Thermal conductivity measurement
Encyclopedia
There are a number of possible ways to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. Two classes of methods exist to measure the thermal conductivity of a sample: steady-state and non-steady-state methods.
In geology
and geophysics
, the most common method for consolidated rock samples is the divided bar. There are various modifications to these devices depending on the temperatures and pressures needed as well as sample sizes. A sample of unknown conductivity is placed between two samples of known conductivity (usually brass plates). The setup is usually vertical with the hot brass plate at the top, the sample in between then the cold brass plate at the bottom. Heat is supplied at the top and made to move downwards to stop any convection within the sample. Measurements are taken after the sample has reached to the steady state (with zero heat gradient or constant heat over entire sample), this usually takes about 10 minutes.
Non-steady-state methods to measure the thermal conductivity do not require the signal to obtain a constant value. Instead, the signal is studied as a function of time. The advantage of these methods are that they can in general be performed more quickly, since there is no need to wait for a steady-state situation. The disadvantage is that the mathematical analysis of the data is in general more difficult.
This same Transient Plane Source is able to test in two basic formats; sensor sandwiched between two pieces of same sample or single sided, where only one piece of sample is required.
The probe is a flat sensor with a continuous double spiral of electrically conducting nickel (Ni) metal etched out of thin foil and clad between two layers of polyimide
film Kapton
. The thin Kapton provides electrical insulation and mechanical stability to the sensor. The sensor is placed between the surfaces of two sample pieces of the sample to be measured. During the measurement a current passes through the nickel and creates an increase in temperature. The heat generated dissipates through the sample on either side of the sensor at a rate depending on the thermal transport characteristics of the material. By recording temperature vs. time response in the sensor, the characteristics of the material can be calculated.
The physical model behind this method is the infinite line source with constant power per unit length. The temperature profile 
at a distance 
at time 
is as follows
where
When performing an experiment, one measures the temperature at a point at fixed distance, and follows that temperature in time. For large times, the exponential integral can be approximated by making use of the following relation
where
This leads to the following expression
Note that the first term in the brackets on the RHS is a constant, while the second term goes as the inverse of time and therefore drops out fairly quickly. Thus if the probe temperature is plotted versus the natural logarithm of time, the thermal conductivity can be determined from the slope given knowledge of Q, if the initial data, before the diffusivity term becomes negligible, are ignored. Typically this means ignorming the first 60 to 120 seconds of data and measuring for 600 to 1200 seconds.
, C0 is constant. Thermal conductivity is determined by the linear slope of ΔT vs. log(ω) curve. The main advantages of the 3ω-method are minimization of radiation effects and easier acquisition of the temperature dependence of the thermal conductivity than in the steady-state techniques. Although some expertise in thin film patterning and microlithography is required, this technique is considered as the best pseudo-contact method available. (ch23)
can be used. For poor conductors of heat, Lees' disc method can be used.
Also
, determines if gems
are genuine diamond
s using diamond's uniquely high thermal conductivity.
Steady-state methods
In general, steady-state techniques perform a measurement when the temperature of the material measured does not change with time. This makes the signal analysis straightforward (steady state implies constant signals). The disadvantage is that a well-engineered experimental setup is usually needed.In geology
Geology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...
and geophysics
Geophysics
Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...
, the most common method for consolidated rock samples is the divided bar. There are various modifications to these devices depending on the temperatures and pressures needed as well as sample sizes. A sample of unknown conductivity is placed between two samples of known conductivity (usually brass plates). The setup is usually vertical with the hot brass plate at the top, the sample in between then the cold brass plate at the bottom. Heat is supplied at the top and made to move downwards to stop any convection within the sample. Measurements are taken after the sample has reached to the steady state (with zero heat gradient or constant heat over entire sample), this usually takes about 10 minutes.
Transient methods
The transient techniques perform a measurement during the process of heating up. The advantage is that measurements can be made relatively quickly. Transient methods are usually carried out by needle probes.Non-steady-state methods to measure the thermal conductivity do not require the signal to obtain a constant value. Instead, the signal is studied as a function of time. The advantage of these methods are that they can in general be performed more quickly, since there is no need to wait for a steady-state situation. The disadvantage is that the mathematical analysis of the data is in general more difficult.
