ISO 12241:2022

INTERNATIONAL ISO
STANDARD 12241
Third edition
2022-06
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 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
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 Symbols . 1
3.3 Subscripts . 3
4 Calculation rules and formulae of heat transfer . 4
4.1 Fundamental formulae for heat transfer . 4
4.1.1 General . 4
4.1.2 Thermal conduction . 4
4.1.3 Surface coefficient of heat transfer . 9
4.1.4 External surface resistance . 16
4.1.5 Thermal transmittance . 16
4.1.6 Heat flow rate . 18
4.1.7 Temperatures of the layer boundaries. 18
4.2 Determination of the influence of thermal bridges . 19
4.2.1 General . 19
4.2.2 Insulation system related thermal bridges . 19
4.2.3 Installation related thermal bridges . 19
4.3 Determination of total heat flow rate for plane walls, pipes and spheres .20
4.4 Surface temperature .20
4.5 Prevention of surface condensation . 21
5 Calculation of the temperature change in pipes, vessels, and containers .22
5.1 General .22
5.2 Longitudinal temperature change in a pipe . 23
5.3 Temperature change and cooling times in pipes, vessels, and containers .23
6 Calculation of cooling and freezing times of stationary liquids.24
6.1 Calculation of the cooling time to prevent the freezing of water in a pipe . 24
6.2 Calculation of the freezing time of water in a pipe . 25
7 Calculation of heat loss for underground pipelines .26
7.1 General . 26
7.2 Single line without channels . 26
7.2.1 Uninsulated pipe .26
7.2.2 Insulated pipe . 27
7.3 Other cases .28
Annex A (informative) Thermal bridges .29
Annex B (informative) Examples .43
Bibliography .52
iii
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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 163, Thermal performance and energy use
in the built environment, Subcommittee SC 2, Calculation methods, in collaboration with the European
Committee for Standardization (CEN) Technical Committee CEN/TC 89, Thermal performance of
buildings and building components, in accordance with the Agreement on technical cooperation between
ISO and CEN (Vienna Agreement).
This third edition cancels and replaces the second edition (ISO 12241:2008), which has been technically
revised.
The main changes are as follows:
— how to calculate the convective part of the external surface coefficient of heat transfer;
— how to introduce thermal bridges in the general heat loss calculation;
— provides detailed data along with the method for calculating fittings (thermal bridges), only
informative.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
Introduction
Methods relating to conduction are direct mathematical derivations from Fourier’s law of heat
conduction, so no significant difference in the formulae 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 formulae have been developed, based
on laboratory data. Different formulae have become popular in different countries, and no exact means
are available to select between these formulae.
Within the limitations given below, these methods can be applied to most types of industrial, thermal-
insulation, heat-transfer problems.
a) These methods do not take into account the permeation of air and the transmittance of thermal
radiation through transparent media.
b) The formulae 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 document 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.
c) When the steady-state calculations are used in a changing thermal environment (process
equipment operating year-round, outdoors, for example), 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 document.
d) In particular, the user should not infer from the methods of this document 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. 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.
e) Except inside buildings, the average temperature of the radiant background seldom corresponds
to the air temperature, and measurement of background temperatures, emissivity and exposure
areas is beyond the scope of this document. 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 document give the methods used for industrial thermal insulation calculations
not covered by more specific standards.
Clauses 6 and 7 of this document are adaptations of the general formula for specific applications of
calculating heat flow, temperature drop, and freezing times in pipes and other vessels. Thermal
insulation to heating/cooling systems such as a boiler and refrigerator are not dealt with by this
document.
Annexes A and B of this document are for information only.
v
INTERNATIONAL STANDARD ISO 12241:2022(E)
