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Yves JANNOT
Université Internationale de Rabat
17 février 2023
THERMAL PROPERTIES
MEASUREMENT OF MATERIALS:
EASY... OR NOT ?
1
22
PLAN
➢Thermal characterization: definitions and principle
➢Example 1: Small super-insulating samples
➢Example 2: Bio-sourced anisotropic insulation
➢Example 3: Anisotropic thin plate
➢Conclusion
33
THERMAL CHARACTERIZATION: DEFINITIONS
The thermal properties of a material:
Thermal conductivity : Resistance to heat transfer
Volumetric heat capacity : Heat storage capacity
Diffusivité thermique : Heat transfer speed
T : Capacity to transfer heat to the environment
Only two independent quantities:
et
Thermal properties measurement
➢Measurement of two quantities
➢Calculation of the other two
44
THERMAL CHARACTERIZATION: PRINCIPLE
Principle of characterization methods:
➢A point, linear or surface heat flow rate is brought to a sample
➢The temperature
is measured in one or several places
➢Temperature is modelled at measurement locations:
➢We estimate the parameters values of the function which make it possible to best represent
the experimental values of the temperature
Modelling
Metrology
Inverse method
Estimation of and
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THERMAL CHARACTERIZATION: AVAILABLE EQUIPMENTS
Many commercial "push-button" devices are available
So it's easy, just buy the right device...
Device for measuring the thermal conductivity of solid,
liquid, powdered or pasty materials
66
THERMAL CHARACTERIZATION: AVAILABLE EQUIPMENTS
Let's take a closer look...
at some concrete examples
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EXAMPLE 1: SUPER-INSULATING SMALL SIZE SAMPLE
Problem: measurement of for a disc with D = 15 mm and e ≈ 3 mm
Specificity: super insulating material with
Solution implemented by materials engineering researchers:
purchase of a commercial Hot Disk device, cost > 30 000 €
Consistent choice according to device specifications
88
EXAMPLE 1: SUPER-INSULATING SMALL SIZE SAMPLE
They began to think that thermal characterization
may require special skills... and came to see us
But not everything went as planned...
Measurement results with the Hot Disk device
Material Thickness
(mm)
(W m-1 K-1)
(W m-1 K-1)
Deviation
(%)
XPS Foam
Super
insulator
99
EXAMPLE 1: SUPER-INSULATING SMALL SIZE SAMPLE
Characterization of a super-insulator with the Hot Disk: why it doesn't work?
If the samples are small and of low thermal conductivity, the (unavoidable) losses
by the heating probe (by fin effect) can be of the same order of magnitude as the
heat flow rate transmitted to the samples
(Implicit) assumption of the model used:
All the heat flow rate produced in the disk by Joule effect is transferred to the samples
10 10
EXAMPLE 1: SUPER-INSULATING SMALL SIZE SAMPLE
Characterization of a super-insulator of small dimensions: how to do?
Result: Measurement on 15 mm diameter samples with ≈5% accuracy
Y. Jannot, S. Schaefer, A. Degiovanni, J. Bianchin, V. Fierro, A Celzard A new method for measuring the
thermal conductivity of small insulating samples, Review of Scientific Instruments; 90, 054901, 2019.
Findings: Losses by wires unavoidable and not negligible
Solution:
➢Make them perfectly reproducible: precise control of measurement conditions
➢Estimate them by measurements with samples of known thermal conductivities
➢Take them into account: 3D transfer model in samples:
11 11
EXAMPLE 1: SUPER-INSULATING SMALL SIZE SAMPLE
Our CTHP (Calibrated Tiny Hot Plate ) steady-state method
with
+
1. Experiments with samples of various thicknesses and known Estimation of and
2. Experiment with an unknown sample (and being known) Estimation of
Aluminium block
Aluminium block
Sample
Sample
Heating disc at uniform
temperature
sol. of:
12 12
EXAMPLE 1: SUPER-INSULATING SMALL SIZE SAMPLE
Results
Material
Thickness
Deviation
vs
Deviation
vs
estimated (heat wires losses = 0
)
(mm) (W m-1 K-1) (W m-1 K-1) (%) (W m-1 K-1) (%)
EPS foam 2.95 0.0324 0.0315 -2.9 0.0468 44
5.80 0.0330 2.0 0.0623 92
Super
-
insulating
material
2.90 0.0141 0.0148 5.2 0.0298 111
4.94 0.0145 2.8 0.0385 173
PE foam 6.30 0.0405 0.0416 2.8 0.0735 81
PVC 5.15 0.184 0.177 -3.8 0.0203 10
13 13
EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
The material to be characterized
Measurement methods
Hot wire (HW): measurement o of the heating wire
Parallel hot wire (PHW): m at a distance
from the heating wire
Wood fibre plate
14 14
EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
Experimental set-up
15 15
EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
Analytical models for an anisotropic material
Parallel hot wire (PHW)
Estimation of and , then the anisotropy factor
is calculated
Hot wire (HW)
avec :
et :
Estimation of
and knowing ,and can be calculated
Jannot Y., Degiovanni A., Schick V., Meulemans J., Apparent thermal conductivity measurement of anisotropic insulating
materials at high temperature by the parallel hot-wire method, International Journal of Thermal Sciences 160 (2021) 106672.