Transient plane source method
Transient Plane Source Method, a plane sensor, a special mathematical model describing the heat conductivity, combined with precise electronics, enables the method to be used to measure Thermal Transport Properties. It covers a thermal conductivity range of 4–5 orders of magnitude and can be used for measuring various kinds of materials, such as solids, powder, liquid, paste and thin films etc. In 2008 it was approved as an ISO-standard for measuring thermal transport properties of polymers (November 2008). This TPS standard also covers the use of this method to test both isotropic as well anisotropic materials.This same Transient Plane Source is able to test in two basic formats; sensor sandwiched between two pieces of same sample or single sided, where only one piece of sample is required.
The probe is a flat sensor with a continuous double spiral of electrically conducting nickel (Ni) metal etched out of thin foil and clad between two layers of polyimide
Polyimide
Polyimide is a polymer of imide monomers. The structure of imide is as shown. Polyimides have been in mass production since 1955...
film Kapton
Kapton
Kapton is a polyimide film developed by DuPont which can remain stable in a wide range of temperatures, from -273 to +400 °C...
. The thin Kapton provides electrical insulation and mechanical stability to the sensor. The sensor is placed between the surfaces of two sample pieces of the sample to be measured. During the measurement a current passes through the nickel and creates an increase in temperature. The heat generated dissipates through the sample on either side of the sensor at a rate depending on the thermal transport characteristics of the material. By recording temperature vs. time response in the sensor, the characteristics of the material can be calculated.
Modified transient plane source (MTPS) method
A variation of the above method is the Modified Transient Plane Source Method (MTPS) developed by Nancy Mathis of the University of New Brunswick and commercialized through her company Mathis Instruments Ltd (now C-Therm Technologies Ltd.). The device uses a one-sided, interfacial, heat reflectance sensor that applies a momentary, constant heat source to the sample. The difference between this method and traditional transient plane source technique described above is that the heating element is supported on a backing, which provides mechanical support, electrical insulation and thermal insulation. This modification provides a one-sided interfacial measurement in offering maximum flexibility in testing liquids, powders, pastes and solids.Transient line source method
at a distance at time is as followswhere
-
is the powerPower (physics)In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
per unit length, in[ WWattThe watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
·mMetreThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
−1] -
is the thermal conductivityThermal conductivityIn physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
of the sample, in[ WWattThe watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
·mMetreThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
−1·KKelvinThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
−1] -
is the exponential integralExponential integralIn mathematics, the exponential integral is a special function defined on the complex plane given the symbol Ei.-Definitions:For real, nonzero values of x, the exponential integral Ei can be defined as...
, a transcendent mathematical function -
is the radial distance to the line source -
is the thermal diffusivityThermal diffusivityIn heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It has the SI unit of m²/s...
, in[ mMetreThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
2·sSecondThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
−1] -
is the amount of time that has passed since heating has started, in [ sSecondThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....]
When performing an experiment, one measures the temperature at a point at fixed distance, and follows that temperature in time. For large times, the exponential integral can be approximated by making use of the following relation
where
-
is the Euler gamma constant
This leads to the following expression
Note that the first term in the brackets on the RHS is a constant, while the second term goes as the inverse of time and therefore drops out fairly quickly. Thus if the probe temperature is plotted versus the natural logarithm of time, the thermal conductivity can be determined from the slope given knowledge of Q, if the initial data, before the diffusivity term becomes negligible, are ignored. Typically this means ignorming the first 60 to 120 seconds of data and measuring for 600 to 1200 seconds.
3ω-method
One popular technique for thermoelectric materials is a 3ω-method, in which thin metal strip evaporated on the sample acts as heat source and a thermometer. The heater is driven with AC current at frequency ω, which causes heat source to oscillate at frequency 2ω. By monitoring AC voltage as a function of the frequency of the applied AC current thermal conductivity can be determined. The measured voltage will contain both ω and 3ω components, because the Joule heating of the film causes small perturbation to its resistance with frequency 2ω as stated in the following equation, C0 is constant. Thermal conductivity is determined by the linear slope of ΔT vs. log(ω) curve. The main advantages of the 3ω-method are minimization of radiation effects and easier acquisition of the temperature dependence of the thermal conductivity than in the steady-state techniques. Although some expertise in thin film patterning and microlithography is required, this technique is considered as the best pseudo-contact method available. (ch23)Other methods
For good conductors of heat, Searle's bar methodSearle's bar method
Searle's bar method is a method of measuring thermal conductivity.Searle's bar method is an experimental procedure to measure thermal conductivity of material. A bar of material is being heated by steam on one side and the other side cooled down by water while the length of the bar is thermally...
can be used. For poor conductors of heat, Lees' disc method can be used.
