EN ISO 13791:2004

SLOVENSKI STANDARD
01-februar-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
13791:2004)
Wärmetechnisches Verhalten von Gebäuden - Sommerliche Raumtemperaturen bei
Gebäuden ohne Anlagentechnik - Allgemeine Kriterien und Validierungsverfahren (ISO
13791:2004)
Performance thermique des bâtiments - Température intérieure en été d'un local non
climatisé - Criteres généraux et méthodes de calculs (ISO 13791:2004)
Ta slovenski standard je istoveten z: EN ISO 13791:2004
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
November 2004
ICS 91.120.10
English version
Thermal performance of buildings - Calculation of internal
temperatures of a room in summer without mechanical cooling -
General criteria and validation procedures (ISO 13791:2004)
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 méthodes de calcul Anlagentechnik - Allgemeine Kriterien und
(ISO 13791:2004) Validierungsverfahren (ISO 13791:2004)
This European Standard was approved by CEN on 7 June 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
© 2004 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13791:2004: E
worldwide for CEN national Members.

Contents
Page
Foreword.4
Introduction .5
1 Scope.6
2 Normative references.6
3 Terms, definitions, symbols and units.6
3.1 Terms and definitions .6
3.2 Symbols and units .8
3.3 Subscripts.9
4 Determination of internal temperatures .9
4.1 Assumptions.9
4.2 Evaluation of the relevant temperatures.10
4.3 Room thermal balance.13
4.4 Boundary conditions .14
4.5 Terms in the thermal balance equations .18
5 Procedure for carrying out calculations .29
5.1 General.29
5.2 Design climatic data.29
5.3 Geometrical and thermophysical characteristics of room elements.30
5.4 Design internal gains .30
5.5 Design occupant behaviour .30
5.6 Calculation procedure .30
6 Report of the calculation .31
7 Validation procedures.31
7.1 Introduction.31
7.2 Validation of heat transfer processes .32
7.3 Validation procedure for the whole calculation method .39
Annex A (informative) Example of solution technique.51
A.1 Introduction.51
A.2 Basic assumptions for the calculation method .51
A.3 Calculation procedure .51
A.4 Room thermal balance.57
Annex B (informative) Convective heat transfer through ventilated air layer.58
B.1 Introduction.58
B.2 Convective heat transfer for a vertical air layer.58
B.3 Convective heat transfer for an external horizontal air layer .62
Annex C (informative) Shading due to overhangs and side fins.64
C.1 Introduction.64
C.2 Calculation path for overhang .65
C.3 Calculation path for vertical projection at the end of the overhang .66
C.4 Calculation path for side fin.67
C.5 Calculation of the sunlit area due to short side fin .68
C.6 External obstruction .68
C.7 Sunlit factor .70
Annex D (informative) Design climatic data in the warm season.71
Annex E (informative) Calculation of the internal long-wave radiation exchanges in buildings .72
E.1 Introduction .72
E.2 Limits of application .72
E.3 Calculation procedure .72
Annex F (informative) External radiative long-wave heat transfer coefficients.73
F.1 Introduction .73
F.2 Terms and calculation procedure.73
Annex G (informative) Solar factors .75
G.1 Introduction .75
G.2 Solar to air factor.75
G.3 Distribution factors .75
G.4 Solar loss factor .76
Annex H (informative) Internal gains.77
H.1 Introduction .77
H.2 Residential building .77
H.3 Non residential building .78
Annex J (informative) Air ventilation.80
J.1 Introduction .80
J.2 Calculation procedure .80
J.3 Example of calculation of natural ventilation rates for simple building.85
Annex K (informative) Detailed results of the validation tests considered in the “whole
validation model” procedure.87
Bibliography.89

