SIST EN ISO 12241:2008

Thermal insulation for building equipment and industrial installations - Calculation rules (ISO 12241:2008)

ISO 12241:2008 gives rules for the calculation of heat-transfer-related properties of building equipment and industrial installations, predominantly under steady-state conditions. ISO 12241:2008 also gives a simplified approach for the treatment of thermal bridges.

Wärmedämmung an haus- und betriebstechnischen Anlagen - Berechnungsregeln (ISO 12241:2008)

Diese Internationale Norm enthält Regeln zur Berechnung der mit dem Wärmetransport im Zusammenhang stehenden Eigenschaften von haus  und betriebstechnischen Anlagen, überwiegend unter stationären Bedingungen. Diese Internationale Norm liefert auch eine vereinfachte Herangehensweise für die Behandlung von Wärmebrücken.

Isolation thermique des équipements du bâtiment et des installations industrielles - Méthodes de calcul (ISO 12241:2008)

L'ISO 12241:2008 donne des méthodes pour calculer les propriétés relatives au transfert de chaleur des équipements de bâtiments et des installations industrielles, principalement en régime stationnaire. Elle fournit également une approche simplifiée de traitement des ponts thermiques.

Toplotna izolacija za opremo stavb in industrijske inštalacije - Pravila za računanje (ISO 12241:2008)

General Information

• Status: Withdrawn
• Publication Date: 05-Aug-2008
• Withdrawal Date: 15-Aug-2022
• ICS: 91.120.10 - Thermal insulation of buildings
• Technical Committee: TOP - Thermal insulation
• Current Stage: 9900 - Withdrawal (Adopted Project)
• Start Date: 01-Aug-2022
• Due Date: 24-Aug-2022
• Completion Date: 16-Aug-2022
• Directive: 305/2011 - Regulation (eu) No 305/2011 of the European Parliament and of the Council of 9 march 2011 laying down harmonised conditions for the marketing of construction products and repealing council directive 89/106/eec
• Directive: 89/106/EEC - Construction products
• Directive: TRRTP126 - Tehnična smernica TSG-01-004:2010 - Učinkovita raba energije v stavbah
• Ref Project: EN ISO 12241:2008 - Thermal insulation for building equipment and industrial installations - Calculation rules (ISO 12241:2008)

Relations

• Replaces: SIST EN ISO 12241:1999 - Thermal insulation for building equipment and industrial installations - Calculation rules (ISO 12241:1998)
• Effective Date: 01-Sep-2008
• Replaced By: SIST EN ISO 12241:2022 - Thermal insulation for building equipment and industrial installations - Calculation rules (ISO 12241:2022)
• Effective Date: 01-Sep-2022

Standards Content (Sample)

SLOVENSKI STANDARD
01-september-2008
1DGRPHãþD
SIST EN ISO 12241:1999
7RSORWQDL]RODFLMD]DRSUHPRVWDYELQLQGXVWULMVNHLQãWDODFLMH3UDYLOD]DUDþXQDQMH
,62
Thermal insulation for building equipment and industrial installations - Calculation rules
(ISO 12241:2008)
Wärmedämmung an haus- und betriebstechnischen Anlagen - Berechnungsregeln (ISO
12241:2008)
Isolation thermique des équipements du bâtiment et des installations industrielles -
Méthodes de calcul (ISO 12241:2008)
Ta slovenski standard je istoveten z: EN ISO 12241:2008
ICS:
91.120.10 Toplotna izolacija stavb Thermal insulation of
buildings
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 12241
NORME EUROPÉENNE
EUROPÄISCHE NORM
June 2008
ICS 91.140.01; 91.120.10 Supersedes EN ISO 12241:1998
English Version
Thermal insulation for building equipment and industrial
installations - Calculation rules (ISO 12241:2008)
Isolation thermique des équipements de bâtiments et des Wärmedämmung an haus- und betriebstechnischen
installations industrielles - Méthodes de calcul (ISO Anlagen - Berechnungsregeln (ISO 12241:2008)
12241:2008)
This European Standard was approved by CEN on 1 May 2008.
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 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 Management Centre has the same status as the
official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, 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 and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2008 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 12241:2008: E
worldwide for CEN national Members.

