for metals, alloys and
ceramics from room
temperature up to
723 °C and for
liquids and solids up
to 1500 °C
For research and
Materials: Fiber Insulation, Metal,
Polymer, Rubber, Oil, Wood,
Concrete, Glass, Ceramic,
Refractory, Powder, and Mold
Contacts: Dr. S. Peter Andersson,
M. Sc. Carl-Åke Däcker,
Why measure the thermal
Knowledge of thermal conductivity is of major importance for
material used in applications where thermal properties inﬂuence
functionality in the products or in control of steps in manufacturing.
Thermal conductivity is a fundamental property for all calculations
of temperature ﬁelds in materials. To answer common question
concerning temperature distribution in materials, the thermal
conductivity must be known.
Typical questions are: investigation of the thermal conductivity, but may also
— What is the temperature distribution in materials be used for measuring the thermal diffusivity and heat
exposed to heating or cooling? capacity.
— How does this change with temperature?
The method has originally been developed in Sweden
— How can I improve the heat transfer?
by Silas Gustafsson at Chalmers University of Tech-
— What is the best material or material combination? nology. Today the method is commercialized by the
— How do I design a system to achieve the company Hot Disk AB. The TPS method is speciﬁcally
requirements? developed for metals, ceramics, polymers and other
common solid materials. It can also be used for liquids.
There is also a scientiﬁc interest, since thermal con- It is possible to measure thin insulating ﬁlms (ranging
ductivity gives basic understanding of the underlying from 10 to 600 microns), sheets with high thermal
mechanism and also some information of the structure conductivity or anisotropic thermal properties of bulk
as well as indications of phase change and change of materials.
With this method the thermal conductivity can be
determined in the temperature range of 20°C to 723 °C.
Equipment at KIMAB The TPS method is usually used with a sensor of a
For metals and electrically insulating materials the very thin double metal spiral in close contact with
transient plane source method (TPS) is the best suited the material to be investigated. The sensor serves
method. For this reason KIMAB invested in the com- both as the heat source device and as a resistance
mersial equipment Hot Disk in year 2005. thermometer. When measurements are carried out
for solids, the sensor is clamped between two surfa-
To analyze the thermal conductivity for electrically in- ces of the same material, as shown in the ﬁgure at
sulting liquids and solids the transient hot-wire method the front page. At the time of measurement a nearly
is usually employed. The transient hot-wire method constant electric current is supplied to the sensor.
is highly suitable for polymers, oils, wood, concrete, The current heats the sensor and thus a change in
rubber, glass, ceramics, refractories and mold powder. its resistance will occur. The temperature increase
The method is developed and has been in operation at depends on the current (power) supplied and the
KIMAB since 2002. heat conducted away through the surrounding ma-
terial (tested material). The heating of the sensor is
continued for a given time. The voltage of the sen-
sor is measured and since the current is held nearly
The Transient Plane Source constant by a resistance bridge, the voltage changes
is proportional to the changes in the resistance of
method (TPS) the sensor.
TPS is a method for measuring the thermal proper-
ties of materials from room temperature up to high With knowledge of the voltage variation with time, it
temperatures. The method is particularly suitable for is possible to calculate the thermal conductivity and
speciﬁc thermal capacity of the material under in-
vestigation. The TPS method gives accurate values for
thermal conductivities up to 400 W/mK.
Thermal conductivity: 0.01 – 400 W/mK
Thermal diffusivity: 0.1 – 100 mm2/s
Heat capacity per unit volume: up to 5 MJ/m3K
Temperature range (furnace): room temperature
– 1573 K
Maximum 1000 K with MICA insulated sensors.
Temperature precision: better than 0.5 K in
Measurement times: 1 – 640 s
Results from measurements of thermal conductiviy
Repeatability: Typically better for a high alloyed cast iron measured with the TPS-
than 1%. method.
Accuracy: Better than 2%.
The Hot-Wire method
The hot-wire method is designed and developed
in order to minimize the inﬂuence of radiation in
measured values. The contribution in the measured
value due to radiation is roughly estimated to be
8 % at 1500 K, wich is about the inaccuracy of
the method at this temperature.
The transient hot-wire is a dynamic, absolute method
based on the integral temperature increase over the
length of a hot-wire between two voltage taps during
a short heat pulse. Both the wire and a thermocouple
(measuring temperature in the sample) are embedded
within the sample, which form the test assembly. The
increase in temperature (resistance) of the wire as a
function of time is measured from the moment the
heating current is switched on. A theoretical expres-
sion, describes the temperature increase of the metal
wire in terms of thermal conductivity and heat capa-
city per unit volume of the substance surrounding the
hot-wire. Consequently, if the theoretical expression
is ﬁtted to the experimental temperature increase of
the wire, we can obtain both thermal conductivity and
heat capacity per unit volume.
Results from measurements of thermal conductiviy
and heat capacity of reference materials with the hot-
The transient hot-wire method is based on a solution
of the Fourier equation. The solution we commonly
use is given with the following assumptions:
1) The hot-wire is inﬁnitely long.
2) The temperature of the hot-wire before the
heat pulse is equal to the static uniform temperature
of the sample.
3) The substance surrounding (the sample) the
hot-wire is inﬁnitely large.
4) The hot-wire is heated with a uniform power
per unit length.
