EN ISO 12241:1998

Thermal insulation for building equipment and industrial installations - Calculation rules (ISO 12241:1998)

Fundamental formulae and methods typically used in the practical calculation of steady-state, one dimensional industrial heat flow variables; also included are simplified calculation methods for some variables. These methods can be applied to most types of industrial thermal insulation heat transfer problems. Do not take account permeation of air or transmittance of thermal radiation through transparent media, either in respect to surface of calculation or to surrounding   surfaces. Mathematical formulae in these methods require for their solution    that some system variables be known, given assumed, or measured.

Wärmedämmung an haus- und betriebstechnischen Anlagen - Berechnungsregeln (ISO 12241:1998)

Diese Norm legt die Regeln zur Berechnung des Wärmetransports in Gebäuden und betriebstechnischen Anlagen unter den Bedingungen vorzugsweise des stationären, eindimensionalen Wärmestroms fest.

Isolation thermique des équipements du bâtiment et des installations industrielles - Méthodes de calcul (ISO 12241:1998)

Toplotna izolacija naprav v stavbah in industrijskih inštalacij – Računske metode (ISO 12241:1998)

General Information

• Status: Withdrawn
• Publication Date: 28-Feb-1998
• Withdrawal Date: 14-Jun-2008
• ICS: 91.120.10 - Thermal insulation of buildings
• ICS: 91.140.10 - Central heating systems
• Technical Committee: CEN/TC 89 - Thermal performance of buildings and building components
• Drafting Committee: CEN/TC 89/WG 3 - Calculation of thermal insulation of equipment in buildings
• Current Stage: 9960 - Withdrawal effective - Withdrawal
• Start Date: 15-Jun-2008
• Completion Date: 15-Jun-2008
• 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
• Ref Project: SIST EN ISO 12241:1999 - Thermal insulation for building equipment and industrial installations - Calculation rules (ISO 12241:1998)

Relations

• Replaced By: EN ISO 12241:2008 - Thermal insulation for building equipment and industrial installations - Calculation rules (ISO 12241:2008)
• Effective Date: 22-Dec-2008

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN ISO 12241:1999
01-september-1999
7RSORWQDL]RODFLMDQDSUDYYVWDYEDKLQLQGXVWULMVNLKLQãWDODFLM±5DþXQVNHPHWRGH
,62
Thermal insulation for building equipment and industrial installations - Calculation rules
(ISO 12241:1998)
Wärmedämmung an haus- und betriebstechnischen Anlagen - Berechnungsregeln (ISO
12241:1998)
Isolation thermique des équipements du bâtiment et des installations industrielles -
Méthodes de calcul (ISO 12241:1998)
Ta slovenski standard je istoveten z: EN ISO 12241:1998
ICS:
91.120.10 Toplotna izolacija stavb Thermal insulation
SIST EN ISO 12241:1999 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
INTERNATIONAL ISO
STANDARD 12241
First edition
1998-03-01
Thermal insulation for building equipment
and industrial installations — Calculation
rules
Isolation thermique des équipements du bâtiment et des installations
industrielles — Méthodes de calcul
A
Reference number
ISO 12241:1998(E)

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
ISO 12241:1998(E)
Contents
Page
1 Scope . 1
2 Normative references . 1
3 Definitions, symbols and abbreviations . 1
3.1 Physical quantities, symbols and units . 2
3.2 Subscripts. 3
4 Calculation methods for heat transfer . 3
4.1 Fundamental equations for heat transfer. 3
4.2 Surface temperature . 16
4.3 Prevention of surface condensation . 19
5 Calculation of the temperature change in pipes, vessels and containers. 19
5.1 Longitudinal temperature change in a pipe. 19
5.2 Temperature change and cooling times in pipes, vessels and containers . 20
6 Calculation of cooling and freezing times of stationary liquids . 21
6.1 Calculation of the cooling time for a given thickness of insulation to
prevent the freezing of water in a pipe . 21
6.2 Calculation of the freezing time of water in a pipe . 22
7 Thermal bridges . 22
8 Underground pipelines. 23
8.1 Calculation of heat loss (single line) . 23
9 Tables and Diagrams. 26
©  ISO 1998
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet [e-mail]
X.400 c=ch; a=400net; p=iso; o=isocs; s=central
Printed in Switzerland
ii

