EN ISO 13792:2005

SLOVENSKI STANDARD
01-julij-2005
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Thermal performance of buildings - Calculation of internal temperatures of a room in
summer without mechanical cooling - Simplified methods (ISO 13792:2005)
Wärmetechnisches Verhalten von Gebäuden - Berechnung von sommerliche
Raumtemperaturen bei Gebäuden ohne Anlagentechnik - Vereinfachtes
Berechnungsverfahren (ISO 13792:2005)
Performance thermique des bâtiments - Température intérieure en été d'un local non
climatisé - Méthodes de calcul simplifiées (ISO 13792:2005)
Ta slovenski standard je istoveten z: EN ISO 13792:2005
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 13792
NORME EUROPÉENNE
EUROPÄISCHE NORM
March 2005
ICS 91.120.10
English version
Thermal performance of buildings - Calculation of internal
temperatures of a room in summer without mechanical cooling -
Simplified methods (ISO 13792:2005)
Performances thermiques des bâtiments - Calcul de la Wärmetechnisches Verhalten von Gebäuden -
température interne d'une pièce sans climatisation Sommerliche Raumtemperaturen bei Gebäuden ohne
mécanique en été - Méthodes simplifiées (ISO Anlagentechnik - Vereinfachtes Berechnungsverfahren
13792:2005) (ISO 13792:2005)
This European Standard was approved by CEN on 30 April 2004.

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 Central Secretariat 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 Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13792:2005: E
worldwide for CEN national Members.

Contents                                                                 page
Foreword.3
Introduction .4
1 Scope.5
2 Normative references.5
3 Terms, definitions, symbols and units.5
3.1 Terms and d efinitions .5
3.2 Symbols and units .7
4 Input data and results .8
4.1 Assumptions .8
4.2 Boundary conditions and input data .8
4.3 Output data.13
5 Calculation procedure.13
6 Validation procedures.14
6.1 Introduction.14
6.2 Validation procedure for the calculation method .14
6.3 Validation procedure for the sunlit factor due to external obstructions .22
Annex A (informative) Examples of solution model .25
A.1 Introduction .25
A.2 RC three-nodes model.25
A.3 Admittance procedure.31
Annex B (informative) Air changes for natural ventilation.39
B.1 Introduction .39
B.2 Evaluation of the air change rate for natural ventilation .39
Annex C (informative) Evaluation of the shaded area of a plane surface due to external
obstructions .41
C.1 Introduction .41
C.2 Calculation procedure.41
Annex D (informative) Internal gains.43
D.1 Introduction .43
D.2 Residential building.43
D.3 Non-residential building.44
Annex E (informative) Examples of calculation .45
E.1 Room characteristics.45
E.2 Example of calculation for the RC3 nodes model .48
E.3 Admittance method.51
Annex ZA (normative) Normative references to international publications with their
corresponding European publications.54

Foreword
This document (EN ISO 13792:2005) has been prepared by Technical Committee CEN/TC 89, "Thermal
performance of buildings and building components", the secretariat of which is held by SIS, in collaboration with
Technical Committee ISO/TC 163, “Thermal performance and energy use in the built environment”, Subcommittee
SC 2, "Calculation methods".
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 August 2005, and conflicting national standards shall be withdrawn at the latest by
August 2005.
This standard is one of a series of standards on calculation methods for the design and evaluation of the thermal
performance of buildings and building elements.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark,
Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