Foreword
This document (EN ISO 13791:2004) 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 May 2005, and conflicting national standards shall be withdrawn at the latest by
May 2005.
This standard is one of a series of standards on calculation methods for the design and the evaluation of the
thermal performance of buildings and building components.
This document includes a Bibliography.
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
This document 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 standard can also
be used as a reference to develop more simplified methods for the above and similar applications.
1 Scope
This document 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 the warm
period, of a single room without any cooling/heating equipment in operation. No specific numerical techniques are
imposed by this document. Validation tests are included in Clause 7. An example of a solution technique is given in
Annex A.
This document 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.
EN 410, Glass in building – Determination of luminous and solar characteristics of glazing.
EN ISO 6946, Building components and building elements – Thermal resistance and thermal transmittance –
Calculation method (ISO 6946:1996).
EN ISO 7345, Thermal insulation – Physical quantities and definitions (ISO 7345:1987).
EN ISO 9251, Thermal insulation – Heat transfer conditions and properties of materials – Vocabulary (ISO
9251:1987).
EN ISO 9288, Thermal insulation – Heat transfer by radiation – Physical quantities and definitions (ISO 9288:1989).
EN ISO 9346, Thermal insulation – Mass transfer – Physical quantities and definitions (ISO 9346:1987).
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 10077-2, Thermal performance of windows, doors and shutters – Calculation of thermal transmittance –
Part 2: Numerical method for frames (ISO 10077-2:2003).
EN ISO 13370, Thermal performance of buildings – Heat transfer via the ground – Calculation methods (ISO
13370:1998).
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, EN ISO 9251, EN ISO 9288
and EN 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 with which an occupant would exchange the same amount of radiant
heat as with the actual non-uniform enclosure
3.1.7
operative temperature
uniform temperature of an enclosure with which an occupant would exchange the same amount of heat by
radiation plus convection as with the actual non-uniform environment
3.2 Symbols and units
For the purposes of this document, the following terms and symbols apply.
Symbol Quantity Unit
A area m
A
sunlit area m
s
C heat capacity J/K
F view factor -
I intensity of solar radiation W/ m
R thermal resistance
m ⋅K/W
T thermodynamic temperature K
U thermal transmittance .
W/(m K)
V volume m
a thermal diffusivity m /s
c
specific heat capacity .
J/(kg K)
c coefficient of discharge -
d
c specific heat capacity of air at constant pressure .
p
J/(kg K)
d thickness m
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 heat flow rate per volume W/m
h surface coefficient of heat transfer .
W/(m K)
l length m
m
mass kg
q mass air flow rate kg/s
a
p pressure Pa
q density of heat flow rate W/m
t
time s
v velocity m/s
x,y,z co-ordinates m
thermal conductance of air layer
Λ ⋅
W/(m K)
heat flow rate W
Φ
J total radiosity W/m
solar absorptance -
α
total hemispherical emissivity -
ε
Celsius temperature °C
θ
thermal conductivity
λ W/(m⋅K)
dynamic viscosity
µ kg/(m⋅s)
solar reflectance -
ρ
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
t
time sr short wave radiation
v ventilation va ventilation through air cavity

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 document 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 EN ISO 13370;
— the effect of thermal bridges are generally neglected, but if they are considered their heat storage contribution 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
∂ θ
a,i
(Aq ) + Φ + Φ + Φ + Φ = c m (1)
c,i j v i,c sa va a a,i
∑
∂ t
j =1
where
N is the number of internal surfaces delimiting the internal air;
A is the area of each building element;
is the density of the heat flow rate by convection (see 4.5.2.2);
q
c,i
Φ is the heat flow rate by ventilation (see 4.5.6);
v
Φ is the convective part of heat flow rate due to internal sources (see 4.5.5);
i,c
Φ is the solar to air heat flow rate (see 4.5.3.4);
sa
Φ is the heat flow rate due to the air entering the room through air layers within the elements bounding the
va
room;
c is the specific heat capacity of air;
a
m is the mass of the internal air;
a,i
θ is the temperature of the internal air;
a,i
t is the time
NOTE Because of the very small value of the term (c m ) the right-hand side of Equation (1) can be assumed to be zero.
a a,i
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
N
q + q + q + q +Φ /( A ) = 0 (2)
∑
lr, j sr,j c, j cd, j i,r j
j =1
where
q is the density of heat flow rate due to long-wave radiation exchanged with other internal surfaces (see
lr
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
is the density of heat flow rate by conduction (see 4.5.1);
q
cd
Φ 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
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):
q + q + q = 0 (3)
cd, j −1 cd, j +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
The temperature at surface j of an air layer (Figure 2) is obtained by solving Equation (4):
q + q + q + q = 0 (4)
c, j lr, j 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):
q + q + q + q = 0 (5)
lr, j sr, j 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.
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
EN 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 EN ISO 13370. Boundary conditions are specified
in 4.4.3.
4.2.6.4 Floor over crawl space
The floor, the crawl space and the soil are treated as a suspended floor according to EN 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:

Π Π Π Π
   θ   Γ 
1,1 1,2 1,N 1,N +1 is,1 1
   
 
Π Π Π Π
  θ Γ
   
2,1 2,2 2,N 2,N +1 is,2 2
⋅ = (6)
 
   
Π Π Π Π
θ Γ
N,1 N,2 N,N N,N +1 is,N N
     
   
 
Π Π Π Π
θ Γ
N +1,1 N +1,2 N +1,N N +1,N+,1 a N +1
     
where
Ν is the number of elements bounding the room corresponding to the internal surfaces delimiting the
internal air;
Π are the coefficients of the unknown temperatures (θ) (from 1 to N relating to the internal surfaces, N + 1
relating to the internal air);
Γ are the coefficients of the known terms (from 1 to N relating to the internal surfaces, N +1 relating to the
internal air);
θ are the unknown temperatures (from 1 to N relating to the internal surfaces, N +1 relating to the internal
air).
The "Π " and "Γ" 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 document 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:

ei
θ θ
a,e a,i
1 2
Key
1 Similar
2 Internal
Figure 4 - Partition vertical wall

θ = θ
a,e a,i
q = q
sr,e sr,i
q = q (7)
lr,e lr,i
h = h
c,e c,i
where
θ is the air temperature of the adjacent room;
a,e
θ
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 wall;
sr,e
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 wall
sr,i
(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 from
lr,i
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:
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
θ = θ
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
θ is the air temperature of the adjacent room;
a,e
θ 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 floor
sr,if
(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 the
lr,ef
other external surfaces;
q is the density of the heat flow rate by long-wave radiation by the internal surface of the floor with the
lr,if
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 the ceiling to
lr,ec
the other external surfaces;
q is the density of the heat flow rate by long-wave radiation from the internal surface of the ceiling to the
lr,ic
other internal surfaces (see 4.5.4.2);
h is the convective heat transfer coefficient at the external surface of the ceiling;
c,ec
h is the convective heat transfer coefficient at the internal surface of the floor (see Table 1);
c,if
h is the convective heat transfer coefficient at the external surface of the floor;
c,ef
h is the convective heat transfer coefficient at the internal surface of the ceiling (see Table 1).
c,ic
4.4.3 Adjacent room with defined value of the air temperature
For each component of the envelope (see Figure 6) the following boundary conditions are considered:
e i
θ ec θ ef
a,e a,e
θ θ
a,e a,i
θ ic θ if
a,i a,i
Key
1 Wall
2 Ceiling
3 Floor
Figure 6 - Wall, ceiling and floor adjacent to room with defined internal conditions
θ = θ
a,e a,d
q = 0
sr,e
h = h
c,e c,i
h = h     (9)
c,ec c,if
h = h
c,ef c,ic
where
θ is the air temperature of the adjacent room;
a,d
q is the density of heat flow rate due to absorbed short-wave radiation at the external surface;
sr,e
h is the convective heat transfer coefficient at the external surface of the vertical wall;
c,e
h is the convective heat transfer coefficient at the internal surface of the vertical wall (see Table 1);
c,i
h is the convective heat transfer coefficient at the external surface of the ceiling;
c,ec
h is the convective heat transfer coefficient at the internal surface of the floor (see Table 1);
c,if
h is the convective heat transfer coefficient at the external surface of the floor;
c,ef
h is the convective heat transfer coefficient at the internal surface of the ceiling (see Table 1).
c,ic
4.4.4 Floor on ground
The heat transfer between the room and the external environment through the ground is calculated as the sum of a
steady state component and a monthly variable component as specified in EN ISO 13370. The monthly variable
component is treated as one-dimensional and perpendicular to the floor surface. The calculation procedure shall