Contents Page
Foreword.3

Foreword
This document (EN ISO 12241:2008) 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 December 2008, and conflicting national standards shall be withdrawn
at the latest by December 2008.
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 12241:1998.
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, 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 and the United Kingdom.
Endorsement notice
The text of ISO 12241:2008 has been approved by CEN as a EN ISO 12241:2008 without any modification.

INTERNATIONAL ISO
STANDARD 12241
Second edition
2008-06-15
Thermal insulation for building
equipment and industrial installations —
Calculation rules
Isolation thermique des équipements de bâtiments et des installations
industrielles — Méthodes de calcul

Reference number
ISO 12241:2008(E)
©
ISO 2008
ISO 12241:2008(E)
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ii © ISO 2008 – All rights reserved

ISO 12241:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols. 1
3.1 Terms and definitions. 1
3.2 Definition of symbols . 2
3.3 Subscripts . 3
4 Calculation methods for heat transfer. 3
4.1 Fundamental equations for heat transfer. 3
4.2 Surface temperature. 14
4.3 Prevention of surface condensation. 17
4.4 Determination of total heat flow rate for plane walls, pipes and spheres . 20
5 Calculation of the temperature change in pipes, vessels and containers. 21
5.1 Longitudinal temperature change in a pipe . 21
5.2 Temperature change and cooling times in pipes, vessels and containers . 22
6 Calculation of cooling and freezing times of stationary liquids . 22
6.1 Calculation of the cooling time for a given thickness of insulation to prevent the freezing
of water in a pipe. 22
6.2 Calculation of the freezing time of water in a pipe. 24
7 Determination of the influence of thermal bridges . 25
7.1 General. 25
7.2 Calculation of correction terms for plane surfaces . 26
7.3 Calculation of correction terms for pipes . 26
8 Underground pipelines. 27
8.1 General. 27
8.2 Calculation of heat loss (single line) without channels. 27
8.3 Other cases . 29
Annex A (normative) Thermal bridges in pipe insulation . 30
Annex B (informative) Projecting thermal bridges of roughly constant cross-section . 33
Annex C (informative) Examples . 38
Bibliography . 45

ISO 12241:2008(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 12241 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 12241:1998), which has been technically
revised, including methods to determine the correction terms for thermal transmittance and linear thermal
transmittance for pipes that are added to the calculated thermal transmittance to obtain the total thermal
transmittance to calculate the total heat losses for an industrial installation.
iv © ISO 2008 – All rights reserved

ISO 12241:2008(E)
Introduction
Methods relating to conduction are direct mathematical derivations from Fourier’s law of heat conduction, so
international consensus is purely a matter of mathematical verification. No significant difference in the
equations used in the member countries exists. For convection and radiation, however, there are no methods
in practical use that are mathematically traceable to Newton’s law of cooling or the Stefan-Boltzman law of
thermal radiation, without some empirical element. For convection in particular, many different equations have
been developed, based on laboratory data. Different equations have become popular in different countries,
and no exact means are available to select between these equations.
Within the limitations given, these methods can be applied to most types of industrial, thermal-insulation, heat-
transfer problems.
These methods do not take into account the permeation of air or the transmittance of thermal radiation
through transparent media.
The equations in these methods require for their solution that some system variables be known, given,
assumed or measured. In all cases, the accuracy of the results depends on the accuracy of the input variables.
This International Standard contains no guidelines for accurate measurement of any of the variables. However,
it does contain guides that have proven satisfactory for estimating some of the variables for many industrial
thermal systems.
lt should be noted that the steady-state calculations are dependent on boundary conditions. Often a solution at
one set of boundary conditions is not sufficient to characterize a thermal system that operates in a changing
thermal environment (process equipment operating year-round, outdoors, for example). In such cases, it is
necessary to use local weather data based on yearly averages or yearly extremes of the weather variables
(depending on the nature of the particular calculation) for the calculations in this International Standard.
In particular, the user should not infer from the methods of this International Standard that either insulation
quality or avoidance of dew formation can be reliably assured based on minimal, simple measurements and
application of the basic calculation methods given here. For most industrial heat flow surfaces, there is no
isothermal state (no one, homogeneous temperature across the surface), but rather a varying temperature
profile. This condition suggests the requirement for numerous calculations to properly model thermal
characteristics of any one surface. Furthermore, the heat flow through a surface at any point is a function of
several variables that are not directly related to insulation quality. Among others, these variables include
ambient temperature, movement of the air, roughness and emissivity of the heat flow surface, and the
radiation exchange with the surroundings (which often vary widely). For calculation of dew formation,
variability of the local humidity is an important factor.
Except inside buildings, the average temperature of the radiant background seldom corresponds to the air
temperature, and measurement of background temperatures, emissivities and exposure areas is beyond the
scope of this International Standard. For these reasons, neither the surface temperature nor the temperature
difference between the surface and the air can be used as a reliable indicator of insulation performance or
avoidance of dew formation.
Clauses 4 and 5 of this International Standard give the methods used for industrial thermal insulation
calculations not covered by more specific standards. In applications where it is not necessary to assure
precise values of heat energy conservation or (insulated) surface temperature, or where critical temperatures
for dew formation are either not approached or not a factor, these methods can be used to calculate heat flow
rates.
Clauses 6 and 7 of this International Standard are adaptations of the general equation for specific applications
of calculating heat flow temperature drop and freezing times in pipes and other vessels.
Annexes B and C of this International Standard are for information only.
INTERNATIONAL STANDARD ISO 12241:2008(E)