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO ISO 12241:1998(E)
Annex A:  (informative) Comments on thermal conductivity . 30
Annex B:  (informative) Examples . 32
B.1 Calculation of the necessary insulation thicknesses for a double layered wall of a
firebox . 32
B.2 Heat flow rate and surface temperature of an insulated pipe. 33
B.3 Temperature drop in a pipe. 34
B.4 Temperature drop in a container . 35
B.5 Cooling and freezing times in a pipe . 36
B.6 Underground pipeline. 37
B.7 Required insulation thickness to prevent surface condensation . 38
Annex C:  (informative) Bibliography . 39
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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO 12241:1998(E) ISO
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.
Draft International Standards adopted by the technical committees are circulated to the member bodies
for voting. Publication as an International Standard requires approval by at least 75 % of the member
bodies casting a vote.
International Standard ISO 12241 was prepared by Technical Committee ISO/TC 163, Thermal
insulation, Subcommittee SC 2, Calculation methods.
Annexes A to C of this International Standard are for information only.
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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO ISO 12241:1998(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 which 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 will depend 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 which have proven satisfactory for estimating some of the
variables for many industrial thermal systems.
It 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 which will
operate in a changing thermal environment (process equipment operating year-round, outdoors, for
example). In such cases local weather data based on yearly averages or yearly extremes of the weather
variables (depending on the nature of the particular calculation) should be used 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 need 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 which 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 (often including a great variety
of interest). 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.
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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO 12241:1998(E) ISO
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 precise values of heat energy
conservation or (insulated) surface temperature need not be assured, 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.
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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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INTERNATIONAL STANDARD  ISO ISO 12241:1998(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, assuming one-
dimensional heat flow only.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions of
this International Standard. At the time of publication, the editions indicated were valid. All standards are
subject to revision, and parties to agreements based on this International Standards are encouraged to
investigate the possibility of applying the most recent editions of the standards indicated below.
Members of IEC and ISO maintain registers of currently valid International Standards.
ISO 7345:1987, Thermal insulation — Physical quantities and definitions
ISO 9346:1987, Thermal insulation — Mass transfer — Physical quantities and definitions
NOTE —  For further publications, see annex C.
3 Definitions, symbols and abbreviations
For the purposes of this International Standard, the definitions given in ISO 7345 and ISO 9346 apply.
1

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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3.1 Physical quantities, symbols and units
Physical quantities Symbol Unit
——————————————————————————————————
heat flow rate Φ W
2
density of heat flow rate q W/m
linear density of heat flow rate q W/m
l
T
thermodynamic temperature K
Celsius temperature θ °C
Δθ
temperature difference K
thermal conductivity λ W/(m·K)
design thermal conductivity λ W/(m·K)
d
2
surface coefficient of heat transfer h W/(m ·K)
2
thermal resistance R m ·K/W
linear thermal resistance R m·K/W
l
linear thermal surface resistance R m·K/W
le
2
surface resistance of heat transfer R m ·K/W
s
R
thermal resistance for hollow sphere K/W
sph
thermal transmittance for hollow sphere U W/K
sph
2
thermal transmittance U W/(m ·K)
linear thermal transmittance U W/(m·K)
l
specific heat capacity at constant pressure c kJ/(kg·K)
p
d
thickness m
diameter D m
3
temperature factor a K
r
2 4
C
radiation coefficient W/(m ·K )
r
emissivity ε -
24
s
Stefan Boltzmann constant (see reference [9]) W/(m·K)
height H m
l
length m
thickness parameter (see 4.2) C′ m
perimeter P m
2
A
area m
3
volume V m
velocity v m/s
t
time s
mass m kg
mass flow rate&m kg/h
3
ρ
density kg/m
specific enthalpy; latent heat of freezing h kJ/kg
fr
relative humidity φ %
2

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO ISO 12241:1998(E)
3.2 Subscripts
ambient a
average av
cooling c
convection cv
design, duct, dewpoint d
exterior,external e
effective ef
final medium fm
freezing fr
interior, internal i
initial medium im
laboratory lab
linear l
pipe p
radiation r
reference ref
surface s
exterior surface se
interior surface si
spherical sph
soil E
total T
vessel v
water w
wall W
4 Calculation methods for heat transfer
4.1 Fundamental equations for heat transfer
The formulae given in this clause apply only to the case of heat transfer in the steady-state, i.e. to the
case where temperatures remain constant in time at any point of the medium considered.
Generally the thermal conductivity design value is temperature dependent (see figure 1, dashed line).
For further purposes of this International Standard, the design value for the mean temperature for each
layer shall be used.
NOTE —This may imply iterative calculation.
4.1.1 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:
dθ
2
q =−λ⋅ Wm (1)
x
d
3

