SIST-TP CEN/TR 15131:2006

SLOVENSKI STANDARD
SIST-TP CEN/TR 15131:2006
01-oktober-2006
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Thermal performance of building materials - The use of interpolating equations in relation
to thermal measurement on thick specimens - Guarded hot plate and heat flow meter
apparatus
Die Anwendung von Interpolationsgleichungen für wärmetechnische Messungen und
dicken Probekörpern - Heizplatten und Wärmestrom-Messapparate
Performance thermique des matériaux pour le bâtiment - Utilisation des équations
d'interpolation dans le cadre des mesurages thermiques sur éprouvette épaisse - Plaque
chaude gardée et appareil a fluxmetre
Ta slovenski standard je istoveten z: CEN/TR 15131:2006
ICS:
91.100.60 0DWHULDOL]DWRSORWQRLQ Thermal and sound insulating
]YRþQRL]RODFLMR materials
91.120.10 Toplotna izolacija stavb Thermal insulation
SIST-TP CEN/TR 15131:2006 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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TECHNICAL REPORT
CEN/TR 15131
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
January 2006
ICS 91.100.60; 91.120.10

English Version
Thermal performance of building materials - The use of
interpolating equations in relation to thermal measurement on
thick specimens - Guarded hot plate and heat flow meter
apparatus
Performance thermique des matériaux pour le bâtiment - Die Anwendung von Interpolationsgleichungen für
Utilisation des équations d'interpolation dans le cadre des wärmetechnische Messungen und dicken Probekörpern -
mesurages thermiques sur éprouvette épaisse - Plaque Heizplatten und Wärmestrom-Messapparate
chaude gardée et appareil à fluxmètre
This Technical Report was approved by CEN on 27 September 2005. It has been drawn up by the Technical Committee CEN/TC 89.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, 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
© 2006 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 15131:2006: E
worldwide for CEN national Members.

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CEN/TR 15131:2006 (E)
Contents page
Foreword .3
1 Scope .4
2 Normative references .4
3 Terms, definitions and symbols .4
4 Modelling thickness effect .5
5 Prediction of the thickness effect with the interpolating functions .11
Bibliography.28

2

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CEN/TR 15131:2006 (E)
Foreword
This Technical Report (CEN/TR 15131:2006) has been prepared by Technical Committee CEN/TC 89 “Thermal
performance of buildings and building components”, the secretariat of which is held by SIS.
3

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CEN/TR 15131:2006 (E)

1 Scope
This Technical Report supplements technical information on modelling of heat transfer in products of high and
medium thermal resistance when the thickness effect may be relevant; by doing this it supplies minimum
background information on the interpolating equations to be used in the procedures described in EN 12939 to test
thick products of high and medium thermal resistance.
All testing procedures to evaluate the thermal performance of thick specimens require utilities, which are essentially
based on interpolating functions containing a number of material parameters and testing conditions. Interpolating
functions and material parameters are not the same for all materials.
Essential phenomena and common interpolating functions are presented in Clause 4, which is followed by separate
equations for each material family.
This Technical Report also gives diagrams derived from the above interpolating equations to assess the relevance
of the thickness effect for some insulating materials.
2 Normative references
The following referenced documents are indispensable for the application of this Technical Report. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced document
(including any amendments) applies.
EN 12939:2000, Thermal performance of building materials and products – Determination of thermal resistance by
means of guarded hot plate and heat flow meter methods – Thick products of high and medium thermal resistance
EN ISO 7345:1995, Thermal insulation – Physical quantities and definitions (ISO 7345:1987)
EN ISO 9288:1996, Thermal insulation – Heat transfer by radiation – Physical quantities and definitions (ISO
9288:1989)
3 Terms, definitions and symbols
For the purposes of this Technical Report, the terms and definitions given in EN ISO 7345:1995,
EN ISO 9288:1996 and EN 12939:2000 apply.
NOTE EN ISO 9288 defines spectral directional extinction, absorption and scattering coefficients and the spectral
directional albedo only, while this Technical Report makes use of total hemispherical coefficients, which can be obtained from
the previous ones by appropriate integrations. To avoid confusion with the monochromatic directional coefficients, they are
referenced here as related to the "two flux model", see Clause 4.
Symbol Quantity Unit
d thickness m
h surface coefficient of heat transfer
J transfer factor
W/(m⋅K)
2
R thermal resistance
m ⋅K/W
T thermodynamic temperature K
total hemispherical emissivity
ε
thermal conductivity
λ W/(m⋅K)
radiativity
λ
r
3
density kg/m
ρ
4