Thermal insulation for building equipment and industrial
installations — Calculation rules
1 Scope
This International Standard gives rules for the calculation of heat-transfer-related properties of building
equipment and industrial installations, predominantly under steady-state conditions. This International
Standard also gives a simplified approach for the treatment of thermal bridges.
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 7345, Thermal insulation — Physical quantities and definitions
ISO 9346, Hygrothermal performance of buildings and building materials — Physical quantities for mass
transfer — Vocabulary
ISO 10211, Thermal bridges in building construction — Heat flows and surface temperatures — Detailed
calculations
ISO 13787, Thermal insulation products for building equipment and industrial installations — Determination of
declared thermal conductivity
ISO 23993, Thermal insulation for building equipment and industrial installations — Determination of design
thermal conductivity
3 Terms, definitions and symbols
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 7345, ISO 9346, ISO 13787 and
ISO 23993 apply.
ISO 12241:2008(E)
3.2 Definition of symbols
Symbol Definition Unit
A
area m
a
temperature factor
K
r
C′ thickness parameter (see 4.2.2) m
2 4
C
radiation coefficient W/(m ⋅K )
r
c
specific heat capacity at constant pressure
kJ/(kg⋅K)
p
D diameter m, mm
d thickness m, mm
H height m
h surface coefficient of heat transfer
W/(m ⋅K)
l length m
m mass kg

m mass flow rate kg/h
P perimeter m
q density of heat flow rate W/m
q
linear density of heat flow rate for ducts W/m
d
q
linear density of heat flow rate W/m
l
R thermal resistance
m ⋅K/W
R
linear thermal resistance of ducts
m⋅K/W
d
R
linear thermal resistance m⋅K/W
l
R
linear thermal surface resistance m⋅K/W
le
R
surface resistance of heat transfer
m ⋅K/W
s
R
thermal resistance for hollow sphere K/W
sph
t
freezing time h
fr
t
cooling time h
v
t
time until freezing starts h
wp
T thermodynamic temperature K
U thermal transmittance W/(m ⋅K)
U
linear thermal transmittance W/(m⋅K)
l
U
thermal transmittance for hollow sphere W/K
sph
U
thermal transmittance of thermal bridge
W/(m ⋅K)
B
additional term corresponding to installation-related and/or irregular
∆U
W/(m ⋅K)
B
insulation-related thermal bridges
U
total thermal transmittance for plane wall W/(m ⋅K)
T
U
total linear thermal transmittance W/(m⋅K)
T,l
U
total thermal transmittance for hollow sphere W/K
T,sph
v air velocity m/s
2 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
Symbol Definition Unit
z, y
correction terms for irregular insulation-related thermal bridges —
z*, y* correction terms for installation-related thermal bridges —