Introduction
Knowledge of the internal temperature of a room in the warm period is needed for several purposes such as:
a) defining the characteristics of a room at the design stage, in order to prevent or limit overheating in summer;
b) assessing the need for a cooling installation.
The internal temperature is influenced by many parameters such as climatic data, envelope characteristics, ventilation
and internal gains. The internal temperature of a room in the warm period can be determined using detailed
calculation methods. EN ISO 13791 lays down the assumptions and the criteria which have to be satisfied for
assessment of internal conditions in the summer with no mechanical cooling. However, for a number of applications
the calculation methods based on EN ISO 13791 are too detailed. Simplified methods are derived from more or less
the same description of the heat transfer processes in a building. Each calculation method has its own simplification,
assumptions, fixed values, special boundary conditions and validity area. A simplified method can be implemented in
many ways. In general the maximum allowed simplification of the calculation method and the input data is determined
by the required amount and accuracy of the output data.
This document defines the level, the amount and the accuracy of the output data and the allowed simplification of the
input data.
No particular calculation methods are included in the normative part of this standard. As examples, two calculation
methods are given in Annex A. They are based on the simplification of the heat transfer processes that guarantees
the amount and the accuracy of the output data and the simplification of the input data required by this standard.
The use of these simplified calculation methods does not imply that other calculation methods are excluded from
standardisation, nor does it hamper future developments. Clause 6 gives the criteria which have to be satisfied in
order that a method complies with this document.
1 Scope
This document specifies the required input data for simplified calculation methods for determining the maximum,
average and minimum daily values of the operative temperature of a room in the warm period:
a) to define the characteristics of a room in order to avoid overheating in summer at the design stage;
b) to define whether the installation of a cooling system is necessary or not.
Clause 6 gives the criteria to be met by a calculation method in order to satisfy this document.
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.
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.
EN 13363-1, Solar protection devices combined with glazing – Calculation of solar and light transmittance – Part 1:
Simplified method.
EN ISO 6946, Building components and building elements – Thermal resistance and thermal transmittance –
Calculation method (ISO 6946:1996).
EN ISO 7345:1995, Thermal insulation – Physical quantities and definitions (ISO 7345:1987).
EN ISO 10077-1, Thermal performance of windows, doors and shutters – Calculation of thermal transmittance –
Part 1: Simplified method (ISO 10077-1:2000).
EN ISO 13370, Thermal performance of buildings – Heat transfer via the ground – Calculation methods (ISO
13370:1998).
EN ISO 13786,Thermal performance of building components – Dynamic thermal characteristics – Calculation
methods (ISO 13786:1999).
EN ISO 13791:2004, Thermal performance of buildings – Calculation of internal temperatures of a room in summer
without mechanical cooling – General criteria and calculation procedures (ISO 13791:2004).

3 Terms, definitions, symbols and units
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in EN ISO 7345:1995 and the following apply.
3.1.1
internal environment
closed space delimited from the external environment or adjacent spaces by an envelope element
3.1.2
room element
wall, ceiling, roof, floor, door or window which separates the room from the adjacent spaces or external environment
3.1.3
room air
air in the room
3.1.4
internal air temperature
temperature of the room air
3.1.5
internal surface temperature
temperature of the internal surface of each element of the envelope
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 enclosure
NOTE  For simplification the mean value of the air temperature and the mean radiant temperature of the room can be used.
3.2 Symbols and units
For the purposes of this document, the following symbols and units apply.
Symbol Quantity Unit
A
area m
C heat capacity J/K
I intensity of solar radiation W/ m
m mass Kg
R thermal resistance
m ⋅K/W
T thermodynamic temperature K
U thermal transmittance under steady state conditions .
W/(m K)
V volume m
c specific heat capacity of air at constant pressure .
p
J/(kg K)
d
thickness m
f solar loss factor -
sl
f sunlit factor -
s
f ventilation factor -
v
g total solar energy transmittance -
h surface coefficient of heat transfer .
W/(m K)
l length m
q mass air flow rate kg/s
a
q density of heat flow rate W/m
q* heat flow rate per volume W/m
t time s
v velocity m/s
Λ thermal conductance ⋅
W/(m K)
heat flow rate W
Φ
solar absorptance -
α
total hemispherical emissivity -
ε
Celsius temperature °C
θ
thermal conductivity
λ W/(m⋅K)
density kg/m
ρ
solar reflectance -
ρ
solar direct transmittance -
τ
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
t time sr short wave radiation
v ventilation va ventilation through air cavity

