Thermal conductivity

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Fire test used to test the heat transfer through firestops and penetrants used in construction listing and approval use and compliance.

In physics, thermal conductivity, $k$, is the property of a material that indicates its ability to conduct heat. It appears primarily in Fourier's Law for heat conduction.

Conduction is the most significant means of heat transfer in a solid. By knowing the values of thermal conductivities of various materials, one can compare how well they are able to conduct heat. The higher the value of thermal conductivity, the better the material is at conducting heat. On a microscopic scale, conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring atoms. In insulators the heat flux is carried almost entirely by phonon vibrations.

Mathematical background

First, heat conduction can be defined by the formula:

$H={\frac {\Delta Q}{\Delta t}}=k\times A\times {\frac {\Delta T}{x}}$

where ${\frac {\Delta Q}{\Delta t}}$ is the rate of heat flow, k is the thermal conductivity, A is the total surface area of conducting surface, ΔT is temperature difference and x is the thickness of conducting surface separating the two temperatures.

Thus, rearranging the equation gives thermal conductivity,

$k={\frac {\Delta Q}{\Delta t}}\times {\frac {1}{A}}\times {\frac {x}{\Delta T}}$

(Note: ${\frac {\Delta T}{x}}$ is the temperature gradient)

In other words, it is defined as the quantity of heat, ΔQ, transmitted during time Δt through a thickness x, in a direction normal to a surface of area A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient.

Alternately, it can be thought of as a flux of heat (energy per unit area per unit time) divided by a temperature gradient (temperature difference per unit length)

$k={\frac {\Delta Q}{A\times {}\Delta t}}\times {\frac {x}{\Delta T}}$

Typical units are SI: W/(m·K) and English units: Btu·ft/(h·ft²·°F). To convert between the two, use the relation 1 Btu·ft/(h·ft²·°F) = 1.730735 W/(m·K).

Examples

In metals, thermal conductivity approximately tracks electrical conductivity according to the Wiedemann-Franz law, as freely moving valence electrons transfer not only electric current but also heat energy. However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of phonon carriers for heat in non-metals. As shown in the table below, highly electrically conductive silver is less thermally conductive than diamond, which is an electrical insulator.

Thermal conductivity depends on many properties of a material, notably its structure and temperature. For instance, pure crystalline substances exhibit very different thermal conductivities along different crystal axes, due to differences in phonon coupling along a given crystal axis. Sapphire is a notable example of variable thermal conductivity based on orientation and temperature, for which the CRC Handbook reports a thermal conductivity of 2.6 W/(m·K) perpendicular to the c-axis at 373 K, but 6000 W/(m·K) at 36 degrees from the c-axis and 35 K (possible typo?).

Air and other gases are generally good insulators, in the absence of convection. Therefore, many insulating materials function simply by having a large number of gas-filled pockets which prevent large-scale convection. Examples of these include expanded and extruded polystyrene (popularly referred to as "styrofoam") and silica aerogel. Natural, biological insulators such as fur and feathers achieve similar effects by dramatically inhibiting convection of air or water near an animal's skin.

Thermal conductivity is important in building insulation and related fields. However, materials used in such trades are rarely subjected to chemical purity standards. Several construction materials' k values are listed below. These should be considered approximate due to the uncertainties related to material definitions.

The following table is meant as a small sample of data to illustrate the thermal conductivity of various types of substances. For more complete listings of measured k-values, see the references.

List of thermal conductivities

This is a list of approximate values of thermal conductivity, k, for some common materials. Please consult the list of thermal conductivities for more accurate values, references and detailed information.

Material	Thermal conductivity W/(m·K)
Cement, portland	0.29
Concrete, stone	1.7
Air	0.025
Wood	0.04 - 0.4
Alcohols and oils	0.1 - 0.21
Silica Aerogel	0.004-0.03
Soil	1.5
Rubber	0.16
Epoxy (unfilled)	0.19
Epoxy (silica-filled)	0.30
Water (liquid)	0.6
Thermal grease	0.7 - 3
Thermal epoxy	1 - 4
Glass	1.1
Ice	2
Sandstone	2.4
Stainless steel	12.11 ~ 45.0
Lead	35.3
Aluminum	237
Gold	318
Copper	401
Silver	429
Diamond	900 - 2320
LPG	0.23 - 0.26

Measurement

Generally speaking, there are a number of possibilities to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. There can be made a distinction between steady-state and transient techniques.