−1
α coefficient of longitudinal temperature drop m

−1
α′ coefficient of cooling time
h
∆h
specific enthalpy; latent heat of freezing kJ/kg
fr
ε emissivity —
Φ heat flow rate W
design thermal conductivity
λ W/(m⋅K)
λ
declared thermal conductivity W/(m⋅K)
d
θ Celsius temperature °C
temperature difference K
∆θ
ρ density
kg/m
relative humidity %
ϕ
2 4
Stefan-Boltzmann constant (see Reference [8])
σ W/(m ⋅K )
3.3 Subscripts
a ambient lab laboratory
av average l linear
B thermal bridge p pipe
c cooling r radiation
cv convection ref reference
d design, duct, dew point s surface
E soil sph spherical
e exterior, external se surface, exterior
ef effective si surface, interior
fm final temperature of the medium T total
fr freezing V vertical
H horizontal v vessel
i interior, internal W wall
im initial temperature of the medium w water
4 Calculation methods for heat transfer
4.1 Fundamental equations for heat transfer
4.1.1 General
The equations given in Clause 4 apply only to the case of heat transfer in a steady-state, i.e. to the case
where temperatures remain constant in time at any point of the medium considered. Generally, the design
thermal conductivity is temperature-dependent; see Figure 1, dashed line, which is derived by iterative
calculations. However, in this International Standard, the design value for the mean temperature for each layer
shall be used.
ISO 12241:2008(E)
4.1.2 Thermal conduction
Thermal conduction normally describes molecular heat transfer in solids, liquids and gases under the effect of
a temperature gradient.
It is assumed in the calculation that a temperature gradient exists in one direction only and that the
temperature is constant in planes perpendicular to it.
The density of heat flow rate, q, for a plane wall in the x-direction is given by Equation (1):
dθ
q = − λ (1)
d x
For a single layer, Equations (2) and (3) hold:
λ
q = (θ − θ ) (2)
si se
d
or
θθ−
⎛⎞
si se
q = (3)
⎜⎟
R
⎝⎠
where
λ is the design thermal conductivity of the insulation product or system;
d is the thickness of the plane wall;
θ is the temperature of the internal surface;
si
θ is the temperature of the external surface;
se
R is the thermal resistance of the wall.

NOTE The straight line shows a negligible temperature dependence on λ and the dashed curve a strong dependence.
Figure 1 — Temperature distribution in a single-layer wall
For multi-layer insulation (see Figure 2), q is calculated according to Equation (4):
θ −θ
si se
q = (4)
′
R
4 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
where R′ is the thermal resistance of the multi-layer wall, as given in Equation (5):
n
d
j
R′ = (5)
∑
λ
j
j=1
NOTE The prime denotes a multi-layer quantity.

