Measuring Thermal Conductivity

June 1, 2002
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Knowing a ceramic material’s thermal conductivity range can be key to obtaining an accurate measurement of its overall thermophysical properties.

Knowing a ceramic material's thermal conductivity can be key to obtaining the optimum performance for a particular application. Ceramic refractories are used as furnace linings because they both withstand the desired temperature and have high insulating capabilities, enabling manufacturers of heat-related products to reduce their energy consumption. Ceramic tiles are used in the heat shield of space shuttles because they can withstand extraordinary temperatures during re-entry into earth’s atmosphere, thereby preventing damage to essential components inside the spacecraft. In modern gas turbine power stations, ceramic coatings (typically stabilized zirconia) are used on the turbine blades to protect the blades against corrosion and to lower the thermal load on the metallic substrate material. And in the microelectronics industry, ceramics have become key components due to their ability to act as efficient heat sinks, preventing heat damage in integrated circuits and other electronic devices.

Further expanding the use of ceramic materials into heat-related markets requires accurate measurement of their thermophysical characteristics. While a number of new testing methods and systems have been developed over the past several decades, not every method is suitable for every application. To achieve accurate values, the right test method must be selected based on the thermal conductivity range of the material and the sample configuration.

Theoretical Basis and Definitions

Heat can be transferred to a medium in three different ways: convection, radiation and conduction. Convection is primarily used for fluids and gases and does not play an important role in heating solids and porous materials.

Heat transfer by radiation has to be considered for translucent or transparent ceramic materials, especially at high temperatures. Besides the optical properties of the material, boundary conditions can also influence the heat transfer in a part. Details of radiative heat transfer have been published elsewhere.1

Equation 1.
Conductive heat transfer is the most important transfer mechanism for ceramic materials and is based on the thermal conductivity of a material—its ability to conduct heat energy. 2 The conductive heat transfer of an infinite extended panel with a thickness of x can be described by the Fourier equation (for one-dimensional heat transfer) (Equation 1), where Q is the heat flow per surface area generated by the temperature gradient (DT) over the thickness (Dx). Both factors are connected by the thermal conductivity (l). In the case of a fixed temperature gradient and fixed geometry (stationary conditions), the thermal conductivity indicates how much energy is required to maintain the temperature gradient.

Equation 2.
When characterizing building materials (such as brick) and insulation, the k-factor is often used. The k-factor refers to the ratio of thermal conductivity and the thickness of a component, as shown in Equation 2. This factor does not refer to the classification of a material but to the final part with a defined thickness.

In modern electronic components and ceramics used for heat sinks, dynamic (transient) processes often occur. Describing these dynamic heat transfer phenomena requires a more complex mathematical model that will not be discussed here.

Measuring Devices

A variety of methods and instruments can be used to determine thermal conductivity. Instruments that use the steady-state conditions described in the Fourier equation are primarily suitable for analyzing materials with low or average thermal conductivities at moderate temperatures. Instruments based on dynamic (transient) methods, such as the hot-wire or flash diffusivity methods, are used to characterize materials with a high thermal conductivity and/or for measurements at high temperatures.

Figure 1. This modern heat flow meter (the NETZSCH HFM 436 Lambda) can be used to analyze materials with low or average thermal conductivities at moderate temperatures.

Steady-State Methods

Heat Flow Meters. For this process, a square sample with a well-defined thickness (usually 30 cm in length and width and 10 cm thick) is inserted between two plates, and a fixed temperature gradient is established. The heat flow through the sample is measured with calibrated heat flow sensors that are in contact with the sample at the plate interface. The thermal conductivity is determined by measuring the thickness, the temperature gradient and the heat flow through the sample.

Figure 1 shows a modern heat flow meter. Samples can be up to 10 cm thick with a length and width between 30 and 60 cm. This method can successfully test materials with thermal conductivities between 0.005 and 0.5 W/m◊K and is typically used to determine the thermal conductivities and k-factors of fiberglass insulation or insulation boards. Depending on the type of instrument used, measurements between -20 and 100?C are possible. Advantages of this method include easy handling, accurate test results and fast measurements, while disadvantages include its limited temperature and measurement range.

Guarded Heat Flow Meters. For larger samples that require a higher measurement range, guarded heat flow meters can be used. The measurement principle is nearly the same as with regular heat flow meters, but the test section is surrounded by a guard heater, resulting in higher measurement temperatures. Additionally, higher thermal conductivities can be measured with this method.