Thermal insulation for building equipment and industrial
installations — Calculation rules
1 Scope
This document gives rules for the calculation of heat-transfer-related properties of building equipment
and industrial installations, predominantly under steady-state conditions. This document also gives a
simplified approach for the calculation of thermal bridges.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 performance of buildings and building components — Physical quantities and definitions
ISO 9346, Hygrothermal performance of buildings and building materials — Physical quantities for mass
transfer — Vocabulary
ISO 13787, Thermal insulation products for building equipment and industrial installations —
Determination of declared thermal conductivity
ISO 13788, Hygrothermal performance of building components and building elements — Internal surface
temperature to avoid critical surface humidity and interstitial condensation — Calculation methods
ISO 23993, Thermal insulation products 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 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1.1
thermally separated end disc
end disc used so that the extremities and end caps are not in contact with the object
Note 1 to entry: This construction is used to avoid thermal bridges and the risk of damaging vapour retarders or
[15]
pipe tracing .
3.2 Symbols
Table 1 gives the definition and unit of symbols used in this document.
Table 1 — Definition and unit of symbol
Symbol Definition Unit
A area m
A solar absorption coefficient
s
a length of a rectangle m
a temperature factor K
r
b width of a rectangle m
2 4
C radiation coefficient W/(m ⋅K )
r
c specific heat capacity at constant pressure J/(kg⋅K)
p
D diameter m
d thickness m
d insulation layer thickness of the pipe m
R
F overall conversion factor for thermal conductivity
Gr Grashof number
H height m
h surface coefficient of heat transfer W/(m ⋅K)
J solar radiation W/m
s
K thermal bridge coefficient W/K
L length m
l characteristic length m
l insulation box inside length m
i
m mass kg
m mass flow rate kg/s
Nu Nusselt number
P perimeter m
p pressure Pa
p water vapour pressure Pa
a
Pr Prandtl number
q density of heat flow rate W/m or W/m
R thermal resistance m ⋅K/W or m⋅K/W or K/W
Re Reynolds number
S space inside the insulation box
T thermodynamic temperature K
t time s
W/(m ⋅K) or W/(m⋅K) or
U thermal transmittance
W/K
w velocity of the air or other fluid m/s
x Bolt length + 20 mm mm
-1
α coefficient of longitudinal temperature drop m
-1
α′ coefficient of cooling time s
Δh latent heat J/kg
ε emissivity
Φ heat flow rate W
λ thermal conductivity W/(m⋅K)
λ declared thermal conductivity W/(m⋅K)
d
λ design thermal conductivity W/(m⋅K)
D
Table 1 (continued)
Symbol Definition Unit
θ Celsius temperature °C
θ point of measurement of the temperature at the fin base °C
b
ρ density kg/m
φ relative humidity %
2 4
σ Stefan-Boltzmann constant (see Reference [8]) W/(m ⋅K )
v kinematic viscosity of air or other fluid m /s
Δ difference
ΔA equivalent area m
ΔL equivalent length m
extra conductivity due to regularly placed components in the
Δλ W/(m⋅K)
insulation system
3.3 Subscripts
Table 2 gives the definition of subscripts used in this document.
Table 2 — Definition of subscripts
A valve i interior (internal)
a ambient, in initial
anc anchor Ka insulation box
av average l linear
B thermal bridge lab laboratory
c cooling lam laminar flow
cv convection MRT mean radiant temperature
cr critical P pump
cs cross section p pipe
d duct r radiation
E soil ref reference
e exterior (external) s surface
ef effective sat saturated vapour
en entrance se exterior surface
ex exit si interior surface
f fluid sph spherical
fa frontal of the fin sq per square
fas fastener T total
FEM Finite Element Method tb insulation related thermal bridge
fi final tur turbulent flow
fin fin V vertical
fl flange v vessel
forced forced W wall
fr freezing w water
free free wp start freezing
H horizontal
4 Calculation rules and formulae of heat transfer
4.1 Fundamental formulae for heat transfer
4.1.1 General
The formulae given in Clause 4 apply only to the case of heat transfer in steady state, i.e. to the case
where temperatures remain constant in time at any point of the medium considered. The design
thermal conductivity is temperature-dependent; see Figure 1, dashed line. However, in this document,
the design value for the mean temperature for each layer shall be used.
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 Formula (1):
dθ
q=⋅λ (1)
D
dx
For a single layer, Formulae (2), (3) and (4) are given:
λ
D
q=⋅()θθ− (2)
si se
d
or
θθ−
 