Figure 2 — Temperature distribution in a multi-layer wall
The linear density of heat flow rate, q , of a single-layer hollow cylinder (see Figure 3) is given in Equation (6):
l
θ −θ
si se
q = (6)
l
R
l
where R is the linear thermal resistance of a single-layer hollow cylinder, as given in Equation (7):
l
D
e
ln
D
i
R = (7)
l
2πλ
Figure 3 — Temperature distribution in a single-layer hollow cylinder
ISO 12241:2008(E)
For multi-layer hollow cylinder (see Figure 4), the linear density of heat flow rate, q , is given in Equation (8):
l
θθ−
se
si
q = (8)
l
R′
l
where R′ is given by Equation (9)
l
n
⎛⎞
D
e j
R′ = ⎜⎟ln (9)
l ∑
⎜⎟
2π λ D
jji
j=1⎝⎠
where
D = D
0 i
D = D
n e
Figure 4 — Temperature distribution in a multi-layer hollow cylinder
The heat flow rate, Φ , of a single-layer hollow sphere (see Figure 5) is as given in Equation (10):
sph
θ − θ
si se
Φ = (10)
sph
R
sph
where R is the thermal resistance of a single-layer hollow sphere, as given in Equation (11):
sph
⎛⎞
11 1
R=− (11)
⎜⎟
sph
2πλ DD
ie
⎝⎠
where
D is the outer diameter of the layer;
e
D is the inner diameter of the layer.
i
6 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
Figure 5 — Temperature distribution in a single-layer hollow sphere
The heat flow rate, Φ , of a multi-layer hollow sphere (see Figure 6) is as given in Equation (12):
sph
θ − θ
si se
Φ = (12)
sph
′
R
sph
where R′ is as given in Equation (13):
sph
n
⎛⎞
11 1 1
R′ ⎜⎟− (13)
sph ∑
⎜⎟
2π λ DD
jj−1 j
j=1⎝⎠
D = D
0 i
D = D
n e
Figure 6 — Temperature distribution in a multi-layer hollow sphere
ISO 12241:2008(E)
The linear density of heat flow rate, q , through the wall of a duct with rectangular cross-section (see Figure 7)
d
is as given in Equation (14):
θ −θ
si se
q = (14)
d
R
d
The linear thermal resistance, R , of the wall of such a duct can be approximately calculated as given in
d
Equation (15):
2d
R = (15)
d
λ()PP+
ei
where
d is the thickness of the insulating layer;
P is the inner perimeter of the duct;
i
P is the external perimeter of the duct, as given in Equation (16):
e
P = P + (8 × d) (16)
e i
Figure 7 — Temperature distribution in a wall of a duct with rectangular cross-section
at temperature-dependent thermal conductivity
4.1.3 Surface coefficient of heat transfer
In general, the surface coefficient of heat transfer, h, is given by Equation (17):
h = h + h (17)
r cv
where
h is the radiative part of the surface coefficient of heat transfer;
r
h is the convective part of the surface coefficient of heat transfer.
cv
NOTE 1 h is dependent on the temperature and the emissivity of the surface. Emissivity is defined as the ratio
r
between the radiation coefficient of the surface and the black body radiation constant (see ISO 9288).
NOTE 2 h is, in general, dependent on a variety of factors, such as air movement, temperature, the relative
cv
orientation of the surface, the material of the surface and other factors.
8 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
4.1.3.1 Radiative part of surface coefficient, h
r
h is given by Equation (18):
r
h = a C (18)
r r r
where
a is the temperature factor;
r
C is the radiation coefficient, as given by Equation (21).
r
The temperature factor, a , is given by Equation (19):
r
()TT−( )
a = (19)
r
TT−
and can be approximated up to a temperature difference of 200 K by Equation (20):
a ≈ 4 × (T ) (20)
r av
where T is the arithmetic mean of the surface temperature and the mean radiant temperature of the
av
surroundings.
The radiation coefficient, C , is given by Equation (21):
r
C = ε σ (21)
r
−8 2 4
where σ is the Stefan-Boltzmann constant [5,67 = 10 W/(m ·K )].
4.1.3.2 Convective part of surface coefficient, h
cv
4.1.3.2.1 General
For convection, it is necessary to make a distinction between the surface coefficient inside buildings and that
in open air. For pipes and containers, there is a difference as well between the internal surface coefficient, h ,