4 Input data and results
4.1 Assumptions
For the scope of this document the following basic assumptions are made:
— the room is considered a closed space delimited by enclosure elements;
— the air temperature is uniform throughout the room;
— the various surfaces of the enclosure elements are isothermal;
— the thermophysical properties of the material composing the enclosure elements are constant;
— the heat conduction through each enclosure element is one dimensional;
— air spaces within the envelope elements are considered as air layers bounded by two isothermal surfaces;
— the mean radiant temperature is calculated as an area-weighted average of the radiant temperature at each
internal surface;
— the operative temperature is calculated as the arithmetic mean value of the internal air temperature and the mean
radiant temperature;
— the distribution of the solar radiation on the internal surfaces of the room is time independent;
— the spatial distribution of the radiative part of the heat flow due to internal sources is uniform;
— the long-wave radiative and the convective heat transfers at each internal surface are treated separately;
— the dimensions of each component are measured at the internal side of the enclosure element;
— the effects of the thermal bridges on heat transfers are neglected.
4.2 Boundary conditions and input data
4.2.1 Boundary conditions
4.2.1.1 General
The elements of the envelope are divided into:
— external elements: these include the elements separating the internal environment from the outside and from other
zones (i.e. attic, ground, crawl space);
— internal elements: these include the elements (vertical and horizontal) separating the internal environment from
other rooms which can be considered to have the same thermal conditions.
4.2.1.2 External elements
External elements are those separating the room from the external environment and from zones at different thermal
conditions (e.g. attic, ground, crawl space).
Boundary conditions consist of defined hourly values of:
— external air temperature;
— intensity of the solar radiation on each orientation;
— sky radiant temperature;
— air temperature for the adjacent zones which cannot be considered at the same thermal conditions as the
examined room.
For elements in contact with the ground the external temperature is assumed to be the mean monthly value of the
external air temperature.
4.2.1.3 Internal elements
Internal elements are those separating the room from other rooms which can be considered to have the same thermal
conditions.
Internal elements are assumed to be adiabatic, which means that the values of the following quantities are considered
to be the same on either side of the element:
— the air temperature;
— the mean radiant temperature;
— the solar radiation absorbed by the surface.
4.2.2 Heat transfer coefficients
For the purposes of this document the following values shall be used:
— internal convective heat transfer coefficient h = 2,5 W/(m ⋅K);
ci
— internal long-wave radiative heat transfer coefficient h = 5,5 W/(m ⋅K);
ri
— external convective heat transfer coefficient h = 8,0 W/(m ⋅K);
ce
— external long-wave radiative heat transfer coefficient h = 5,5 W/(m ⋅K);
re
— internal surface coefficient of heat transfer h = 8,0 W/(m ⋅K);
i
— external surface coefficient of heat transfer h = 13,5 W/(m ⋅K).
e
4.2.3 Geometrical and thermophysical parameters of the room envelope
4.2.3.1 Opaque elements
For each element the following data are required:
— area calculated using the internal dimensions;
— summertime thermal transmittance (U*);
— thermal inertia characteristics [see EN ISO 13786];
— for external elements, sunlit factor and solar energy transmittance.
The summertime thermal transmittance, U*, is given by:
*
U = (1)
1 1 1
− 0,17 + +
U h h
i e
where
U is the conventional thermal transmittance with standard surface resistances defined below;
0,17 is the sum of the conventional internal and external surface resistances as defined in EN ISO 6946;
h is the external surface coefficient of heat transfer defined in 4.2.2;
e
h is the internal surface coefficient of heat transfer defined in 4.2.2.
i
The thermal transmittance, U, may be determined from:
— building elements in contact with the external air: EN ISO 6946;
— building elements in contact with the ground: EN ISO 13370.
The thermal inertia characteristics shall be determined according to EN ISO 13786.
NOTE The sunlit factor differs from the shading correction factor, defined in ISO 13790, which includes diffuse solar radiation.
The sunlit factor, f , is given by:
s
A
s
f = (2)
s
A
where
A is the area of the sunlit part of the wall (see 6.3);
s
A is the total area of the wall.
The solar energy transmittance, g, is the ratio of the heat flow through the element due to the absorbed solar
radiation, to the incident solar radiation. It is given by:
— element with no air cavity (or closed air cavity):
α U *
g = (3)
h
e
where α is the direct solar absorptance of the external surface.
— element with open air cavity (external air):
g = f S + (1− f ) S (4)
v fc v fv
where
f is the ventilation coefficient derived from Table 1 as a function of ventilation in the cavity;
v
S is the solar energy transmittance for the closed cavity;
fc
S is the solar energy transmittance for the ventilated cavity, given by:
fv
* *
 