si se
q= (3)
 
R
 
and
d
R= (4)
λ
D
where
λ is the design thermal conductivity of the insulation product or system, expressed in W/(m⋅K);
D
d is the thickness of the plane wall, expressed in m;
θ is the temperature of the internal surface, expressed in °C;
si
θ is the temperature of the external surface, expressed in °C;
se
R is the thermal resistance of the wall, expressed in m ⋅K/W.

a) Temperature distribution in a b) Thermal conductivity as function of the
single-layer temperature
NOTE The dashed curve in Figure 1a), represents the temperature variation in a wall, considering that
the thermal conductivity depends on the temperature, such as the dashed curve in Figure 1b). In case that the
thermal conductivity is considered as temperature-independent (the solid line in Figure 1b), the variation of the
temperature inside a wall is represented by the straight line in Figure 1a).
Figure 1 — Temperature distribution
For a multi-layer wall (see Figure 2), q is calculated according to Formula (3), where R is the thermal
resistance of the multi-layer wall, as given in Formula (5):
n
d
j
R= (5)
∑
λ
D
j=1 j
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
l
Formula (6):
θθ−
si se
q = (6)
l
R
l
where R is the linear thermal resistance of a single-layer hollow cylinder [m⋅K/W], as given in
l
Formula (7):
De
ln
D
i
R = (7)
l
2⋅⋅π λ
D
where
D is the outer diameter of the layer, expressed in m;
e
D is the inner diameter of the layer, expressed in m.
i
a) Temperature distribution in a sin- b) Front view of a hollow cylinder
gle layer-hollow cylinder
Figure 3 — Temperature distribution in a single-layer hollow cylinder
For a multi-layer hollow cylinder (see Figure 4), the linear density of heat flow rate, q , is given in
l
Formula (6), where R is given by Formula (8)
l
n
 
D
1 1 e,j
 
R = ln (8)
l ∑
2⋅π λ D 
D i,j
j=1
j
 
where
D = D
i,1 i
D = D
e,n e
Figure 4 — Temperature distribution in a multi-layer hollow cylinder
For curved surfaces with a diameter larger than 1 200 mm, it is recommended to use formulae for a
plane wall.
The heat flow rate of a sphere, Φ , of a single-layer hollow sphere (see Figure 5) is given by Formula (9):
sph
θθ−
si se
Φ = (9)
sph
R
sph
where R is the thermal resistance of a single-layer hollow sphere [K/W], as given in Formula (10):
sph
1  11 
R = − (10)
sph  
2⋅⋅π λ DD
 
D ie
Figure 5 — Temperature distribution in a single-layer hollow sphere
For a multi-layer hollow sphere (see Figure 6), the heat flow rate of a sphere, Φ , is given in Formula (9),
sph
where R is given by Formula (11):
sph
n
 
1 1 11
R = ⋅⋅ − (11)
 
sph ∑
 
2⋅π λ DD
D jj−1
 
j=1
j
where
D = D
0 i
D = D
n e
Figure 6 — Temperature distribution in a multi-layer hollow sphere
The linear density of heat flow rate, q , through the wall of a duct with rectangular cross-section (see
l
Figure 7) is given by Formula (12):
θθ−
si se
q = (12)
l
R
l
The linear thermal resistance of a duct, R [m⋅K/W], of the wall of such a duct can be approximately
l
calculated by Formula (13):
2⋅d
R = (13)
l
λ ⋅+()PP
D ei
where
d is the thickness of the insulating layer, expressed in m;
P is the inner perimeter of the duct, expressed in m;
i
P is the external perimeter of the duct, expressed in m, as given in Formula (14):
e
P =+⋅Pd8 (14)
()
ei
Figure 7 — Temperature distribution in a wall of a duct with rectangular cross-section
with temperature-dependent thermal conductivity
4.1.3 Surface coefficient of heat transfer
In general, the radiative and convective heat transfer at the surface area given by Formulae (15) and
(16) occurs at the surface:
q =⋅h ()θθ− (15)
rr 1 MRT
qh=⋅ θθ− (16)
()
cv cv 1a
where
q is the density of radiative heat flow, expressed in W/m ;
r
q is the density of convective heat flow, expressed in W/m ;
cv
h is the radiative part of the surface coefficient of heat transfer, expressed in W/(m ⋅K);
r
h is the convective part of the surface coefficient of heat transfer, expressed in W/(m ⋅K);
cv
θ is the surface temperature of surface 1, expressed in °C;
θ is the mean radiant temperature of the surrounding, expressed in °C;
MRT
θ is the ambient air temperature, expressed in °C.
a
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.
The combined surface heat transfer can be given by Formula (17):
qq=+qh=⋅ θθ− +⋅h θθ− (17)
() ()
rcvr 1MRT cv 1a
When the mean radiant temperature is almost equal to the ambient air temperature, the combined heat
transfer at the surface is given by Formula (18):
qh=⋅ θθ− +⋅hhθθ− =+hh⋅−θθ =⋅ θθ− (18)
() () () () ()
r1 acv1 ar cv 1a se se a
where
h is the external surface coefficient of heat transfer, expressed in W/(m ⋅K);
se
θ is the external surface temperature, expressed in °C.
se
In 4.1.4 and 4.1.5, the coefficient h = h + h is used to calculate the external surface resistance, R
se r cv se
and thermal transmittance, U, hence the approximation, mean radiant temperature equals the ambient
temperature, is considered.
NOTE 3 When a surface receives the solar radiation (e.g outdoor pipes, tank roofs), the total heat flow due to
radiant and convective heat transfer is calculated using the following Formula (19).
AJ⋅
 