In general the steady-state techniques perform a measurement when the temperature of the material that is measured does not change with time. This makes the signal analysis straight forward (steady state implies constant signals). The disadvantage generally is that it takes a well-engineered experimental setup. The Divided Bar (various types) is the most common device used for consolidated rock samples.

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 (inserted into samples or plunged into the ocean floor).

For good conductors of heat, Searle's bar method can be used. For poor conductors of heat, Lees' disc method can be used. An alternative traditional method using real thermometers can be used as well. A thermal conductance tester, one of the instruments of gemology, determines if gems are genuine diamonds using diamond's uniquely high thermal conductivity.

Standard Measurement Techniques

• IEEE Standard 442-1981, "IEEE guide for soil thermal resistivity measurements" see als soil_thermal_properties.), area A and thickness L:

• thermal conductance = k/L, measured in W·K⁻¹·m⁻²;
• thermal resistance (R value) = L/k, measured in K·m²·W⁻¹;
• thermal transmittance (U value) = 1/(Σ(L/k)) + convection + radiation, measured in W·K⁻¹·m⁻².

Textile industry

In textiles, a tog value may be quoted as a measure of thermal resistance in place of a measure in SI units.

Origins

The thermal conductivity of a system is determined by how atoms comprising the system interact. There are no simple, correct expressions for thermal conductivity. There are two different approaches for calculating the thermal conductivity of a system.

The first approach employs the Green-Kubo relations. Although this employs analytic expressions which in principle can be solved, in order to calculate the thermal conductivity of a dense fluid or solid using this relation requires the use of molecular dynamics computer simulation.

The second approach is based upon the relaxation time approach. Due to the anharmonicity within the crystal potential, the phonons in the system are known to scatter. There are three main mechanisms for scattering (Srivastava, 1990):

• Boundary scattering, a phonon hitting the boundary of a system;
• Mass defect scattering, a phonon hitting an impurity within the system and scattering;
• Phonon-phonon scattering, a phonon breaking into two lower energy phonons or a phonon colliding with another phonon and merging into one higher energy phonon.

See also

• Heat
• Specific heat
• Specific heat capacity
• Thermal bridge
• Thermistor
• Thermocouple
• Electrical conductivity

References

ISBN links support NWE through referral fees

• Baierlein, Ralph. 2003. Thermal Physics. Cambridge: Cambridge University Press. ISBN 0521658381.

• Halliday, David, Robert Resnick, and Jearl Walker. 1997. Fundamentals of Physics. 5th ed. New York: Wiley. ISBN 0471105589.

• Serway, Raymond A. and John W. Jewett. 2004. Physics for Scientists and Engineers. Belmont, CA: Thomson-Brooks/Cole. ISBN 0534408427.

• Srivastava, G. P. 1990. The Physics of Phonons. Bristol: A. Hilger. ISBN 0852741537.

• Young, Hugh D. and Roger A. Freedman. 2003. Physics for Scientists and Engineers. San Fransisco, CA: Pearson. ISBN 080538684X.

External links

• Table with the Thermal Conductivity of the Elements
• http://physics.nist.gov/Pubs/SP811/appenB9.html
• http://www.npl.co.uk/thermal/faq_index.html#heat%20transfer%20property thermophysics FAQ5
• http://www.ornl.gov/roofs+walls/research/detailed_papers/rastra/dynamic.htm
• http://www.tak2000.com/data2.htm
• http://thermophys.savba.sk
• Calculation of the Thermal Conductivity of Glass Calculation of the Thermal Conductivity of Glass at Room Temperature from the Chemical Composition
• http://www.mathisinstruments.com/index.asp?pathinfo=/html/content/technology/tech_glossary.asp&dbbypass=
• Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air

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