Also
Thermoreflectance
Thermoreflectance is a method by which the thermal properties of a material can be measured, most importantly thermal conductivity. This method can be applied most notably to thin film materials (up to hundreds of nanometers thick), which have properties that vary greatly when compared to the same materials in bulk. The idea behind this technique is that once a material is heated up, the change in the reflectance of the surface can be utilized to derive the thermal properties. The reflectivity is measured with respect to time, and the data received can be matched to a model which contain coefficients that correspond to thermal properties.Measuring devices
A thermal conductance tester, one of the instruments of gemologyGemology
Gemology or gemmology is the science dealing with natural and artificial gems and gemstones. It is considered a geoscience and a branch of mineralogy...
, determines if gems
Gemstone
A gemstone or gem is a piece of mineral, which, in cut and polished form, is used to make jewelry or other adornments...
are genuine diamond
Diamond
In mineralogy, diamond is an allotrope of carbon, where the carbon atoms are arranged in a variation of the face-centered cubic crystal structure called a diamond lattice. Diamond is less stable than graphite, but the conversion rate from diamond to graphite is negligible at ambient conditions...
s using diamond's uniquely high thermal conductivity.
Standards
- EN 12667, "Thermal performance of building materials and products. Determination of thermal resistance by means of guarded hot plate and heat flow meter methods. Products of high and medium thermal resistance", ISBN 0-580-36512-3.
- ISO 8301, "Thermal insulation -- Determination of steady-state thermal resistance and related properties -- Heat flow meter apparatus" http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=15421
- ISO 8497, "Thermal insulation -- Determination of steady-state thermal transmission properties of thermal insulation for circular pipes", ISBN 0-580-26907-8 http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=15707
- ISO 22007-2:2008 "Plastics -- Determination of thermal conductivity and thermal diffusivity -- Part 2: Transient plane heat source (hot disc) method" http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=40683
- ISO 22007-2:2008 "Plastics -- Determination of thermal conductivity and thermal diffusivity -- Part 2: Transient plane heat source (hot disc) method" http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=40683
- IEEE Standard 442-1981, "IEEE guide for soil thermal resistivity measurements", ISBN 0-7381-0794-8. See also soil thermal propertiesSoil thermal propertiesThe thermal properties of soil are a component of soil physics that has found important uses in engineering, climatology and agriculture. These properties influence how energy is partitioned in the soil profile...
. http://ieeexplore.ieee.org/servlet/opac?punumber=2543
- IEEE Standard 98-2002, "Standard for the Preparation of Test Procedures for the Thermal Evaluation of Solid Electrical Insulating Materials", ISBN 0-7381-3277-2 http://ieeexplore.ieee.org/servlet/opac?punumber=7893
- ASTM Standard C518 - 10, "Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus" http://www.astm.org/Standards/C518.htm
- ASTM Standard D5334-08, "Standard Test Method for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe Procedure"
- ASTM Standard D5470-06, "Standard Test Method for Thermal Transmission Properties of Thermally Conductive Electrical Insulation Materials" http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/D5470.htm?E+mystore
- ASTM Standard E1225-04, "Standard Test Method for Thermal Conductivity of Solids by Means of the Guarded-Comparative-Longitudinal Heat Flow Technique" http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/E1225.htm?L+mystore+wnox2486+1189558298
- ASTM Standard D5930-01, "Standard Test Method for Thermal Conductivity of Plastics by Means of a Transient Line-Source Technique" http://www.astm.org/cgi-bin/SoftCart.exe/STORE/filtrexx40.cgi?U+mystore+wnox2486+-L+THERMAL:CONDUCTIVITY+/usr6/htdocs/astm.org/DATABASE.CART/REDLINE_PAGES/D5930.htm
- ASTM Standard D2717-95, "Standard Test Method for Thermal Conductivity of Liquids" http://www.astm.org/cgi-bin/SoftCart.exe/DATABASE.CART/REDLINE_PAGES/D2717.htm?L+mystore+wnox2486+1189564966
- Indian Standard 3346-1980, "Guarded Hot Plate Apparatus", Bureau of Indian Standards Institution, New Delhi, India.
External links
- An alternative traditional method using real thermometers is described at http://web.archive.org/web/20080528125725/http://www.uow.edu.au/eng/phys/200labs/phys235/badcon.pdf.
- A brief review of new methods measuring thermal conductivity, thermal diffusivityThermal diffusivityIn heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It has the SI unit of m²/s...
and specific heat within a single measurement is available at http://thermophys.savba.sk/Methods.htm.