ss
qq=+qh=⋅ θθ−− (19)
rcvses ea 
h
 
se
where
J is the solar radiation, expressed in (W/m );
s
A is the absorption coefficient of solar radiation.
s
4.1.3.1 Radiative part of surface coefficient, h
r
The radiative part of surface coefficient between two surfaces at different temperatures, h , is given by
r
Formula (20):
ha=⋅C (20)
r rr
where
a is the temperature factor, expressed in K ;
r
2 4
C is the radiation coefficient, expressed in W/(m ⋅K ), as given by Formula (23).
r
The temperature factor, a , is given by Formula (21):
r
4 4
TT−
1 2
a = (21)
r
TT−
where
T is the absolute temperature of surface 1, expressed in K;
T is the absolute temperature of surface 2, expressed in K.
Formula (21) can be approximated as follows.
TT+
 
12 3
a ≈⋅4 =⋅4 T (22)
r   av
 
where T is the arithmetic mean of the temperatures T and T , expressed in (K).
av 1 2
NOTE This approximation is only valid up to 200 K temperature difference between the component (surface
1) and the surroundings (surface 2).
When a component is surrounded by different surfaces at different temperatures, the temperature T
should be the mean radiant temperature of the surroundings.
The radiation coefficient, C , is given by Formula (23):
r
C =⋅εσ (23)
r
where
−8 2 4
σ is the Stefan-Boltzmann constant [5,67×10 W/(m ·K )];
ε is the effective emissivity consisted of emissivity ε , ε and configuration factor as shown in
1 2
Figure 8.
a) Open system b) Closed system
Key
1 is surface 1;
2 is surface 2.
[8]
Figure 8 — Radiation exchange between two surfaces
When the mean radiant temperature is considered, the surface 2 is assumed as black (ε =1 ), and
εε= .
Usually, the surrounding surface consists of several surfaces, each of them has generally different
temperature, emissivity, and configuration factor. Here, we assume (approximate) that the surrounding
surface has hypothetical uniform temperature T and emissivity ε .
2 2
Table 3 gives some general values of emissivity for different surfaces. The emissivity value varies
significantly depending on external agents, e.g. dust, corrosion, surface finish.
Table 3 — Emissivity values
Surface ε
Aluminium, bright rolled 0,05
Aluminium, oxidized 0,13
Galvanized sheet metal, blank 0,26
Galvanized sheet metal, dusty 0,44
Austenitic steel 0,15
Aluminium-zinc sheet, lightly oxidized 0,18
Non-metallic surfaces 0,94
[8]
For more detailed information about surfaces emissivity refer to the VDI 2055 .
4.1.3.2 Convective part of surface coefficient, h
cv
4.1.3.2.1 General
[8]
Formulae for the convective part have been taken from . B.1 shows examples of the following
calculations.
Convection is a heat transport mechanism that occurs in liquids and gases which involves heat flows
in form of internal energy flow by a mass movement. The concept of free or natural convection is used
if the movement is caused by buoyancy due to temperature or concentration difference, while forced
convection is caused by external forces like the wind or a fan.
For convection, it is necessary to make a distinction between the internal, h , and external, h , surface
si se
coefficients. h is defined from the point of view of the confined medium (e.g. inside pipes, vessels,
si
boilers) and h is defined from the surrounding medium.
se
NOTE 1 In most cases, h can be very large and so the inner surface temperature nearly equals the temperature
si
of the medium.
In order to describe the convection, experimental methods and their corresponding dimensionless
numbers are used. The dimensionless numbers involve some fluid properties, such as thermal
conductivity, density, viscosity, and heat capacity, which are determined at the mean temperature of
the interface boundary layer by Formula (24):
θθ=⋅05, +θ (24)
()
fsea
The Nusselt number, Nu, which describes the relation between the convective heat transfer of a fluid
layer and the conductive part within the fluid, is given by Formula (25):
hl⋅
cv
Nu= (25)
λ
f
where