16 16
EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
Hot wire (HW) method Parallel hot wire (PHW) method
Estimated thermal conductivities
Very different values:
Why and what is measured in both cases?
17 17
EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
Why values are very different?
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
020 40 60 80 100 120
Teneur en eau (kgeau / kgms)
HR (%)
Isotherme de sorption de la laine de bois
Heating Mass transfer modifying temperature field
Wood wool sorption isotherm
Water content (kgwater kgdry matter-1)
We used a coupled heat/mass transfer model to understand what is measured
What is measured?
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EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
Heat transfer: Mass transfer:
Equivalent thermal conductivity:
Water vapour diffusivity in the material:
Water vapour diffusivity in air:
Saturated vapour pressure :
Sorption isotherm (GAB model) :
0 < a < 1
f(tortuosity)
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No liquid diffusion
19 19
EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
Method
➢Numerical resolution of 1D axisymmetric coupled transfers
➢Numerical simulation of temperature at measuring points for a material with known
thermal properties, sorption isotherm and mass diffusivity
➢Estimation from these simulated curves using thermal model
➢Interpretation of the values estimated by the hot wire and the parallel hot wire methods.
20 20
EXAMPLE 2: BIOSOURCED ANISOTROPIC INSULATING MATERIAL
What is measured?
Hot wire (HW): we measure ≈
Parallel hot wire (PHW): we measure ≈
Mass diffusivity
Phase change latent heat
From a simulation From an experiment
Y. Jannot, H. Bal, C. Moyne, Influence of mass transfer on the estimation of the thermal conductivity of a wet material by the
hot wire and parallel hot wire methods, International Journal of Heat and Mass Transfer 202 (2023) 123732.
Other methods: ???
21 21
EXAMPLE 3: THIN ANISOTROPIC PLATE
Problem:
Measurement of the in-plane thermal conductivity a thin
anisotropic plate PCB holder
Specificity: e < 1mm, anisotropic material, semi-transparent
HFM Hot wire , Hot disk , Flash
Solution considered:
➢Measurement of specific heat by DSC
➢Measurement of density by weighing and volume measurement
➢Measurement of thermal diffusivity by the transient fin method
22 22
EXAMPLE 3: THIN ANISOTROPIC PLATE
Principle of the method for measuring thermal diffusivity
23 23
EXAMPLE 3: THIN ANISOTROPIC PLATE
Measurement under vacuum to minimize convection and especially to
prevent conduction in air not taken into account in the model
But: conduction in air not necessarily negligible
It should work, but have we thought of everything?
24 24
EXAMPLE 3: THIN ANISOTROPIC PLATE
The experimental set-up
heating
measurement of
measurement of
25 25
EXAMPLE 3: THIN ANISOTROPIC PLATE
Results
050 100 150 200 250
-2
0
2
4
6
8
t(s)
T(°C)
T2exp
T2mod
Residues-1°C
0
0.2
0.4
0.6
0.8
1
1.2
0.001 0.01 0.1 1 10 100 1000
l(W m-1 K-1)
P (mbar)
Arlon 35N e=0.6mm Arlon 35N e=0.8mm
Rad. Rad. + cond. Rad. + cond. + conv.
➢Correct measurement with our device
only if
➢Error > 30 % at
Y. Jannot, A. Degiovanni, A. Aubert, F. Lechleiter, In-plane thermal diffusivity measurement of thin plates by the transient fin
method, Review of Scientific Instruments, 89, 2018.
Estimation from a COMSOL simulation
Estimation from experiments
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Conven
tional
method
s do not
apply
26
REVIEW
➢Example 1: Small size super-insulating samples
➢Example 2: Bio-sourced material
➢Example 3: Thin anisotropic plate
You can find anything
The result depends on the method
Conventional methods do not apply
27 27
Thank for your
attention!
THERMAL CHARACTERIZATION
Finally,
it is not that
easy…