α U ⋅U
e i
S = (5)
 
fv
* *
h
U + U + h′
e e i
 
where
U* is the thermal transmittance between the external environment and the air cavity defined as in Equation (1);
e
U* is the thermal transmittance between the internal environment and the air cavity defined as in Equation (1);
i
h is the external surface coefficient of heat transfer (defined in 4.2.2);
e
α is the direct solar absorptance of the external surface of the element;
with
h' = h (h + 2 h )/ h (6)
c c r r
where
h is the convective heat transfer coefficient between the surface of the ventilated air layer and the air in the
c
cavity;
h is the radiative heat transfer coefficient between the two surfaces of the air layer.
r
2 2
Using the following values: h = 5 W/(m ·K) h = 5 W/(m ·K)
c r
h' = 15 W/(m ·K),
Table 1 gives the ventilation coefficient f depending on the ratio between the cavity area (A ) and the wall area (A ).
v c w
The cavity area is the air flow area; the wall area is the conduction heat flow area.
Table 1 – Ventilation coefficient f
v
A /A ≤0,005 0,005 < A /A ≤ 0,10 0,10 < A /A
c w c w c w
f
0,8 0,5 0,2
v
In the absence of an actual measured value, the direct solar absorptance of the external surface may be derived from
Table 2 as function of its colour.
Table 2 – Direct solar absorptance of external surface
Light colour Medium colour Dark colour
0,3 0,6 0,9
α
4.2.3.2 Glazed elements
For each glazing element the following data are required:
— area calculated including the frame;
— summertime thermal transmittance (U* value);
— total solar transmittance (g) (τ in EN 410);
— secondary solar heat gain (q ) of the glazing by convection and long-wave radiation due to the absorbed solar
i
radiation;
— tertiary heat transfer factor (S ) of the glazing by ventilation due to the absorbed solar radiation;
f3
— the sunlit factor due to external obstruction f .
s
The summertime thermal transmittance, U*, is determined by using Equation (1).
The thermal transmittance, U, is determined according to EN 673 and EN ISO 10077-1.
The solar direct transmittance, (τ), and the secondary and tertiary heat transfer factors S and S are determined
f2 f3
from EN 13363-1.
a) Solar-to-air factor
The solar-to-air factor, f , is the fraction of solar heat entering the room through the glazing which is immediately
sa
transferred to the internal air. This fraction depends on the presence of internal elements with very low heat capacity,
such as carpets and furniture. It is assumed to be time independent and, unless otherwise specified, the values in
informative Annex G of EN ISO ISO 13791:2004 may be used.
b) Solar loss factor
The solar loss factor, f , is the fraction of the solar radiation entering the room which is reflected back outside. It
sl
depends on the solar position, solar properties, dimensions and exposure of the glazing system, the room geometry
and the reflectivity of the internal room surfaces. It is assumed to be time independent. Unless otherwise specified,
values of f in informative Annex G of EN ISO 13791:2004 may be used.
sl
NOTE The procedure for evaluating the sunlit factor due external obstruction f can be defined in national standards. Such a
s
procedure is given in Annex C.
4.2.3.3 Special elements
a) Ceiling below attic
The element formed by the ceiling, the air space and the roof is considered as a single horizontal element with one-
dimensional heat flow. The air space is considered as an air cavity and treated according to EN ISO 6946.
b) Floor on ground
The ground formed by the floor and the soil is considered as a single horizontal layer, which may include an air gap.
The heat flow through the element is the sum of a monthly mean value and a variable term. The monthly mean value
is calculated using the mean internal and external temperatures, and (taken as constant and equal to the mean
monthly value) the thermal transmittance determined according to EN ISO 13370. The variable term is calculated
assuming the mean temperature difference is zero. The depth of soil is taken to be 0,5 m.
c) Cellar
A cellar can be considered as an adjacent room with fixed air temperature.
d) Crawl space
A crawl space is treated as a floor on ground according to EN ISO 13370.
4.2.4 Air change rate
The air change rate depends on the tightness of the envelope and on the opening of any doors and windows.
At a design stage the air change rate is expressed as a function of the:
— location of the building;
— pattern of air ventilation;
— number of facades with windows.
The location may be categorised as:
— city centre area;
— suburban area;
— open area.
The pattern of air ventilation is related to the time schedule of the opening and closing of windows and whether
windows are located on one or on more facades.
The following time schedules are considered:
— windows open day and night;
— windows closed day and night;
— window closed during the day and open during the night.
NOTE Data on the time of opening and closing of the windows and on hourly air change rates can be defined at a national level.
Annex B gives examples of appropriate values of the air change rates.