combine this heat flow rate with the thermal storage of the floor construction together with a 0,5 m thick layer of soil
beneath it.
NOTE One acceptable way is to introduce a monthly varying boundary temperature at a depth of 0,5 m beneath the floor
construction. This boundary temperature is defined so that the heat flow rate from the room air at its mean monthly temperature
to the boundary layer equals the heat flow rate to and through the ground calculated according to EN ISO 13370.
4.4.5 Cellar or crawl space
A cellar is treated as an unheated basement according to EN ISO 13370. Heat transfers are calculated as in 4.4.4,
including 0,5 m of soil at each side of the cellar and below the cellar. A crawl space is treated as a suspended floor
according to EN ISO 13370. Boundary conditions are as specified in 4.4.3.
4.4.6 Ceiling below attic
According to the assumptions of 4.2.6.1, the boundary conditions are represented by:
θ is the external air temperature;
a,e
q is defined by Equation (17) in 4.5.3.1;
sr,e
q is defined by Equation (24) in 4.5.4.1.
lr,e
4.5 Terms in the thermal balance equations
4.5.1 Heat conduction through components
For elements with constant thermal conductivity and specific heat capacity, the density of heat flow by conduction is
governed by the following equations:
∂θ
q = −λ( ) (10)
n
∂n
2 2 2
∂ θ ∂ θ ∂ θ ∂θ
λ( + + ) + g = cρ (11)
2 2 2
∂ t
∂ x ∂ y ∂ z
where
θ is the temperature of the component (in direction of the heat flow) at the time t;
q is the density of heat flow rate in direction n;
λ is the thermal conductivity of the medium;
c is the specific heat capacity of the medium;
ρ is the density of the medium;
g is the heat source term (heat flow rate per volume);
x,y,z are co-ordinates.
These equations may be solved by any appropriate procedure which provides results in accordance with the
validation procedure given in Clause 7.
NOTE A suitable procedure is described in Annex A.
4.5.2 Convective heat transfer
4.5.2.1 General
Convective heat transfer occurs at the boundary surfaces of each building element and through air layers.
4.5.2.2 Convective heat flow rate at the surfaces of an element

The density of convective heat flow rate at the internal and external surface of element is given by:
q = h (θ −θ ) (12)
c s a
c
where
h is the convective heat transfer coefficient of the surface;
c
θ is the surface temperature;
s
θ is the air temperature.
a
At the external surface the values of the convective heat transfer coefficient h , is given by:
c,e
h = 4 + 4v (13)
c,e
where
v is the wind velocity near the surface.
The wind velocity near the surface, v, depends on the climatic data of the locality and on the envelope
characteristics. Unless otherwise specified, the value of 1 m/s shall be used. The values of the convective heat
transfer coefficient at the internal surface, h , are given in Table 1.
c,i
Table 1 - Convective heat transfer coefficient at the internal surface
Vertical wall Heat flow upwards Heat flow downwards
2 2 2
W/(m ⋅K) W/(m ⋅K) W/(m ⋅K)
2,5 5,0 0,7
NOTE The values in Table 1 were determined using the equations given in EN ISO 6946 for
the following conditions:
- temperature difference (θ - θ ) < 10 K;
s,i a,i
- surface hydraulic diameter = 4,5 m (4 × area/perimeter).
The air temperature required in Equation (12) is:
— for internal surfaces: the room air temperature;
— for external surfaces: the conditions given in Table 2.
Table 2 - Air temperature
Buildings element Air temperature conditions
External wall, roof External air temperature
Partition wall, ceiling and roof to similar room Internal air temperature
Partition wall, ceiling and roof to adjacent Air temperature of the adjacent room
room with different conditions
Floor on ground Mean monthly external air temperature
Floor on cellar Temperature of the cellar