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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For a single layer
λ
2
q=⋅θθ− Wm (2)
()
si se
d
or
θθ−
si se 2
q = Wm (2a)
R
where
.
l is the thermal conductivity of the material, in W/(m K);
d is the thickness of the plane wall, in m;
o
q
is the temperature of the internal surface, in C;
si
o
q is the temperature of the external surface, in C;
se
R is the thermal resistance of the wall in (m²{K)/W.
NOTE — The straight curve shows the negligible, the dashed one the strong temperature dependence of λ.
:
Figure 1 Temperature distribution in a single layer wall
4

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO ISO 12241:1998(E)
For multi-layer insulation
θθ−
2
si se
(3)
q =
Wm
R ′
where R´ is the thermal resistance of the multi-layer wall
n
d
j
2
.
R ′ = m KW (4)
∑
λ
j
j =1
NOTE —  The prime denotes a multi-layer quantity.
:
Figure 2 Temperature distribution in a multi-layer wall
5

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The linear density of heat flow rate q of a single layer hollow cylinder:
l
θθ
−
si se
q = Wm (5)
l
R
l

where R is the linear thermal resistance of a single layer hollow cylinder:
l
D
e
ln
D
i
R = mK⋅ W (6)
l
2⋅⋅π λ
D is the exterior diameter of the layer, in m;
e
D is the interior diameter of the layer, in m.
i
Figure 3: Temperature distribution in a single layer hollow cylinder
6

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO ISO 12241:1998(E)
For multi-layer hollow cylinder:
θθ−
si se
q = W/m (7)
l
R′
l
where
n
 D 
1 1 ej
′
R  
= ⋅ ln mK⋅ /W (8)
∑
l  
2⋅ π λ D
 
j ij
1
j=
with D ≡ D and D ≡ D
0 i n e
Figure 4: Temperature distribution in a multi-layer hollow cylinder
7

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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The heat flow rate of a single layer hollow sphere is
θθ−
si se
(9)
Φ = W
sph
R
sph
R
where is the thermal resistance of a single layer hollow sphere in K/W.
sph
 
1 11
R = − (10)
  KW
sph
2⋅π⋅λ DD
 
ie
D is the outer diameter of the layer, in m;
e
D is the inner diameter of the layer, in m.
i
Figure 5: Temperature distribution in a single layer hollow sphere
8

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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The heat flow rate of a multi layer hollow sphere is
θθ−
si se
Φ = W (11)
sph
′
R
sph
where
n
 
11 1
′ 1
 
R=⋅ − K W (12)
sph∑
2π  
λ DD
jj −1 j
j=1
D ≡ D D ≡ D
with  and
0 i n e .
Figure 6: Temperature distribution in a multi-layer hollow sphere
9

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO 12241:1998(E) ISO
The heat flow rate through the wall of a duct with rectangular cross section is
given by
θθ−
si se
q =
Wm (13)
d
R
d
The linear thermal resistance of the wall of such a duct can be approximately
calculated by
2⋅d
R= mK⋅ W (14)
d
λ⋅+PP
( )
ei
where
P
is the inner perimeter of the duct, in m;
i
P is the external perimeter of the duct, in m;
e
d  is the thickness of the insulating layer, in m.
P = P + (8{d) (14a)
e i
Figure 7: Temperature distribution in a wall of a duct with rectangular cross section
10

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO ISO 12241:1998(E)
4.1.2 Surface coefficient of heat transfer
In general the surface coefficient of heat transfer is given by:
2
hh=+h Wm⋅K (15)
rcv ()
where
h is the radiative part of the surface coefficient of heat transfer;
r
h is dependent on the temperature and the degree of emissivity of the
r
surface.
NOTE —  The emissivity is defined as the ratio between the radiation coefficient of the surface and the black body
radiation constant (see ISO 9288).
h is the convective part of the surface coefficient of heat transfer.
cv
h is in general dependent on a variety of factors such as air movement,
cv
temperature, the relative orientation of the surface, the material of the
surface and other factors.
4.1.2.1 Radiative part of surface coefficient h
r
h
is given by:
r
2
h a { C Wm ⋅K
=
r r r
() (16)

a is the temperature factor. It is given by:
r
44
TT−
() ( )
12 3
a=
  K (17)
r
TT−
12
and can be approximated up to a temperature difference of 200 K by
3
3
aT
 ≈⋅4  K (17a)
()
r av
where
T is 0,5 3 ( surface temperature + ambient or surface temperature of a radiating surface in
av
the neighbourhood), in K;
2 4
C is the radiation coefficient, in W/(m {K ).
r
C is given by
r
C = ε ⋅ σ
r
—8 4
σ = 5,67 ⋅ 10 W/(m²{K )
11