4.2.5 Internal gain
Internal gains derive from lighting, equipment and occupant. The pattern of the heat flow due to internal gains is
related to the occupants’ behaviour and to the utilisation of the room.
NOTE Data on the time schedule of utilisation of the room, and the heat flow for each type of utilisation, can be defined at a
national level. If information is not available the values included in Annex D can be used.
4.3 Output data
Results of the calculations are the maximum, average and minimum daily values of the operative temperature of the
considered room under defined external and internal conditions.
5 Calculation procedure
The calculation procedure is based on the following steps:
a) definition of the climatic data of the location;
b) definition of the room for which the control is required;
c) definition of the elements of the envelope enclosing the room (area, exposure, boundary conditions);
d) calculation of the thermophysical parameters (steady state and transient conditions) and the solar energy
transmittance of opaque and transparent elements;
e) definition of the ventilation pattern;
f) definition of the internal gains;
g) evaluation of the maximum, average and minimum daily values of the operative temperature.
The level of accuracy of a calculation procedure shall be checked using the validation procedure given in Clause 6,
leading to a classification into one of three accuracy classes 1, 2 and 3 (see 6.2).
6 Validation procedures
6.1 Introduction
This document does not impose any specific calculation method for the evaluation of the operative temperature of a
single room nor the calculation of the sunlit factor. The cases used in Clause 6 are based on EN ISO 13791.
6.2 Validation procedure for the calculation method
6.2.1 General
The model validation includes the calculation of the operative temperature under cyclic conditions for several cases
indicated below, and the comparisons of these values with those reported in Table 11.
6.2.2 Geometry
The values of geometrical characteristics of the rooms (based on external dimensions) are given in Table 3.
Table 3 – Room data
Element Geometry A Geometry B
Area (m ):
External opaque wall  6,58 3,08
Glazing area  3,50  7,00
Partition wall (left) 15,40 15,40
(right) 15,40 15,40
(back) 10,08 10,08
Floor 19,80 19,80
Ceiling 19,80 19,80
Volume (m) 55,44 55,44
The room geometry is shown in Figure 1.
2,8 m
A
W
North
West
3,6 m
Figure 1 – Room geometries A and B
6.2.3 Description of elements
The thermophysical characteristics of the walls, ceiling and floor are reported in Table 4. The thermophysical
properties of the glass panes composing the glazing system and the external shade are reported in Figure 2.
As far as these test cases are concerned, the solar properties of glass panes are independent of the angle of
incidence. The optical properties of each panel are reported in Table 5.