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CEN/TR 15131:2006 (E)
2 4
-8
W/(m ·K )
σ Stefan-Boltzmann's constant (5,66997×10 )
Celsius temperature
θ °C

4 Modelling thickness effect
4.1 General
The following qualitative description of heat transfer in low density homogeneous insulating materials formed the
basis for the development of a model to get interpolating functions.
A graph of thermal resistance versus specimen thickness for all homogeneous insulating materials has the form of
that in Figure 1. The extrapolation to zero thickness, R , of the straight portion (bold continuous line) depends both
0
on material properties and testing conditions, in particular the emissivity of the surfaces bounding the specimen or
product.
Only the slope of the straight portion of the plot of thermal resistance versus thickness is an intrinsic material
property; the incremental ratio ∆d/∆R for d > d is called thermal transmissivity, see EN ISO 9288.
∞
Guarded hot plate or heat flow meter apparatus basically measure a thermal resistance, R. If the specimen
thickness, d, is measured, then the transfer factor, J = d/R, can be calculated. The transfer factor is often referred to
in technical literature as measured, equivalent or effective thermal conductivity of a specimen and, for low density
insulating materials, depends not only on such material properties as the coefficient of radiation extinction, the
thermal conductivity of the gas and solid matrix and air flow permeability but also on such testing or end-use
conditions as product thickness, mean test temperature, temperature difference and emissivity of the bounding
surfaces. When the specimen thickness is large enough, the transfer factor becomes independent of specimen
thickness and emissivity of the surfaces of the apparatus, i.e. becomes a material property called thermal
transmissivity.
NOTE 1 When different materials are considered, having the same thermal transmissivity, the same coefficient of radiation
extinction and the same thermal conductivity of the gas and solid matrix, the thickness di, at which the straight portion of the plot
starts, is larger for cellular plastic materials than for mineral wool. This is due to the different mechanism of the radiation
extinction. Consequently for cellular plastic materials the thicknesses corresponding to the dashed portion of the plot, i.e. d < d ,
i
may more frequently than for mineral wool be larger than actual specimen thicknesses. For these reasons the procedures of this
Technical Report should be differentiated by material families.
The following equations, describing the above phenomena, are those used in EN 12939 as interpolating tools.
NOTE 2 The model used assumes that all radiation beams crossing a plane in all possible directions can be grouped into
those crossing the plane from its side A to the side B and those crossing the same plane from the side B to the side A, i.e. the
radiation crossing the plane is reduced to a forward radiation intensity and a backward radiation intensity. This way of handling
radiation is known as the "two-flux model". To radiation heat transfer, heat transfer by conduction was coupled.
The thermal resistance, R, of a flat specimen of low-density material may be expressed as:
R = R’ + d/λ (1)
0 t
where R ' is not necessarily independent of the thickness d, and
0

λ = λ + λ (2)
t cd r
According to EN ISO 9288 λ is the thermal transmissivity, λ is the combined gaseous and solid thermal
t cd
conductivity and λ is the radiativity. Possible expressions for the gaseous and solid conductivity, that are material-
r
dependent, will be considered in the following subclauses.
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CEN/TR 15131:2006 (E)

The thickness d indicates the beginning of the straight portion of the plot of thermal resistance, R. A reduction of
∞
apparatus emissivity shifts the bold line upwards.
if d < d The ratio of an increment in specimen thickness, ∆d, to the corresponding increment in measured thermal
∞
resistance, ∆R, is not constant; the thermal transmissivity, λ , cannot be measured; the transfer factor, J, is
t
not an intrinsic material property, as it depends on experimental conditions.
if d > d The ratio ∆d/∆R is constant; the thermal transmissivity λ , that is an intrinsic material property independent
t
∞
of experimental conditions, can be measured. In this case, the radiativity λ and the gaseous and solid
r
thermal conductivity λ can also be defined as material properties and put λ = λ + λ . Nevertheless J =
cd t cd r
d/R is not yet independent of the thickness d, see dashed and dotted lines.
Figure 1 — Thermal resistance, R, as a function of the specimen thickness, d
-8 2 4
If T is the mean test thermodynamic temperature, σ = 5,66997×10 W/(m ·K ) the Stefan-Boltzmann's constant, ε
m n
the total hemispherical emissivity of the apparatus, β' a mass extinction parameter, ϖ an albedo, ρ the bulk
* ∗
density of the material, the following expressions are introduced:
F = (1 - ϖ *) (3)
∗
3
h = 4 σ T (4)
r n m
the radiativity, λ , is expressed as follows:
r
h
r
(5)
λ =
r
ρ
'
β ⋅
*
2
and the term R ' is expressed as follows:
0
h
' r
R = (6)
0
 