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4.1.2.2 Convective part of surface coefficient h
cv
For convection a distinction has to be made between surface coefficient inside buildings and in open air.
h
For pipes and containers there is a difference as well between internal surface coefficient and the
i
external surface coefficient h .
se
a) Inside buildings:
h
In the interior of buildings can be calculated for plane vertical walls and vertical pipes for laminar
cv
3 3
free convection (H {Dq ≤ 10 m {K) by
Δθ
2
⋅
4
h=⋅
1,32 W (m K) (18a)
cv
H
where
D =θθ −θ
, in K;
se a
q is the surface temperature of the wall, in °C;
se
q is the temperature of the ambient air inside the building, in °C;
a
H is height of the wall or diameter of a pipe, in m.
For vertical plane walls, vertical pipes and in approximation for large spheres inside buildings the
3 3
convective part h for turbulent free convection (H {Δθ > 10 m {K) is given by:
cv
2
3 .
h=1,74 WΔθ (mK) (18b)
cv
h
For horizontal pipes inside buildings is given by
cv
3 3
D {Dq ≤ {
- laminar airflow ( 10 m K)
e
Δθ
2
h =⋅1,25 4 W m⋅K (18c)
cv ( )
D
e
3 3
- turbulent airflow (D {Dq > 10 m {K)
e
3 2
⋅
h =⋅ Δθ
1,21 W (m K) (18d)
cv
b) Outside buildings:
For vertical plane walls outside of buildings and in approximation for large spheres the convective part
h of the surface coefficient is given by:
cv
2
v · H ≤
laminar airflow (  8 m /s):
v
2
⋅
h =⋅3W,96 (mK) (18e)
cv
H
12

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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2
- turbulent air flow (v{H > 8 m /s):
4
v
2
5
(18f)
h =⋅5W,76 (m⋅K)
cv
H
For horizontal and vertical pipes which are outside buildings the following equation applies:
-3 2
- laminar airflow (v ⋅ D ≤ 8,55 × 10 m /s) :
e
−3
8,1× 10 v
2
⋅
3,14
h = +⋅ W(m K) (18g)
cv
D D
ee
-3 2
- turbulent airflow (v · D > 8,55 × 10 m /s) :
e
0,9
v
2
h =⋅ {
8,9 W/(m K) (18h)
cv
0,1
D
e

where
D is the external insulation diameter, in m;
e
v
is the wind velocity, in m/s.
NOTE —  For calculation of surface temperature, formulas (18a) to (18d) should be used for wall and pipe instead
of formulas (18e) to (18h) when the presence of wind is not established.
Table 1 gives a selection of appropriate equations to be used for calculation of h
cv.
Table 1 —Selection of h
cv
Location Walls Pipes
vertical horizontal vertical horizontal
laminar turbulent laminar turbulent laminar turbulent laminar turbulent
inside  18a 18b  1) 1)  18a 18b  18c 18d
buildings
outside  18e  18f  18e  18f  18g  18h  18g  18h
buildings
1) Not important for most practical purposes
All the equations for the convective part of the outer thermal surface coefficient inside buildings apply for
the heat transfer between surfaces and air at temperature differences DT < 100 K.
4.1.2.3 Approximation for the calculation of h
se
For approximate calculations the following equations for the outer surface coefficient h can be used
se
inside buildings.
For horizontal pipes
h = C + 0,05 ⋅ Dq  W/(m²⋅K) (19)
se A
13