External, cavity and internal
1 2
thermal resistances
R = 0,074 m ⋅K/W
se
R = 0,080 m ⋅K/W
ec
R = 0,173 m ⋅K/W
ic
R = 0,125 m ⋅K/W
si
R R R R
es ec ic si
Key
1 External shade (or blind)
2 External pane, 6 mm
3 Internal pane, 6 mm
Figure 2 – Double pane (DP) glazing system with external shading device
5,5 m
Table 4 – Thermophysical properties of the opaque components
d c
λλ  ρ ρ
λλ ρρ
p
m
W/(m⋅K) kg/m
kJ/(kg⋅K)
Type no. 1 (external
wall)
Outer layer 0,115 0,99 1800 0,85
Insulation layer 0,06 0,04 30 0,85
Masonry 0,175 0,79 1600 0,85
Internal plastering 0,015 0,70 1400 0,85
Type no. 2 (internal wall)
Gypsum plaster 0,012 0,21 900 0,85
Mineral wool 0,10 0,04 30 0,85
Gypsum plaster 0,012 0,21 900 0,85
Type no. 3 (ceiling/floor)
Floor covering 0,004 0,23 1500 1,5
Concrete floor 0,06 1,40 2000 0,85
Insulation 0,04 0,04 50 0,85
Concrete 0,18 2,10 2400 0,85
Type no. 4 (ceiling/floor)
Plastic floor covering 0,004 0,23 1500 1,5
Concrete floor 0,06 1,40 2000 0,85
Insulation 0,04 0,04 50 0,85
Concrete 0,18 2,10 2400 0,85
Mineral wool 0,10 0,04 50 0,85
Acoustic board 0,02 0,06 400 0,84
Type no. 5 (roof)
External layer 0,004 0,23 1500 1,3
Insulation 0,08 0,04 50 0,85
Concrete 0,20 2,1 2400 0,85
Table 5 - Solar characteristics of the glazed element and the shade for all incident angles
Component ττττ ρρρρ
n n
Pane 0,84 0,08
Shade 0,2 0,50
6.2.4 Combination of elements
Three combinations of elements are considered as given in Table 6. The numbers in Table 6 refer to the wall types in
Table 4. For the definition of adiabatic see 4.2.1.3
Table 6 – Test cases
Test External Internal Adiabatic Adiabatic Roof
no. opaque wall adiabatic wall ceiling floor
1 1 2 4 4
2 1 2 3 3
3 1 2 3 5
6.2.5 Climatic data
The climatic data are given in Tables 7, 8 and 9.
Table 7 – Solar radiation 15 July
Climate A Climate B
Hour
Horizontal Vertical Horizontal Vertical
West West
2 2 2 2
W/m W/m W/m W/m
4 0 0 0 0
5 4 2 69 22
6 168 45 225 55
7 369 78 388 80
8 557 103 539 101
9 719 122 669 117
10 842 137 768 128
11 920 145 831 135
12 946 160 852 150
13 920 381 831 366
14 842 576 768 558
15 719 720 669 703
16 557 787 539 778
17 369 740 388 756
18 168 511 225 604
19 4 20 69 271
20 0 0 0 0
Any combination of solar parameters that leads to the values given in Table 7 is acceptable.
Table 8 – External air temperature for climate A (15 July)
Hour Hour Hour Hour
θθθθ θθθθ θθθθ θθθθ
ao ao ao ao
°C °C °C °C
1 23,6 7 22,8 13 32,7 19 29,9
2 23,0 8 23,9 14 33,6 20 28,4
3 22,5 9 25,8 15 34,0 21 27,0
4 22,1 10 27,3 16 33,6 22 25,8
5 22,0 11 29,3 17 32,8 23 24,9
6 12 18 24
22,2 31,2 31,5 24,2
Table 9 – External air temperature for climate B
Hour Hour Hour Hour
θθθθ θθθθ θθθθ θθθθ
ao ao ao ao
°C °C °C °C
1 14,1 7 13,1 13 26,2 19 22,6
2 8 14 20
13,3 14,6 27,5 20,5
3 12,6 9 16,6 15 28,0 21 18,7
4 12,2 10 19,0 16 27,5 22 17,1
5 12,0 11 21,8 17 26,4 23 15,8
6 12,3 12 24,3 18 24,6 24 14,9

The values of the solar radiation and temperatures reported in Tables 7, 8 and 9 correspond to instantaneous value at
the given hour (for example the solar radiation is 225 W/m for a horizontal surface at 6:00). The evolution during an
hour is assumed to be linear between the value at the beginning and the end of the hour. The input data have to be
adapted to each calculation method following these assumptions.
The sky radiant temperature is equal to external air temperature.
6.2.6 Internal energy sources
The total heat flow rate per floor area due to internal sources is given in Table 10. The heat flow is assumed to be
transferred to the room by convection and radiation in equal proportions (50 % for each).
Table 10 – Total heat flow due to internal sources per floor area
Hour ΦΦΦΦ Hour ΦΦΦΦ Hour ΦΦΦΦ Hour ΦΦΦΦ
ic ic ic ic
2 2 2 2
W/m W/m W/m W/m
0 to1 0 6 to 7 0 12 to 13 10 18 to19 15
1 to 2 0 7 to 8 1 13 to 14 10 19 to 20 15
2 to 3 0 8 to 9 1 14 to15 10 20 to 21 15
3 to 4 0 9 to10 1 15 to16 1 21 to 22 15
4 to 5 0 10 to11 1 16 to17 1 22 to 23 10
5 to 6 0 11 to 12 10 17 to 18 1 23 to 24 0