h is the convective part of the surface coefficient, expressed in W/(m ⋅K);
cv
l
is the characteristic length, expressed in m;
λ is the thermal conductivity of the air or other fluid, expressed in W/(m⋅K).
f
NOTE 2 The characteristic length l corresponds to a body dimension, which varies according to the specific
application case. It can be the diameter of a pipe or the length from the leading edge in the direction of the flow
on a wall.
EXAMPLE For the determination of the Nusselt number for crossflow over cylinders, the characteristic
length is the streamwise length, as shown in Figure 9:
l =⋅0,5π⋅D
Figure 9 — Characteristic length for the determination of Nusselt number for cross-flow over a
[16]
cylinder
Consider the proper characteristic length in each case, see Table 4, characteristic length, l. For any other
cases the characteristic length can be approximated by Formula (26):
A
l= (26)
P
where
A is the area, expressed in m ;
P is the perimeter, expressed in m.
The Grashof number, Gr, is the ratio of the buoyancy force to the viscosity force within the fluid. It must
be noted that the Gr is the most important dimensionless number to describe the free convection, and is
given by Formula (27):
gl⋅⋅||Δθ
Gr = (27)
ν ⋅T
ff
T =+θ 273,15 (28)
ff
where
g is the acceleration of gravity, expressed in m/s ;
||Δθ
is the absolute value of temperature difference between surface and ambient air or fluid, ex-
pressed in °C;
v is the kinematic viscosity of the air or other fluid, expressed in m /s;
f
T is the temperature of the air or other fluid, expressed in K.
f
The Prandtl number, Pr, is the ratio of the momentum diffusivity to thermal diffusivity, i.e. the Pr
describes the relation between the flow field and the temperature field. It is given by Formula (29):
ρν⋅⋅c
ff p
f
Pr = (29)
λ
f
where
ρ is the density of the air or other fluid, expressed in kg/m ;
f
c is the specific heat capacity of the air or other fluid, expressed in J/(kg⋅K);
pf
λ is the thermal conductivity of the air or other fluid, expressed in W/(m⋅K).
f
NOTE 3 The Prandtl number depends only on fluid properties according to their temperature and pressure.
The Reynolds number, Re, specifies the relation between the inertia force and the friction force within
the fluid, and is given by Formula (30).
wl⋅
f
Re= (30)
ν
f
where, w is the velocity of the air or other fluid, expressed in (m/s).
f
The numerical value of Re is the crucial criterium to decide whether a flow remains in a stable laminar
mode, or it may undergo a transition to turbulent flow: For the fluid flow inside a circular pipe, the
critical Reynolds number is Re = 2 300. For Re < Re the flow is laminar, for Re > Re it can become
cr cr cr
turbulent. The characteristic length l in this case is usually taken as the inner diameter of the tube.
For parallel flow over a flat plate, the characteristic length l is the length in flow direction, measured
from the leading edge. The critical Reynolds number for this flow is about Re = 5·10 .
cr
In case of dry air at standard pressure, Formulae (31), (32), and (33) shall be applied.
These formulae are only valid for air as a fluid and for the given range of temperature.
Thermal conductivity of the air in W/(m⋅K), is given by Formula (31):
−−58
λθ=+0,,024 37 842 11⋅⋅02−⋅,075 510 ⋅θ (31)
ff
f
where θ is between −170 °C and 1 000 °C.
f
Kinematic viscosity of the air in m /s, is given by Formula (32):
−92,5
4,211 31⋅⋅0 T
f
ν = (32)
f
112+T
f
where θ is between −50 °C and 100 °C.
f
Density of the air in kg/m , is given by Formula (33):
348,35
ρ = (33)
f
T
f
The specific heat capacity and the Prandtl number of the air in a temperature range of −50 °C to 100 °C
can be expressed as an average value according to Formulae (34) and (35):
c = 1 007 J/(kg.K) (34)
p
Pr = 0,709 (35)
4.1.3.2.2 Formulae to determine the convective part of the surface coefficient h , and h
se si
The Nusselt number shall be determined to calculate the convective part of the surface coefficient,
