj+1
q
sr,j
q
q
cd,j+1
cd,j-1
Figure 1 — Surface delimiting two layers
The temperature at surface j delimiting two layers in an element (Figure 1) is obtained by solving Equation (3):
(3)
qqq 0
cd, 1jjcd, 1 sr, j
where
q is the density of heat flow rate by conduction from the j1 surface (see 4.5.1);
cd, ,j-1
q is the density of heat flow rate by conduction from the j+1 surface (see 4.5.1);
cd, j+1
q is the density of heat flow rate due to the solar radiation absorbed by the surface j.
sr, j
4.2.4 Surface of an air layer
j
j-1
q
sr,j
q q
c,j cd,j
q
lr,j
Key
1 air layer
Figure 2 — Surface delimiting an air layer
8 © ISO 2012 – All rights reserved

ISO 13791:2012(E)
The temperature at surface j of an air layer (Figure 2) is obtained by solving Equation (4):
qqq q  0 (4)
c,jjlr, cd,j sr,j
where
q is the density of the total heat flow rate released to the air layer (see 4.5.2);
c
q is the density of the heat flow rate received by long-wave radiation across the air layer (see 4.5.4);
lr
q is the density of the heat flow by conduction (see 4.5.1);
cd
q is the density of heat flow rate absorbed due to an external source (e.g. solar radiation).
sr
4.2.5 External surface of a room element
j
q
sr,j
q q
c,j cd,j
q
lr,j
Figure 3 — External surface of an element
The temperature at surface j of a room element (Figure 3) is obtained by solving Equation (5):
(5)
qqqq  0
lr,jjsr, c,j cd,j
where
q is the density of heat flow rate by long-wave radiation at the surface (see 4.5.4.1);
lr
q is the density of heat flow rate due to the short-wave radiation absorbed by the surface (see 4.5.3.1);
sr
q is the density of heat flow rate by convection with the air (see 4.5.2.2);
c
q is the density of the conduction heat flow rate (see 4.5.1).
cd
4.2.6 Relevant temperatures for special construction elements
4.2.6.1 Ceiling below an attic
The ceiling, the air space and the roof are considered as a single horizontal element with one-dimensional
heat flow. The air space is considered as an air layer, treated in 4.5.2.3 and 4.5.2.4.
ISO 13791:2012(E)
4.2.6.2 Floor on ground
The floor and the soil are considered as a single horizontal element with the heat flow treated according to
ISO 13370. Boundary conditions are specified in 4.4.4.
4.2.6.3 Floor over cellar
The cellar is treated as an unheated basement according to ISO 13370. The calculation procedure is
according to ISO 13370. Boundary conditions are specified in 4.4.5.
4.2.6.4 Floor over crawl space
The floor, the crawl space and the soil are treated as a suspended floor according to ISO 13370. Boundary
conditions are specified in 4.4.5.
4.2.6.5 Glazed element
A glazed element is composed of a number of planes (glazing panes and possibly blinds) which are in thermal
equilibrium with one another. The evaluation of temperatures of each plane is made using the following
assumptions:
 the heat storage effects in the various planes are neglected;
 the heat flow by convection through the air layers between each pane is calculated according to 4.5.2.3
and 4.5.2.4;
 the density of heat flow rate due to the long-wave radiation between the various planes is calculated
according to 4.5.4.3;
 the density of heat flow rate due to the short-wave radiation absorbed by each plane is treated as a
source term.
4.3 Room thermal balance
In each equation of 4.2, the time-dependent heat flow rates shall be expressed in terms of operators which
relate the heat flow rate at the internal surface of each element to the temperature at the internal and external
surface, and that of the internal air, by using suitable mathematical models of the heat transfer processes. The
temperature of the internal air, together with the temperature of the different surfaces, shall be determined by
solving the global equation system at each time step considered. A general expression of the equation system
is expressed in Equation (6):
ΠΠ Π Π
θ
Γ
1,1 1,2 1,NN1, 1 is,1 