The daily total value of the internal gains is 117 Wh/m .
6.2.7 Ventilation pattern
Three different ventilation patterns are considered, with air changes rates as follows:
-1
a) 1 h , constant;
-1 -1
b) 0,5 h from 06:00 to 18:00 and 10 h from 18:00 to 06:00;
-1
c) 10 h constant.
The characteristics of air are as follows:
— specific heat capacity: 1008 J/(kg⋅K);
— density: 1,139 kg/m .
6.2.8 Test results
For each test the following data, determined in cyclic conditions, shall be calculated:
— daily average value of the operative temperature θ
op,av
— daily minimum value of the operative temperature θ
op,min
— daily maximum value of the operative temperature θ
op,max
The maximum and minimum value are extracted from the 24 hourly values obtained as the average for each hour
(e.g. from 07:00 to 08:00).
NOTE  More information is given in the paper of P. Romagnoni and J.-R. Millet in the ASHRAE Transactions 2002, V. 108, Pt 2.

Table 11 – Reference values of the operative temperature
Room Ventilation
θθθθ θθθθ θθθθ
op,max op,ave op,min
°C °C °C
a) 38,8 35,9 33,6
A.1
b) 34,1 29,5 25,6
c) 33,6 29,1 25,4
a) 37,7 35,9 34,5
A.2
b) 32,3 29,5 26,6
c) 32,4 29,1 26,4
a) 40,6 38,6 37,0
A.3 b) 35,0 31,4 28,0
c) 33,6 30,2 27,4
a) 35,9 30,8 27,1
B.1
b) 30,0 22,3 16,5
c) 28,3 21,6 16,3
a) 33,9 30,8 28,6
B.2
b) 26,9 22,3 18,1
c) 26,5 21,6 17,8
a) 35,8 32,5 30,2
B.3
b) 29,3 24,0 19,2
c) 27,5 22,6 18,7
Each test case is classified into one of three classes 1, 2, 3 on the basis of the difference ∆ between the calculated
value and the reference value. The considered procedure is classified according to the worst resulting test. For the
three classes, the limiting ∆ values are as follows. The following classes are defined:
Class 1 ±1 K
Class 2 +2, -1 K
Class 3 +3, -1 K
6.3 Validation procedure for the sunlit factor due to external obstructions
The calculation of the sunlit factor, defined in 4.5.3.5 of EN ISO 13791:2004, is to be validated for a vertical surface
with the following dimensions:
Height: 2,8 m
Width: 3,6 m
3,6 m
Figure 3 – Dimensions of the wall for test cases

The calculation shall refer to 15 July, latitude 52° N. The validation procedure consists of three test cases.

Figure 4a – Test No.1: Infinite horizontal overhang – South orientation (north hemisphere)

1 m
2,8 m
Figure 4b – Test No.2: Loggia – South orientation (north hemisphere)