Figure 2. The thermal conductivity of both marble and cellular concrete at 45 and 65C, measured using a guarded heat flow meter.
Figure 2 shows the thermal conductivities of a cellular concrete and a marble sample at 45C and 65C measured with a guarded heat flow meter. It can clearly be seen that the thermal conductivity of both materials decreases with temperatures. The thermal conductivity of the cellular concrete is on a much lower level compared to the dense marble material. Due to its high thermal conductivity, the marble tested here is ideally suited for a floor heating system in a house.

Figure 3. The schematic structure of a (guarded) hot-plate apparatus.
Guarded Hot-Plate Instruments. The hot-plate or guarded hot-plate apparatus uses an operating principle similar to the heat flow meter with hot and cold plates. The basic design of a guarded hot plate system is shown in Figure 3. The heat source is positioned in the center between two samples of the same material. Two samples are used to guarantee symmetrical heat flow upward and downward, as well as complete absorption of the heater’s energy by the test samples. A well-defined power is put into the hot plate during the test. The measurement temperatures and temperature gradient are adjusted between the heat source and the auxiliary plates by adjusting the power input into the auxiliary heaters. The guard heater(s) around the hot plate and the sample set-up guarantee a linear, one-dimensional heat flow from the hot plate to the auxiliary heaters. The auxiliary heaters are in contact with a heat sink to ensure heat removal and improved control. By measuring the power input into the hot plate, the temperature gradient and the thickness of the two samples, the thermal conductivity can be determined according to the Fourier equation.

Figure 4. The thermal conductivity of a mineral fiber insulation versus packing density, measured using a guarded hot plate.
The advantages of guarded hot plates compared to the heat flow meters are their broader temperature range (-180 to 650C) and measuring range (up to 2 W/mK). Additionally, the guarded hot-plate technique is an absolute measurement technique—no calibration of the unit is required.

Figure 4 shows the thermal conductivity of a fiberboard material versus packing density. It can clearly be seen that the thermal conductivity increases with lower densities. This can be explained by the increased radiative and/or convective heat transfer. At 18 kg/m3, a minimum is visible in the thermal conductivity, representing the optimum packing value for this kind of material. At densities above 18 kg/m3, the thermal conductivity increases again. Here, the contribution of the thermal conductivity in the fibers becomes increasingly dominant.

Dynamic (Transient) Measuring Methods

Transient measuring methods have become established in the last few decades for studying materials with high thermal conductivities and for taking measurements at high temperatures. Besides their high precision and broad measuring range, transient methods feature a comparably simple sample preparation and the ability to measure up to 2000C.

Hot-Wire Method. In the hot-wire method, a wire is embedded in a sample, generally a large brick. During the test run, a constant heating power is applied to this wire, causing the temperature of the wire to rise. The temperature increase is measured versus time at the heating wire itself or at a well-defined distance parallel to the wire. Because this measurement depends on the thermal conductivity of the tested materials, it provides an evaluation of this thermal conductivity.

Various methods can be used to measure the temperature rise of the wire. With the cross-wire method, the temperature increase is measured with a thermocouple that is directly welded onto the hot wire. With the parallel-wire method, the temperature increase is measured in a defined distance to the hot wire. With the T(R)-method, the heating wire itself is used to measure the temperature increase. Here, the well-known correlation between the electrical resistance of the hot wire (which is typically platinum) and the temperature is used.

The magnitude of the thermal conductivity to be measured is an important consideration in selecting the right method. The cross-wire method is suitable for measuring thermal conductivities below 2 W/mK, while the T(R) and parallel-wire methods are used for materials with higher thermal conductivities (15 and 20 W/mK, respectively).

Some instruments allow the use of all three methods. In one such instrument,* tests can be carried out between room temperature and 1500C. During the tests, the sample is brought to the required temperature. After the sample temperature has stabilized, the hot wire test can be run. This method provides the ability to measure large samples and characterize inhomogeneous ceramic materials and refractory products.

Figure 5. The thermal conductivity of various refractory materials versus temperature, measured using a hot-wire instrument (the NETZSCH TCT 426).
Figure 5 shows the thermal conductivity of various refractory materials versus temperature. All of the samples were measured using different measurement techniques. At room temperature, the magnesium oxide and alumina bricks show a thermal conductivity of around 10 W/mK and/or slightly below. The thermal conductivity of these materials decreases with increasing temperature. The fireclay brick has a thermal conductivity of approximately 1 W/mK at room temperature. Here, a slight rise in the increasing temperature can be detected. In turn, the calcium silicate brick shows the lowest thermal conductivity. In this case, a comparably larger increase of the results versus temperature can be seen.