4.5.2.3 Convective heat transfer through unventilated air layers
The density of convective heat flow rate through an unventilated air layer, q , is given by:
c
q = Λ ∆θ (14)
c a
where
∆θ is the temperature difference between the surfaces delimiting the layer;
Λ is the thermal conductance of the air layer.
a
The thermal conductance of an unventilated air layer is calculated according to:
— EN ISO 6946 between opaque surfaces;
— EN ISO 10077-1 between transparent surfaces.
NOTE For transparent surfaces, the thermal conductance of an unventilated air layer can be calculated assuming the
following reference conditions:
— air density: 1,139 kg/m
-5
— dynamic viscosity: 1,861 × 10 kg/(m⋅s)
— thermal conductivity: 0,0264 W/(m·K)
— specific heat capacity: 1008 J/(kg·K)
— thermodynamic temperature: 300 K
— temperature difference: 5 K.
Table 3 gives some values of thermal conductance, Λ , for vertical and horizontal unventilated air layers between
a
transparent components. For other thicknesses, thermal conductances may be derived by interpolation.
Table 3 - Thermal convective conductance of unventilated air layers
Air layer thickness Vertical air layer Horizontal air layer
m Thermal Heat flow upwards Heat flow
conductance downwards
Λ
a
Λ
a
W/(m ·K)
W/(m ·K)
Thermal Thermal
conductance conductance
Λ Λ
a a
2 2
W/(m ·K) W/(m ·K)
0,01 2,65 2,06 2,06
0,05 1,16 1,71 0,41
0,10 1,29 1,50 0,21
0,20 1,42 1,48 0,10
4.5.2.4 Convective heat transfer through ventilated air layer
The convective heat flow rate through a ventilated air layer, Φ , depends on the air flow rate in the air layer. The
va
heat flow rates to be considered are:
a) the convective heat flow rate, Φ , due to air passing through the air layer and into the room, given by:
va
Φ = m c (θ −θ ) (15)
va a,v a l a,i
where
m is the mass air flow through the air layer;
a,v
θ is the temperature of the air leaving the layer;
l
b) the convective heat flow rate, Φ , between surfaces and air, given by:
c,j
Φ = h A (θ −θ )
c, j a c j eq
Φ = h A (θ −θ ) (16)
c, j +1 a c j +1 eq
where
A is the area of the surface in contact with the air layer;
c
h is the convective heat transfer coefficient for ventilated layers;
a
θ is the equivalent temperature of the air in the layer;
eq
j and j + 1 refer to the surfaces delimiting the air layer.
NOTE A procedure for determining the parameters in Equations (15) and (16) is given in Annex B.
4.5.3 Short-wave radiation heat transfers
4.5.3.1 Short-wave radiation heat transfer at the external surface of opaque element
The density of short-wave radiation heat flow rate at the external surface of an opaque element is given by:
q = α (f I + I ) (17)
sr,e sr s D d
where
αsr is the solar absorptance;
f is the sunlit factor;
s
I is the direct component of the solar radiation reaching the surface;

D
I is the diffuse component of the solar radiation reaching the surface.
d
The values of solar absorptance of external opaque surfaces, α , depend on the characteristics of the external
sr
surface of the element. Table 4 gives values of the solar absorptance as a function of the colour of the external
surface that may be used when no specific values are available.
Table 4 - Solar absorptance of external opaque surfaces

Light Intermediate Dark colour
colour colour
0,3 0,6 0,9
α
...