 
2
ρ ε 1
   
'
λ ⋅ β ⋅ Z +
 
t *
 
2 2 − ε
  d λ
 
cd
 
tanh E F
 
 2 λ 
 
t
 
Z = 1 for all materials except expanded polystyrene and insulating cork boards, see 4.3, while E is a modified
extinction parameter, due to coupled conduction and radiation heat transfer, expressed as:
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CEN/TR 15131:2006 (E)
λ
'
t
E = β ⋅ ρ F (7)
*
λ
cd
'
'
κ
It becomes zero when the absorption parameter is zero, i.e. the extinction parameter β becomes simply the
* *
'
scattering parameterσ . E tends to infinity when conduction becomes negligible, i.e. when λ = 0.
cd
*

If the specimen thickness, d, is measured, the transfer factor can be calculated using Equation (1) as follows:
1
J = λ (8)
t
λ
t '
1+ R
0
d
4.2 Interpolating functions for mineral wool and wood wool products
4.2.1 One layer of homogeneous mineral wool and wood wool product
For mineral wool and wood wool products the parameter F that appears in Equation (7) has values between 0,2
and 0,5, see [1] in the Bibliography. Consequently the majority of the specimens have thicknesses such that
(E d/2) >3, i.e. tanh(E d/2) does not differ from 1 by more than 1 %. In this situation the thermal resistance R ',
0
expressed by Equation (6), becomes a thermal resistance R independent of specimen thickness.
0
h
r
R = (9)
0
 
 
2
ρ ε 1
   
'
λ ⋅ β ⋅ +
 
t *
 
2 2 − ε
  λ
cd
 
F
 
λ
t
 
Introducing two parameters A and B, the term λ , that represents the combined conduction through the gaseous
cd
ρ ) of the insulating material, is expressed as:
phase and the solid matrix (of density
s
 
Bρ
 
λ = A 1+ (10)
cd
 
1+ B ρ ⋅ ρ
s
 
3 3
For glass wool products, B is close to 0,016 m /kg and ρ is close to 2400 kg/m . For the same products an even
s
simpler expression is λ = A (1 + 0,0015 ρ); this expression underestimates the conduction in the solid matrix at
cd
low densities, but for these densities this contribution is of minor importance.
When the density tends to zero, λ approaches the thermal conductivity of the gaseous phase, represented in
cd
Equation (10) by the value of the parameter A.
h
r
By introducing an additional parameter C = 2 , and taking account of Equations (5) and (10), Equation (2) can
'
β
*
be rewritten as in Equation (11), see its representation in Figure 2:
 
Bρ c
 
λ = A 1+ + (11)
T
 
ρ
1+ B ρ ⋅ ρ
s
 

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CEN/TR 15131:2006 (E)

The dashed line represents the transfer factor, J, of a layer of constant mass per area, ρ d.
Figure 2 — Thermal transmissivity λλ and its components A, A B ρ /(1 + B ρρ ) as a function of
λλ
t
s
density, ρ , for a semi-transparent material (continuous line)

In the proposed model there are three material parameters that enter in the definition of the thermal transmissivity
'
according to Equations (5) and (11), namely the parameters A and B and the mass extinction parameter β . In
*
addition the material bulk density and the mean test temperature shall be known. The definition of the thermal
resistance or the transfer factor requires an additional material parameter, F (or its complement to 1, the albedo
ω ), and an additional testing condition, the emissivity, ε , of the apparatus.
*
In principle, any material parameter is temperature dependent. For mineral wool the effect of temperature on
thermal resistance or transfer factor can be concentrated in the term h appearing in the radiativity and in the
r
parameter A.
Around room temperature, the parameter A, i.e. the thermal conductivity of the air, can be expressed as a function
of the Celsius temperature, θ, by the following expression:
−6 2
λ = 0,0242396 (1+ 0,003052 ϑ −1,282 ×10 ϑ ) (12)
a
To verify the proposed model, the expression within brackets in Equation (12) can be retained to express the
correlation with temperature, while the constant 0,0242396 W/(m⋅K) can be replaced by an unknown, A , to be
0
determined in the data regression to validate the model. Then, in gene
...