This example shows that materials that exhibit low room-temperature thermal conductivity will not necessarily exhibit low thermal conductivity at the application temperature. For this reason, it is important to determine the thermal conductivity versus application temperature when evaluating a refractory material.

Flash Diffusivity Method. Another technique that can be used to investigate highly conductive materials and/or samples with small dimensions is the flash diffusivity method, also known as the laserflash method.3 This method directly measures the thermal diffusivity of a material. If the specific heat and density of the sample are known, thermal conductivity can be determined. The specific heat can be directly measured with flash diffusivity using a comparative method; however, a differential scanning calorimeter is recommended to obtain the highest accuracies. Density and/or density alteration subject to temperature can be determined using dilatometry.4

Using the flash diffusivity method, a plane-parallel sample is run in a furnace to the required test temperature. Afterwards, the front surface of the sample is heated with a short (<1 ms) light pulse produced by a laser or a flash lamp. The heat diffuses through the sample, leading to a temperature rise on the sample’s rear surface. This temperature rise is measured versus time with an infrared detector. It is important to note that only the time-dependent behavior of the measuring signal is decisive, not its height.

Figure 6. The schematic design of a modern laserflash apparatus (the NETZSCH LFA 427).
A schematic of a modern laserflash apparatus is shown in Figure 6.5 The head of an Nd:GGG-laser is positioned in the lower part of the instrument and generates pulses with lengths between 0.2 and 1.2 ms and energies of up to 25 J. The sample is located on a sample holder in the center of a tube furnace. Depending on the furnace type, the sample can be run at temperatures up to 2000?C (graphite furnace). The temperature rise at the rear surface is determined using an InSb-detector, which is located on top of the system. The vertical construction allows a good signal-to-noise ratio, as well as a high flexibility in the sample shape. The design of this instrument enables it to measure liquids and powders, as well as solid samples with different geometries.

Figure 7. This flash diffusivity instrument (the NETZSCH LFA 437 Microflash®) can be used to analyze ceramic materials that are used as heat sinks or packaging in the electronics industry.
Figure 7 shows another flash diffusivity instrument that can be used to analyze ceramic materials that are used as heat sinks or packaging in the electronics industry. This system is used at much lower temperatures of up to 300C.

Due to its high precision (<3 %) and the small necessary sample geometries, the flash diffusivity method has entered many areas of research and development and quality control in the production of ceramic materials. The success of this method is mainly due to its short measurement times—the instruments can go from room temperature up to 2000?C in less than one day. The flash diffusivity technique can be applied to materials ranging from pressed fiberboards, with thermal conductivities of less than 0.05 W/mK, to diamond, which can have thermal conductivity of more than 2000 W/mK. This method can also be used to measure multilayer-systems, such as the characterization of thermal barrier coatings on turbine blades.

Figure 8. The thermal diffusivity and thermal conductivity of silicon carbide-filled MoSi2 between room temperature and 1300C, measured using flash diffusivity.
Figure 8 shows the temperature diffusivity and thermal conductivity of a molybdenum disilicide (MoSi2) sample, a material that is often used as a heating element for high-temperature furnaces. The specific heat required for the thermal conductivity determination was measured using a differential scanning calorimeter.** It can clearly be seen that both the thermal diffusivity and thermal conductivity decrease sharply with increasing temperature. The thermal conductivity drops by approximately 50% over the test temperature range. Such behavior has to be considered in the application of the material to avoid problems such as inhomogeneous temperature profiles inside a furnace equipped with MoSi2 heating elements.

Thermophysical properties such as thermal diffusivity and thermal conductivity often play an important role in the application of ceramic materials. These properties must be measured accurately to avoid quality problems and to ensure the continued market expansion of ceramic products in heat-related applications. While many different methods are available to measure these data with high precision, the material’s expected range of thermal conductivity must be considered to ensure that the right measurement method is used.

For More Information

For more information about measuring thermal conductivity, contact NETZSCH-Geratebau GmbH, Wittelsbacherstr. 42 95100 Selb/Bavaria, Germany; (49) 9287-881-49; fax (49) 9287-881-44; e-mail j.blumm@ngb.netzsch.com; or visit http://www.ngb.netzsch.com. (U.S. contact: NETZSCH Instruments, Inc., 37 North Ave., Burlington, MA 01803; (781) 272-5353; fax (781) 272-5225; e-mail info@netzsch.net; http://www.e-Thermal.com.)

*The NETZSCH TCT 426.
**The NETZSCH DSC 404 C.

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