Determination of thermal conductivity for metals

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					Determination of
thermal conductivity
for metals, alloys and
ceramics from room
temperature up to
723 °C and for
electrically insulating
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
                                 the sample.
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-
wire method.
Theoretical background
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
                                   2 ∞
                                    −                     2
∆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.

Measuring device.
Experimental arrangement
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.

Measurement device
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
the screen.
Technical data
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,
Chassis                                 SCXI-1000
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
                                              ì    rsm
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
measuring unit.
   World-leading research,
appointments and equipments

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