i
and the external surface coefficient, h .
se
NOTE In most cases, h can be neglected by assuming that the inner surface temperature equals the temperature of
i
the medium.
4.1.3.2.2 Inside buildings
In the interior of buildings, h can be calculated for plane vertical walls and vertical pipes for laminar, free
cv
3 3
convection (H ∆θ u 10 m ·K) by Equation (22):
∆θ
h = 1,32 × (22)
cv
H
where
∆θ = |θ − θ |;
se a
θ is the surface temperature of the wall;
se
θ is the temperature of the ambient air inside the building;
a
H is the height of the wall or diameter of a pipe.
ISO 12241:2008(E)
For vertical plane walls and vertical pipes, and as an approximation for large spheres inside buildings, the
3 3
convective part, h , for turbulent, free convection (H ∆θ > 10 m ·K) is given by Equation (23):
cv
h = 1,74 × ∆θ (23)
cv
Equations (22) and (23) may also be used for horizontal surfaces inside buildings.
NOTE This means that the same coefficient is used for all surfaces of a rectangular duct.
3 3
For horizontal pipes inside buildings, h is given by Equation (24) for laminar airflow (D ∆θ u 10 m ⋅K) and
cv e
3 3
by Equation (25) for turbulent airflow (D ∆θ > 10 m ⋅K):
e
∆θ
h = 1,25 × (24)
cv
D
e
h = 1,21 × ∆θ (25)
cv
4.1.3.2.3 Outside buildings
For vertical plane walls outside buildings and as an approximation for large spheres, the convective part, h ,
cv
of the surface coefficient is given by Equation (26) for laminar airflow (vH u 8 m /s) and by Equation (27) for
turbulent airflow (vH > 8 m /s):
v
h = 3,96 × (26)
cv
H
v
h = 5,76 × (27)
cv
H
Equations (26) and (27) may also be used for horizontal surfaces outside buildings.
For horizontal and vertical pipes that are outside buildings, Equation (28) applies for laminar airflow
−3 2 −3 2
(vD u 8,55 × 10 m /s) and Equation (29) for turbulent airflow (vD > 8,55 × 10 m /s):
e e
−3
8,1 × 10 v
h = +×3,14 (28)
cv
D D
ee
0,9
v
h = 8,9 × (29)
cv
0,1
D
e
where
D is the external insulation diameter, expressed in metres;
e
v is the air velocity, expressed in metres per second.
For calculation of the surface temperature, Equations (22) to (25) should be used for wall and pipe instead of
Equations (26) to (29) when the presence of wind is not established.
Table 1 the gives number of the appropriate equation to use to calculate h for different building elements.
cv
10 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
Table 1 — Selection of the equation to calculate h
cv
Walls Pipes
Location
vertical horizontal vertical horizontal
laminar turbulent laminar turbulent laminar turbulent laminar turbulent
inside
(22) (23) (22) (23) (22) (23) (24) (25)
buildings
outside
(26) (27) (26) (27) (28) (29) (28) (29)
buildings
All the equations for the convective part of the outer thermal surface coefficient inside buildings apply to the
heat transfer between surfaces and air at temperature differences ∆T < 100 K.
NOTE The change from an equation for laminar flow to that for turbulent flow can result in a step change in the
convection coefficient for an incremental change in v or H. This is a result of the approximations used for the equations.
4.1.3.3 Approximation for the calculation of h
se
The outer surface coefficient, h , can be calculated approximately using the coefficients in Table 2, together
se
with Equation (30) for horizontal pipes inside buildings or Equation (31) for vertical pipes and walls inside
buildings:
h = C + 0,05 × ∆θ (30)
se H
h = C + 0,09 × ∆θ (31)
se V
Equation (30) can be used for horizontal pipe in the range D = 0,25 m to 1,0 m and Equation (31), for vertical
e
pipe of all diameters.
Table 2 — Coefficients C and C for approximate calculation
H V
of total exterior thermal surface coefficient
−8
C × 10
r
C C
Surface
ε
H V
2 4
W/(m ⋅K )
Aluminium, bright rolled 2,5 2,7 0,05 0,28
Aluminium, oxidized 3,1 3,3 0,13 0,74