2q 1 − exp( u
∆T (t ) = T (t )− T0 = 3 ∫ u
u 3∆(u , )
∆(u , ) = [u 0 (u )−
J J1 (u )] + [Y
u 0 (u )− Y1 (u )]
2 cp t
= , = 2
wire wire c p rwire
J 0 and J 1 are Bessel functions. ∆T is the tempera-
ture increase of the wire, q is the power supplied per
unit length of wire, T0 is the static uniform tempera-
ture of the sample, is the thermal conductivity of
the sample, p is the heat capacity per unit volume,
wire c wire is the heat capacity per volume of the wire,
t is the time and rwire is the radius of the wire. Furnace and sensor.
The hot-wire sample cell which is constructed from
alumina, is shown on the right. The hot-wire is usually
a platinum wire of about 40 mm length and 0.2 mm
diameter. Since platinum has a fairly good temperature
dependence and does not react with other material
or oxidize it is well suited for hot-wire experiments.
The temperature in the cell is measured using a type
S thermocouple, which has been calibrated against a
commercially available reference thermocouple in a
reference furnace by Isotech Pegasus 91, Basic calibra-
tor, Isothermal Technology LDT using a FLUKE-743 as
a calibration instrument.
If measurements concern a sample which is solid,
such as insulating ﬁbers, then the hot-wire is
sandwiched between two circular plates of the
sample. If the sample is a liquid or melted, it is
simply poured into the cell at liquid temperature.
The hot-wire cell is loaded into a 6 kW high tempe-
rature vertical single zone tube furnace. The tempe-
rature of the experimental arrangement is measured
by furnace thermocouple (type R) and regulated by
a PID (Eurotherm 2604) control system. The tempe-
rature of the specimen is measured separately. The
isothermal measurements of thermal conductivity are
performed by ﬁrst increasing the temperature at a
constant rate (using ramp function on the PID) to the
isothermal measuring point and then it continues with Hot-wire cell for preparation of solids a top and side
the same rate to the next point up to the end tem- view.
perature (1550 °C). Measurements with decreasing
temperature are performed in a similar way. Before
measurement, the system waits until the temperature
difference is less than ± 0.2K. Using this system, the
temperature of the furnace can be kept within ± 0.2K
during isothermal measurement.
The measuring unit is shown below, and consists of
a SourceMeter 2420, SCXI-1125 card connected to
NI-DAQ device and furnace PID Eurotherm 2604.
The platinum wire is connected to the Source-Meter
2420 and the thermocouple temperature is measured
by the SCXI-1125 card. The furnace controller com-
municates by RS-232 to a local OPC server. A PC
program in Labview controls all measurements and
all actions for the devices. The result of thermal
conductivity measurements are shown directly on
Lenton Furnaces Ldt.
Type of furnace Vertical single zone tube furnace Model LTF16/75/450
Heated length 450 mm, uniform 300 mm
Furnace bore To accept 60 mm worktube
Temperature range 20 ºC to 1 550 ºC
Maximum continuous temperature 1 600ºC
Heating elements Silicon carbide rods mounted parallel to the worktube
Temperature control Eurotherm 2604
Temperature sensor Thermocouple R
Power control Two Eurotherm TE10S Single Phase Thyristor
Power rating 6 kW
Temperature measurement for the sample
SCXI, National Instrument
Device SCXI Modular System,
Module SCXI-1125, 8- Channel isolated ampliﬁer
Terminal block SCXI-1320, general purpose terminal block with onboard
temperature sensor for measuring reference junction
temperature when using thermocouples
Control Device DAQ device PCI-MIO-16XE-50
Inaccuracy in cool junction sensor ± 1.6 °C
Nonlinearity ± 0.02% of full scale range (range ± 20 mV)
Maximum offset error ± 0.012 mV
V rsm K -1
Offset drift ± 21
Maximum gain error ± 0.08% (gain=250)
Gain drift ± 20 ppm/K
Normal mode rejection 4 Hz ﬁlter enable 60dB
Common mode rejection 4 Hz ﬁlter enable 160dB
Bandwidth 4 Hz, -3 dB
Filter type 3rd order butterworth
System noise 0.4
Total estimate error in measurement ± 3.4 K
Total inaccuracy using thermocouple S ± 7.3 K (at 1823 K)
Resistance measurement for the hot-wire
SourceMeter 2420, Keithley Instrument Inc.
Voltage measurement resolution 0.001 mV (range 200 mV)
Voltage measurement resolution 0.010 mV (range 2 V)
Voltage measurement accuracy ±0.224 mV (at 200 mV)
Voltage measurement accuracy ±0.540 mV (at 2 V)
Current source resolution 0.050 mA (range 1 A)
Current source resolution 0.150 mA (range 3 A)
Current source accuracy ±1.2 mA (at 1A)
Current source accuracy ±4.5 mA (at 3A)
Normal mode rejection 60dB (for 20 ms integration time)
Common mode rejection 120dB (for 20 ms integration time
Inaccuracy in thermal conductivity ± 3% ( at 300 K)
Peter Andersson and the
appointments and equipments
KIMAB is Europe’s leading corrosion and metals
research institute with around 130 employees.
The constant need of trade and industry for enhanced
knowledge and better understanding of materials and
processes is a very important part of our activity. Our
areas of operation (Materials and Processn Develop-
ment, Application of Materials and Corrosion) have
a central focus on, industrial users and their develop-
Research and development work takes place in close
cooperation with Swedish and international compa-
nies within the steel, metals, electronics, engineering,
paper, vehicle, manufactoring, plastics and power
industries. For custoners, our research work should be
a good investment for future revenue.
Korrosions- och Metallforskningsinstitutet AB (KIMAB)
Drottning Kristinas väg 48, 114 28 Stockholm, Sweden Member of the Group
Tel +46 8 440 48 00, Fax +46 8 440 45 35, www.kimab.com