solving the Formula (25), as follows:
Nu⋅λ
f
h = (36)
cv
l
When calculating the Nusselt number, a distinction shall be made between the case of external and
internal convection. For the external convection the medium is flowing around the object in question,
see Table 4, and for internal convection a confined medium is considered, see Table 5.
In case of a directional mixed convection there is a superposition of free and forced convection. The
heat transfer coefficient can be calculated using Formulae (37) and (38):
For unidirectional mixed convection:
3 3
Nu=+Nu Nu (37)
forced free
For mixed convection in the opposite direction:
3 3
Nu=−Nu Nu (38)
forced free
Table 4 — Formulae for the determination of Nusselt number — External convection case
Free convection
Range of Characteristic
Case Nusselt Number
validity length, l
16/ 2
Wall l = H
Nu =+(,0 825 0,)306 3⋅Gr
free
0,14 < Gr <1,4
16/ 2
Pipe l = H
Nu =+(,0 825 0,)306 30⋅+Gr ,(87⋅ lD/) 12
freee ⋅ 10
π ⋅D
16/ 2 e
Pipe
Nu =+(,0 752 0,)303⋅Gr l =
free
Laminar
Gr ≤ 2,4 ⋅ 10
Wall: heat dissi-
15/
Nu =⋅0,593 Gr
free,lam
pation on the top
(or cooling on the
Turbulent
bottom)
ab⋅
Gr > 2,4 ⋅ 10
13/
l =
Nu =⋅0,098 8 Gr
free,tur
2(⋅+ab)
Wall: heat dissipa-
tion on the bottom 4 ⋅ 10 < Gr <4
15/
Nu =⋅0,453 Gr
free
(or cooling on the ⋅ 10
top)
Forced convection
Laminar
12/
Nu =⋅0,592 Re
lam
Turbulent
08,
0,026 2⋅Re
Nu =
tur
05,
1−
01,
Re
Horizontal Vertical
Table 4 (continued)
Free convection
Range of Characteristic
Case Nusselt Number
validity length, l
l longitude of the
2 2
Wall wall in the direc-
Nu =+Nu Nu
forced lam tur
tion of the flow
10 π ⋅D
e
Pipe
l =
Nu =+03, Nu +Nu
forced lamtur
Table 5 — Formulae for the determination of Nusselt number — Internal convection case
Characteristic
Case Nusselt number Range of validity
length, l
08,,00 4
2 300 < Re
Nu =⋅0,(021 4 Re −⋅100) Pr
forced
and 0,5 < Pr < 1,5
Flow through cir-
l = D
i, pipe
cular cross section
08,,70 4
2 300 < Re
Nu =⋅0,(012 Re −⋅280) Pr
forced
and 1,5 < Pr < 500
4 6
10 ≤ Re ≤ 10
(/ξ 8)⋅⋅Re Pr
Flow through
Nu =
forced
4⋅A
23/
non-circular cross 11+⋅27,/ξ 81⋅−()Pr and
l =
P
section
−2
ξ =⋅(,18 log(Re),−15)
0,1 4.1.4 External surface resistance
The reciprocal of the outer surface coefficient, h , is the external surface resistance.
se
For plane walls, the surface resistance, R , is given by Formula (39):
se
R = (39)
se
h
se
For pipe insulation, the linear surface resistance, R , is given by Formula (40):
l,se
R = (40)
l,se
hD⋅⋅π
se e
For hollow spheres, the surface resistance, R , is given by Formula (41):
sph,se
R = (41)
sph,se
hD⋅⋅π
se e
4.1.5 Thermal transmittance
The thermal transmittance, U [W/m K], is defined by Formula (42):
q
U= (42)
θθ−
ia
where
θ is the ambient air (or fluid) temperature, expressed in °C;
a
θ is the internal air temperature for plane walls or the temperature of the medium inside pipes,
i
ducts and vessels, expressed in °C.
For plane walls, the thermal transmittance, U, can be calculated by Formula (43):
11 1
=+R+=RR++RR= (43)
si se T
Uh h
si se
For pipe insulation, the linear thermal transmittance, U [W/m⋅K], can be calculated by Formula (44):
l
11 1
= ++R ==RR++RR (44)
l l,si ll,sel,T
Uh ⋅⋅ππD hD⋅⋅
lsii se e
For rectangular ducts, the linear thermal transmittance, U [W/m⋅K], can be calculated by Formula (45):
d
11 1
=+R +=RR++RR= (45)
d d,si dd,sed,T
Uh P hP
dsii se e
For hollow spheres, the thermal transmittance, U [W/K], is given by Formula (46):
sph
11 1
= ++R ==RR++RR (46)
sph sph,si sphsph,se sph,,T
2 2
U
hD⋅⋅ππhD⋅⋅
sph
si i se e
In Formulae (5), (8), (11), and (13), R, R , R , and R are surface-to-surface thermal resistances. They
l sph d
shall be calculated using the design values of thermal conductivity which represent the conditions
of the expected application. According to ISO 23993, the design thermal conductivity, λ , takes into
D
consideration two factors. The first one is overall conversion factor, F, that takes into consideration