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
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ISO 12241:1998(E) ISO
For vertical pipes and walls
h C ⋅ Dq ⋅
= + 0,09   W/(m² K) (20)
se B
using the coefficients in table 2.
Equations 19 and 20 can be used for horizontal pipes in range of D = 0,25 m to 1,0 m and for vertical
e
pipes for all diameters.
Table 2 — Coefficients C and C for approximate calculation of total
A B
exterior thermal surface coefficient
—8
C C
Surface ε C 3 10
A B r
4
W/(m²⋅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
nonmetallic 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
D
coefficient can be calculated in good approximation by equation (18 c). For larger diameters i.e. >0,25
e
m the equation for plane walls (18 a) can be applied. The respective accuracy is 5 % for diameters
D >0,4m and 10% for diameters 0,25 e e
cross-section, having a width and height of similar magnitude.
4.1.2.4 External surface resistance
The reciprocal of the outer surface coefficient h is the external surface resistance.
se
2
For plane walls the surface resistance R , in m {K/W, is given by
se
2
1
⋅
R = mK W (21)
se
h
se
For pipe insulation the linear thermal surface resistance R is given by:
le
1
R = mK⋅ W (22)
le
hD⋅⋅π
se e
For hollow spheres the thermal surface resistance R is given by
sph e
1
R = KW  (23)
sph e
2
hD⋅⋅π
se e
14

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ISO ISO 12241:1998(E)
4.1.3 Thermal transmittance
Thermal transmittance U is given by
q
2
⋅
U = W(m K) (24)
θθ−
ia
For plane walls the thermal transmittance U can be calculated
11 1
2
.
=+R+ =RR+ +R mKW (25)
si
se
Uh h
ise
For pipe insulation the linear thermal transmittance U can be calculated
l
11 1
2
.
= +R+ =+RR+R mKW (26)
e
l li l l
Uh⋅⋅ππD hD⋅⋅
li i se e
For hollow spheres the thermal transmittance U is given by:
sph
11 1
= ++R KW (27)
sph
2 2
U
hD⋅⋅ππhD⋅⋅
sph
i se e
i
The surface resistance of flowing media in pipes R (in the cases predominantly considered here) is
si
h
small and can be neglected. For the external surface coefficient , equations (19) and (20) apply. For
se
ducts one also has to use the internal surface coefficient.
The reciprocal of thermal transmittance U is the total thermal resistance R for plane walls and
T

respectively the total linear thermal resistance R for pipe insulation and R for hollow spheres
Tl T sph
insulations.
The thermal transmittance of a duct with rectangular cross sections can be obtained by eq. (25) by
R R
replacing by (eq. 14).
d
4.1.4 Temperatures of the layer boundaries
The general equation for the heat loss in a multi-layer wall may be written in the following general form:
θθ−
ia 2
=
q Wm (28)
R
T
and
R = R + R + R + … + R + R  m²⋅K/W (29)
T si 1 2 n se
R R R R
where , . are the thermal resistances of the individual layers and , are the thermal
l 2 si se
surface resistances of the interior and exterior surface.
15

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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
©
ISO 12241:1998(E) ISO
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 will give a measure of the temperature change across the particular layer or surface in K.
R
si
θθ−= ⋅θθ− K (30)
( )
isi ia
R
T

R
1
θθ−= ⋅θ−θ K
( )
si 1
ia
R
T
R
2
θθ−= ⋅θ−θ K
( )
12
ia
R
T
.
.
.
R
se
θθ−= ⋅θ−θ K
( )
se a ia
R
T
R is defined for plane walls according to equation (25), for cylindrical pipes according to
T
eq. (26), and for spherical insulations by equation (27).
4.2 Surface temperature
The surface temperature can be calculated by using eq. (30)
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SIST EN ISO 12241:1999SIST EN ISO 12241:1999
©
ISO ISO 12241:1998(E)
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. The surface
temperature is no measure for the quality of the thermal insulation. This depends not only on the heat
transmission but also on operating conditions which cannot be readily determined or warranted by the
manufacturer. These include among other things: ambient temperature, movement of the air, state of
the insulation surface, effect of adjacent radiating bodies, meteorological conditions etc. Further, it will
be necessary to make assumptions for the operating parameters. With all these parameters it is
possible to estimate the required insulation thickness using equation (30) or diagram 1 (see
reference [10]). It must be pointed out, however, that these assumptions will correspond to the
subsequent operating conditions only in very rare cases.
Since an accurate registration of all relevant parameters will be 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 must also be known (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,
mostly departs essentially from the temperature of other surfaces with which the insulation surface is in
radiative exchange.
Diagram 1: Determination of insulating layer thickness for a pipe at a given
heat flux density or for a set surface temperature (see next page)
  
θθ−
1
im a
C ′=⋅2λ⋅ − (a)
 
qh
 
 se
 
  
θθ−
2 ⋅ λ
im a
C′ = ⋅   − 1 (b)
 
h θθ−
 
...