Galvanized sheet metal, blank 4,0 4,2 0,26 1,47
Galvanized sheet metal, dusty 5,3 5,5 0,44 2,49
Austenitic steel 3,2 3,4 0,15 0,85
Aluminium-zinc sheet 3,4 3,6 0,18 1,02
Non-metallic surfaces 8,5 8,7 0,94 5,33
For cylindrical ducts with a diameter less than 0,25 m, the convective part of the external surface coefficient
can be calculated to a good approximation by Equation (24). For larger diameters, i.e. D > 0,25 m, the
e
equation for plane walls, Equation (22), can be applied. The respective accuracy is 5 % for diameters
D > 0,4 m and 10 % for diameters 0,25 m < D < 0,40 m. Equation (22) is also used for ducts with a
e e
rectangular cross-section, having a width and height of similar magnitude.
4.1.3.4 External surface resistance
The reciprocal of the outer surface coefficient, h , is the external surface resistance.
se
ISO 12241:2008(E)
For plane walls, the surface resistance, R , is given by Equation (32):
se
R = (32)
se
h
se
For pipe insulation, the linear thermal surface resistance, R , is given by Equation (33):
le
R = (33)
le
hDπ
se e
For hollow spheres, the thermal surface resistance, R , is given by Equation (34):
sph,e
R = (34)
sph,e
hDπ
se e
4.1.4 Thermal transmittance
4.1.4.1 General
The thermal transmittance, U, for plane walls and the linear thermal transmittance, U, for pipes shall be
l
calculated in accordance with 4.1.4.2, using the design values of thermal conductivity according to ISO 23993.
After this calculation, the values of the thermal transmittances U and U shall be increased in accordance with
l
4.1.4.3 to take into account influences of either installation-related or irregular insulation-related thermal
bridges to determine the total thermal transmittance.
4.1.4.2 Thermal transmittance without thermal bridge corrections
The thermal transmittance, U, is defined by Equation (35):
q
U = (35)
θ −θ
ia
where
θ is the ambient external temperature;
a
θ is the internal air temperature for plane walls or the temperature of the medium inside for pipes,
i
ducts and vessels.
For plane walls, the thermal transmittance, U, can be calculated by Equation (36):
11 1
=+ R+ (36)
Uh h
ise
= R + R + R
si se
= R
T
For pipe insulation, the linear thermal transmittance, U , can be calculated by Equation (37):
l
11 1
=+ R+ (37)
l
UhππD h D
li i se e
= R + R + R
li l le
= R
T,l
12 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
For rectangular ducts, the linear thermal transmittance, U , can be calculated by Equation (38):
d
11 1
=+ R+ (38)
d
UhP hP
dii ee
= R
T,d
For hollow spheres, the thermal transmittance, U , is given by Equation (39):
sph
11 1
=+ R+ (39)
sph
U
hDππh D
sph
ii se e
= R
T,sph
In Equations (36) to (39), R, R and R are surface-to-surface thermal resistances.
l sph
The surface resistance of flowing media in pipes, R (in the cases predominantly considered here) is small
si
and can be neglected. For the external surface coefficient, h , Equations (30) and (31) apply. For ducts, it is
se
necessary to include the internal surface coefficient as well. It can be approximated using the appropriate
equations in Clause 4, taking into account the velocity of the medium in the duct.
The reciprocal of thermal transmittance, U, is the total thermal resistance, R , for plane walls, the total linear
T
thermal resistance, R , for pipe insulation and R for hollow sphere insulation.
T,l T,sph
4.1.4.3 Determination of total thermal transmittance
For plane walls, the total thermal transmittance, U , shall be determined by Equation (40):
T
UUU=+∆ (40)
TB
For pipes, the total linear thermal transmittance, U , shall be determined by Equation (41):
T,l
UU=+∆U (41)
T,l l B,l
For hollow spheres, the total thermal transmittance, U , shall be determined by Equation (42):
T,sph
UU=+∆U (42)
T,sph sph B,sph
where ∆U , ∆U and ∆U are calculated in accordance with Clause 7.