effects like ageing or open joint, among others. The second one represents the influence of elements
placed into the insulation material as spacers, Δλ.
Components which are regularly placed in the insulating layer such as sub-constructions, modify
the thermal performance of the installed insulation material, adding an extra conductivity, Δλ, to the
declared thermal conductivity of the insulation, F⋅λ , i.e. the design thermal conductivity can be larger
d
than the declared.
The design thermal conductivity can be calculated by Formula (47)
λλ��=⋅F +Δλ (47)
D d
where
λ is the design thermal conductivity, expressed in W/(m⋅K);
D
λ is the declared thermal conductivity, expressed in W/(m⋅K);
d
F is overall conversion factor for thermal conductivity;
Δλ is the extra conductivity due to regularly placed components in the insulation system, ex-
pressed in W/(m⋅K).
NOTE Estimated values for the extra conductivity due to regularly placed components which are part of the
insulation system are given in Annex A.
In most cases, h can be very large which leads to a very small surface resistance of the flowing media
si
inside a pipe R , , and therefore it can be neglected. For the external surface coefficient, h , formulae
l si se
from Table 4 (4.1.3.2.2) apply. For ducts, it is necessary to include the internal surface coefficient. It
can be calculated using the appropriate formulae in Table 5 (4.1.3.2.2) taking into consideration 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
T
linear thermal resistance, R , for pipes and R for hollow sphere.
l,T sph,T
4.1.6 Heat flow rate
The heat flow rate is expressed in W.
The heat flow rate of a plane wall is given by Formula (48):
Φ =⋅UA⋅−()θθ (48)
ia
The heat flow rate of a pipe is given by Formula (49):
Φ =⋅UL⋅−()θθ (49)
li a
l
The heat flow rate of a sphere is given by Formula (50):
Φ =⋅U ()θθ− (50)
sphsph ia
4.1.7 Temperatures of the layer boundaries
The general formula for the density of the heat flow rate in a multi-layer wall is written in the general
form given by Formulae (51) and (52) (see also Figure 10):
θθ−
ia
q= (51)
R
T
RR=+ RR++.++RR (52)
Tsin12 se
where
R …R are the thermal resistances of the individual layers, expressed in (m ∙K/W);
1 n
R and R are the surface resistances of the internal and external surfaces, respectively, expressed
si se
in (m ∙K/W).
Figure 10 — Temperature distribution for a multi-layer plane wall in relation to the 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 °C, as given in Formulae (53) to (56):
R
si
θθ−= ⋅−()θθ (53)
isi ia
R
T
R
θθ−= ⋅−()θθ (54)
si 1 ia
R
T
R
θθ−= ⋅−()θθ (55)
12 ia
R
T
R
se
θθ−= ⋅−()θθ (56)
se a ia
R
T
R is calculated for plane walls according to Formula (43), for cylindrical pipes according to Formula (44),
T
for rectangular ducts according to Formula (45) and for spherical insulation according to Formula (46).
4.2 Determination of the influence of thermal bridges
4.2.1 General
In industrial installations there are two types of thermal bridges; thermal bridges linked to the
insulation system itself and thermal bridges linked to the installation. In both cases, they represent an
additional heat transfer. Their influence is explained in 4.2.2 and 4.2.3.
4.2.2 Insulation system related thermal bridges
In heat transfer calculation, the influence of insulation related thermal bridges, such as spacers or
support construction, is taken into consideration using the design thermal conductivity according to
4.1.5.
4.2.3 Installation related thermal bridges
Every installation related thermal bridge, such as hangers, valves, or other fittings, represents an extra
heat flow. Their influence on the heat transfer calculation shall be determined individually for each
thermal bridge using the thermal bridge coefficient K according to Formula (57):
Φ =⋅K ()θθ− (57)
tb ia
where
Φ is the additional heat flow rate due to an installation related thermal bridge, expressed in W;
tb
K is t
...