Figure 4c – Test No.3: Infinite right side fin – West orientation
Figure 4 – Test cases
Following Table gives results for the reference sunlit factor (f ) obtained for the three test cases.
s
It gives also, for information, the value of projection of the azimuthal solar angle compared to the wall perpendicular
vector (ΘΘ).
ΘΘ
1 m
1 m
Table 12 – Reference values of the sunlit factor
Test case 1 Test case 2 Test case 3
Hour f f f
ΘΘΘΘ ΘΘΘΘ ΘΘΘΘ
s s s
0.5 - - - - - -
1.5 - - - - - -
2.5 - - - - - -
3.5 - - - - - -
4.5 - - - - - -
5.5 - - - - - -
6.5 - - - - - -
7.5 86,8 0,0 - - 86,8 0,00
8.5 77,2 0,00 - - 77,3 0,00
9.5 69,0 0,26 - - 69,0 0,15
10.5 63,0 0,36 - - 63,0 0,28
11.5 59,8 0,39 - - 59,8 0,37
12.5 59,8 0,39 83,0 0,00 59,8 0,37
13.5 63,0 0,36 691 0,65 63,0 0,28
14.5 69,0 0,26 55,5 0,82 69,0 0,15
15.5 77,2 0,00 42,4 0,92 77,2 0,00
16.5 86,8 0,00 30,7 0,98 86,8 0,00
17.5 - - 22,6 1,00 - -
18.5 - - 22,6 1,00 - -
19.5 - - 30,7 1,00 - -
20.5 - - 42,2 1,00 - -
21.5 - - 53,8 1,00 - -
22.5 - - 64,5 1,00 - -
23.5 - - 72,2 1,00 - -
For each case, the absolute difference between the calculated f value and the reference must be less than 0,05.
s
Annex A
(informative)
Examples of solution model
A.1 Introduction
This Annex gives two examples of simple calculation methods for the evaluation of the operative temperature of a
room according to the type of inputs defined in this document.
The calculation methods are based on the following representation of the heat transfer processes:
a) a network of resistances and capacities (RC three-nodes model) of the heat transfers between the internal and
external environment;
b) separation of the steady state contribution from the variable contribution described by predetermined harmonic
heat transfer parameters (admittance procedure).
A.2 RC three-nodes model
A.2.1 Presentation
The calculation model is based on the simplifications of the heat transfer between the internal and external
environment reported in the following Figure.
Φ
i
θ R θ
ei ei a,i
Φ
R
s
is
θ θ
es s
R
es
Φ
R
m ms
θ θ
em m
R
em
C
m
Figure A.1 – Network of resistances and capacities (RC three-nodes model)
According to this representation the envelope components are divided as:
— light opaque external components;
— heavy opaque external components;
— glazing components;
— internal components.
The relevant nodes are defined related to:
θ , indoor air temperature;
a i
θ star temperature;
s
θ mass temperature;
m
θ outdoor air temperature;
ei
θ θ equivalent outdoor air temperature of external components.
,
es em
The equivalent resistances (K/W) and heat capacity (J/K) between the internal and the external environment
considered are:
R thermal resistance due to air ventilation;
ei
R , R thermal resistances of external components between outside and inside;
es em
R , R thermal resistance correspondent to the heat exchanges, between the internal surfaces and the

is ms
internal air;
C heat capacity of the enclosure elements.
m
The heat flows (W) considered are:
Φ heat flow to θ node;
i
i
Φ heat flow to θ node;
s
s
Φ heat flow to θ node.
m
m
For each components the following parameters are required:
- light opaque external components thermal transmittance U
(depth ≤ 12 cm)
solar factor S
f
solar radiation I
sr
area A
- heavy opaque external components thermal transmittance U
(depth > 12 cm)
solar factor S
f
solar radiation I
sr
area A
- glazing components thermal transmittance U
solar direct transmittance S
f1
(τ in EN 410)
secondary heat transfer factor S
f2
towards inside
(q in EN 410)
i
tertiary heat transfer coefficient S
f3
solar radiation I
sr
area A
- all components heat capacity per area C
A
area
n
- room air flow rate
V
room volume
A.2.2 Determination of the air and operative temperatures
The solution model is based on the scheme of Crank-Nicolson considering a time step of one hour. The temperatures
are the average between time t and t - 1 except for θ and θ that are instantaneous values at time t and t - 1.
m,t m,t-1
For a given time step, θ is calculated from the previous value θ by:
m,t m,t-1
θ = [θ ( C / 3600 – 0,5 (H +H ) + Φ ] / [C / 3600 + 0,5 (H +H )] (A.1)
m,t m,t-1 m 3 em mtot m 3 em
For the time step considered, the average values of nodes temperatures are given by:
θ = (θ + θ ) / 2 (A.2)
m m,t m,t-1
θ = [H θ + Φ + H θ + H (θ + Φ / H )] / ( H + H + H ) (A.3)
s ms m s es es 1 ei i ei ms es 1
θ = [H θ + H θ + Φ ] / ( H + H ) (A.4)
i is s ei ei i is ei
and the operative temperature (average between air and mean radiant temperature) by
θ = [θ + (1+ h / h ) θ - h θ / h ] / 2 (A.5)
op i ci rs s ci i rs
with
h = 1,2 h
rs ri
H = 1 / (1 / H + 1 / H )
1 ei is
H = H + H
2 1 es
H
...