ΠΠ Π Π θ
Γ
2,1 2,2 2,NN2, 1
is,2

  (6)
ΠΠ Π Π Γ
 θ

NN,1 ,2 N,N N,N1 N
is,N 


Γ
ΠΠ Π Π
θ
N1
NN1,1 1,2 N1,N N1,N,1 a

where
N is the number of elements bounding the room corresponding to the internal surfaces delimiting the
internal air;
 are the coefficients of the unknown temperatures () (from 1 to N relating to the internal surfaces,
N  1 relating to the internal air);
 are the coefficients of the known terms (from 1 to N relating to the internal surfaces, N  1 relating to
the internal air);
10 © ISO 2012 – All rights reserved

ISO 13791:2012(E)
 are the unknown temperatures (from 1 to N relating to the internal surfaces, N  1 relating to the
internal air).
The “” and “” terms are obtained by rewriting Equation (1) and Equation (2) in order to separate the
unknown parameters [air temperature at the given time t for Equation (1) and the internal surface temperature
for each component at the given time t for Equation (2)] from the known parameters. The form of these
equations depends on the solution technique adopted.
4.4 Boundary conditions
4.4.1 Single room
A single room model requires the knowledge of the conditions of adjacent rooms. The two following situations
are considered:
 adjacent room with the same conditions (similar rooms);
 adjacent room with defined internal conditions.
If boundary conditions are very different from the above, the simple room model specified in this International
Standard shall not be used and it is necessary to calculate the real boundary conditions by a multi-room
model able to take account of the heat transfer between the different rooms. This may be achieved by:
a) simultaneous solution of the global system equations for all rooms, or
b) iterative procedure by considering, as boundary conditions for each room, the temperatures determined
at the previous time step.
4.4.2 Similar rooms
4.4.2.1 Partition (vertical) wall
Referring to Figure 4, the following boundary conditions are considered as shown in Equation (7):
ei
θθ
a,e a,i
1 2
Key
1 similar
2 internal
Figure 4 — Partition vertical wall
ISO 13791:2012(E)
 = 
a,e a,i
q = q
sr,e sr,i
q = q (7)
lr,e lr,i
h = h
c,e c,i
where
 is the air temperature of the adjacent room;
a,e

a,i is the air temperature of the room;
q is the density of heat flow rate due to absorbed short-wave radiation at the external surface of the
sr,e
wall;
q is the density of the heat flow rate by long-wave radiation exchanged with the other surfaces of the
lr,e
adjacent room;
q is the density of heat flow rate due to absorbed short-wave radiation at the internal surface of the
sr,i
wall (see 4.5.3.2);
q is the density of the heat flow rate received by long-wave radiation at the internal surface of the wall
lr,i
from the other internal surfaces (see 4.5.4.2);
h is the convective heat transfer coefficient at the external surface;
c,e
h is the convective heat transfer coefficient at the internal surface (see Table 1).
c,i
4.4.2.2 Ceiling/floor
Referring to Figure 5, the following boundary conditions are considered as shown in Equation (8):
θ
ec
a,e
ic
θ
a,i
if
ef
θ
a,e
Key
1 similar room
2 ceiling
3 room
4 floor
5 similar room
Figure 5 — Ceiling/floor adjacent to similar rooms
12 © ISO 2012 – All rights reserved

ISO 13791:2012(E)
 = 
a,e a,i
q = q
sr,ec sr,if
q = q
lr,ec lr,if
q = q (8)
sr,ef sr,ic
q = q
lr,ef lr,ic
h = h
c,ec c,if
h = h
c,ef c,ic
where
 is the air temperature of the adjacent room;
a,e
 is the air temperature of the room;
a,i
q is the density of heat flow rate due to absorbed short-wave radiation at the external surface of the
sr,ec
ceiling;
q is the density of heat flow rate due to absorbed short-wave radiation at the internal surface of the
sr,ic
ceiling (see 4.5.3.2);
q is the density of heat flow rate due to absorbed short-wave radiation at the external surface of the
sr,ef
floor;
q is the density of heat flow rate due to absorbed short-wave radiation at the internal surface of the
sr,if
floor (see 4.5.3.2);
q is the density of the heat flow rate by long-wave radiation by the external surface of the floor with
lr,ef
the other external surfaces;
q is the density of the heat flow rate by long-wave radiation by the internal surface of the floor with
lr,if
the other internal surfaces (see 4.5.4.2);
q is the density of the heat flow rate by long-wave radiation from the external surface of th
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