B B,l B,sph
4.1.5 Temperatures of the layer boundaries
The general equation for the density of the heat flow rate in a multi-layer wall is written in the general form
given by Equations (43) and (44) (see also Figure 8):
θ −θ
ia
q = (43)
R
T
R = R + R + R + . + R + R (44)
T si 1 2 n se
where
R …R are the thermal resistances of the individual layers and R and R are the thermal surface
1 n si se
resistances of the internal and external surfaces, respectively.
ISO 12241:2008(E)
Figure 8 — The temperature distribution for a multi-layer plane wall in relation to the thermal surface
resistance and the thermal resistances of layers
The ratio between the resistance of each layer or the surface resistance with respect to the total resistance
gives a measure of the temperature change across the particular layer or surface, expressed in K, as given in
Equations (45) to (48):
R
si
θ − θ = (θ − θ ) (45)
i si i a
R
T
R
θ − θ = (θ − θ ) (46)
si 1 i a
R
T
R
θ − θ = (θ − θ ) (47)
1 2 i a
R
T
R
se
θ − θ = (θ − θ ) (48)
se a i a
R
T
R is calculated for plane walls according to Equation (36), for cylindrical pipes according to Equation (37), for
T
rectangular ducts according to Equation (38) and for spherical insulation according to Equation (39).
4.2 Surface temperature
4.2.1 General
The surface temperature can be calculated by using Equation (45) or Equation (48).
For operational reasons, it is often stipulated in practice that a certain surface temperature or temperature of
the surface higher than that of the ambience should be maintained. However, the surface temperature is not
necessarily a measure of the quality of the thermal insulation. This depends on the design thermal
conductivity but also on operating conditions, which cannot be readily determined or warranted by the
manufacturer. These include operating temperatures of the medium, ambient temperature, movement of the
air, state of the insulation surface, effect of adjacent radiating bodies, meteorological conditions, etc.
With all these parameters, it is possible to estimate the required insulation thickness using Equation (48) or
Figure 9 (see Reference [9]). It is necessary to point out, however, that these assumptions correspond to the
subsequent operating conditions only in very rare cases.
14 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
Since an accurate registration of all relevant parameters is impossible, the calculation of the surface
temperature is inexact and the surface temperature cannot be warranted. The same restrictions apply to the
warranty of the temperature difference between surface and air, also called excess temperature. Although it
includes the effect of the ambient temperature on the surface temperature, it assumes that the heat transfer
by convection and radiation can be covered by a total heat transfer coefficient whose magnitude it is also
necessary to know (see 4.1.2). However, this condition is generally not fulfilled because the air temperature in
the immediate vicinity of the surface, which determines the convective heat transfer, usually differs from the
temperature of other surfaces with which the insulation surface is in radiative exchange.
4.2.2 Example calculation for the thickness parameter, C'
The thickness parameter, C', is calculated as given by Equations (49) and (50):
⎡⎤
⎛⎞θθ−
im a
′
C=−2λ⎢⎥ (49)
⎜⎟
⎜⎟
qh
⎢⎥
se
⎝⎠
⎣⎦
⎡⎤
⎛⎞θθ−
2λ
im a
′
C=−⎢⎥1 (50)
⎜⎟
⎜⎟
h θθ−
⎢⎥
se se a
⎝⎠
⎣⎦
Example using Equation (49): Set heat flux, q Example using Equation (50): Set surface
temperature for dew prevention
θ = 300 °C λ = 0,068 W/(m⋅K) θ = −20 °C λ = 0,039 W/(m⋅K)
im im
θ = 20 °C D = 0,324 m θ = 20 °C D = 0,108 m
a a
2 2 2
h = 5,7 W/(m ⋅K) q = 63 W/m h = 5,4 W/(m ⋅K) ϕ = 85 %
se se
In accordance with Figure 9: In accordance with Table 4:
|θ − θ | = |θ − θ | = 2,6 K
⎛⎞θθ− d a se a
im a
C′=−2λ
⎜⎟
⎜⎟
qh
⎛⎞
se θθ−
⎝⎠ 2λ
im a
′
C=−⎜⎟1
⎛⎞ ⎜⎟
300 − 20
1 h θθ−
se se a
⎝⎠
=×2 0,068 − = 0,58 m
⎜⎟
⎜⎟
63 5,7
⎛⎞−−20 20
⎝⎠
20× ,039
=−1= 0,208 m
⎜⎟
⎜⎟
5,4 2,6
⎝⎠
Result: d = 200 mm Result: d = 70 mm
ISO 12241:2008(E)
Key
D diameter, expressed in millimetres
d thickness, expressed in millimetres
C ' thickness parameter, expressed in metres
Figure 9 — Determination of insulating layer thickness for a pipe
at a given heat flux density or for a set surface temperature
16 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
The equations for the thickness parameter C′ are derived from Equations (35) and (37) by elementary
transformations. Equation (49) enables the calculation of the necessary insulation thickness for a given linear
density of heat flow rate, whereas Equation (50) enables the calculation of the required insulation thickness for
a given temperature difference between the pipe surface (with insulation) and the ambient temperature.
In both cases, h is assumed or calculated (see Clause C.7).
se
4.3 Prevention of surface condensation
Surface condensation depends not only on the parameters affecting the surface temperature but also on the
relative humidity of the surrounding air, which very often cannot be stated accurately by the customer. The
higher the relative humidity, the more the fluctuations of humidity or of surface temperatures increase the risk
of surface condensation. Unless other data are available, it is necessary to make assumptions as in Table 3 to
calculate the necessary insulation thickness to prevent dew formation on pipes. Using Equation (48), the
necessary insulation thickness to prevent dew formation can be obtained by iterative techniques. The allowed
temperature difference, expressed in K, between surface and the ambient air for different relative humidities at
the start of dew formation is given in Table 4.
ISO 12241:2008(E)
Table 3 — Insulation thickness required to prevent dew formation for refrigerant pipes
Relative air humidity 80 %
Ext.
pipe Temperature of the medium
Ø
°C
mm
+15 +10 +5 0 −5 −10 −15 −20 −25 −30 −35 −40 −45 −50 −55 −60 −65 −70 −75
17,2
21,3
26,9
33,7 15 25 30 40 50  65
42,4
48,3
60,3         80
76,1
82,5
88,9         90
101,6
114,3
127         100
139,7
177,8
193,7
219,1
244,5
298,5         120
323,9
355,6 15 25 30 40 50 65 80
406,4
419      90
508       100
558,8
609,6        120
711,2
812,2         140
914,4
1 016
∞
The following values are assumed:
⎯ thermal conductivity of the insulation at θ = 10 °C, λ = 0,04 W/(m·K);
⎯ thermal conductivity of the insulation at θ = −100 °C, λ = 0,033 W/(m·K);
⎯ ambient air temperature of 20 °C;
⎯ h = 6 W/(m ·K).
se
18 © ISO 2008 – All rights reserved

ISO 12241:2008(E)
of different diameters and different temperatures at different relative humidities of the ambient air
Relative air humidity 85 %
Ext.
Temperature of the medium pipe
Ø
°C
mm
+15 +10 +5 0 −
...