Thermal conductivity (often denoted k, λ, or κ) is the property of a material to conduct heat. It is evaluated primarily in terms of the Fourier’s Law for heat conduction. In general, thermal conductivity is a tensor property, expressing the anisotropy of the property.
Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications and materials of low thermal conductivity are used as thermal insulation. The thermal conductivity of a material may depend on temperature. The reciprocal of thermal conductivity is called thermal resistivity.
Units of thermal conductivity[edit]
In the International System of Units (SI), thermal conductivity is measured in watts per meter-kelvin (W/(m⋅K)). The dimension of thermal conductivity is M1L1T−3Θ−1, expressed in terms of the dimensions mass (M), length (L), time (T), and temperature (Θ). In Imperial units, thermal conductivity is measured in BTU/(hr⋅ft⋅°F).[note 1][1]
Other units which are closely related to the thermal conductivity are in common use in the construction and textile industries. The construction industry makes use of units such as the R-value (resistance) and the U-value (transmittance). Although related to the thermal conductivity of a material used in an insulation product, R- and U-values are dependent on the thickness of the product.[note 2]
Likewise the textile industry has several units including the tog and the clo which express thermal resistance of a material in a way analogous to the R-values used in the construction industry.
Measurement[edit]
There are a number of ways to measure thermal conductivity. Each of these is suitable for a limited range of materials, depending on the thermal properties and the medium temperature. There is a distinction between steady-state and transient techniques.
In general, steady-state techniques are useful when the temperature of the material 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. The Divided Bar (various types) is the most common device used for consolidated rock solids.
Thermal conductivity is important in material science, research, electronics, building insulation and related fields, especially where high operating temperatures are achieved. Several materials are shown in the list of thermal conductivities. These should be considered approximate due to the uncertainties related to material definitions.
High energy generation rates within electronics or turbines require the use of materials with high thermal conductivity such as copper (see: Copper in heat exchangers), aluminium, and silver. On the other hand, materials with low thermal conductance, such as polystyrene and alumina, are used in building construction or in furnaces in an effort to slow the flow of heat, i.e. for insulation purpose
The reciprocal of thermal conductivity is ‘thermal resistivity’, usually expressed in kelvin-meters per watt (K⋅m⋅W−1). For a given thickness of a material, that particular construction’s thermal resistance and the reciprocal property, thermal conductance, can be calculated. Unfortunately, there are differing definitions for these terms.
Thermal conductivity, k, often depends on temperature. Therefore, the definitions listed below make sense when the thermal conductivity is temperature independent. Otherwise a representative mean value has to be considered; for more, see the equations section below.
Conductance[edit]
For general scientific use, thermal conductance is the quantity of heat that passes in unit time through a plate of particular area and thickness when its opposite faces differ in temperature by one kelvin. For a plate of thermal conductivity k, area A and thickness L, the conductance calculated is kA/L, measured in W⋅K−1 (equivalent to: W/°C). ASTM C168-15, however, defines thermal conductance as “time rate of steady state heat flow through a unit area of a material or construction induced by a unit temperature difference between the body surfaces” and defines the units as W/(m2⋅K) (Btu/(h⋅ft2⋅°F))[2]
The thermal conductance of that particular construction is the inverse of the thermal resistance. Thermal conductivity and conductance are analogous to electrical conductivity(A⋅m−1⋅V−1) and electrical conductance (A⋅V−1).
There is also a measure known as heat transfer coefficient: the quantity of heat that passes in unit time through a unit area of a plate of particular thickness when its opposite faces differ in temperature by one kelvin. The reciprocal is thermal insulance. In summary:
- thermal conductance = kA/L, measured in W⋅K−1 or in ASTM C168-15 as W/(m2⋅K)[2]
- thermal resistance = L/(kA), measured in K⋅W−1 (equivalent to: °C/W)
- heat transfer coefficient = k/L, measured in W⋅K−1⋅m−2
- thermal insulance = L/k, measured in K⋅m2⋅W−1.
The heat transfer coefficient is also known as thermal admittance in the sense that the material may be seen as admitting heat to flow.
Resistance[edit]
Thermal resistance is the ability of a material to resist the flow of heat.
Thermal resistance is the reciprocal of thermal conductance, i.e., lowering its value will raise the heat conduction and vice versa.
When thermal resistances occur in series, they are additive. Thus, when heat flows consecutively through two components each with a resistance of 3 °C/W, the total resistance is 3 °C/W + 3 °C/W = 6 °C/W.
A common engineering design problem involves the selection of an appropriate sized heat sink for a given heat source. Working in units of thermal resistance greatly simplifies the design calculation. The following formula can be used to estimate the performance:
- {\displaystyle R_{hs}={\frac {\Delta T}{P_{th}}}-R_{s}}
where:
- Rhs is the maximum thermal resistance of the heat sink to ambient, in °C/W (equivalent to K/W)
- ΔT is the required temperature difference (temperature drop), in °C
- Pth is the thermal power (heat flow), in watts
- Rs is the thermal resistance of the heat source, in °C/W
For example, if a component produces 100 W of heat, and has a thermal resistance of 0.5 °C/W, what is the maximum thermal resistance of the heat sink? Suppose the maximum temperature is 125 °C, and the ambient temperature is 25 °C; then ΔT is 100 °C. The heat sink’s thermal resistance to ambient must then be 0.5 °C/W or less (total resistance component and heat sink is then 1.0 °C/W).
Transmittance[edit]
A third term, thermal transmittance, sub way the thermal conductance of a structure along with heat transfer due to convection and radiation. It is measured in the same units as thermal conductance and is sometimes known as the composite thermal conductance. The term U-value is often used.
Admittance[edit]
The thermal admittance of a material, such as a building fabric, is a measure of the ability of a material to transfer heat in the presence of a temperature difference on opposite sides of the material. Thermal admittance is measured in the same units as a heat transfer coefficient, power (watts) per unit area (square meters) per temperature change (kelvins). Thermal admittance of a building fabric affects a building’s thermal response to variation in outside temperature.[3]
Co-efficient of thermal conductivity: The co-efficient of thermal conductivity of the material of a substance is numerically equal to the quantity of heat that conducts in one second normally through a slab of unit length and unit area, the difference of temperature between its end faces being one degree.
Influencing factors[edit]
Effect of temperature on thermal conductivity[edit]
The effect of temperature on thermal conductivity is different for metals and nonmetals. In metals, heat conductivity is primarily due to free electrons. Following the Wiedemann–Franz law, thermal conductivity of metals is approximately proportional to the absolute temperature (in kelvins) times electrical conductivity. In pure metals the electrical conductivity decreases with increasing temperature and thus the product of the two, the thermal conductivity, stays approximately constant. However, as temperatures approach absolute zero, the thermal conductivity decreases sharply.[4] In alloys the change in electrical conductivity is usually smaller and thus thermal conductivity increases with temperature, often proportionally to temperature. Many pure metals have a peak thermal conductivity between 2 K and 10 K.
On the other hand, heat conductivity in nonmetals is mainly due to lattice vibrations (phonons). Except for high quality crystals at low temperatures, the phonon mean free path is not reduced significantly at higher temperatures. Thus, the thermal conductivity of nonmetals is approximately constant at high temperatures. At low temperatures well below the Debye temperature, thermal conductivity decreases, as does the heat capacity, due to carrier scattering from defects at very low temperatures.[4]
Chemical phase[edit]
When a material undergoes a phase change from solid to liquid or from liquid to gas the thermal conductivity may change. An example of this would be the change in thermal conductivity that occurs when ice (thermal conductivity of 2.18 W/(m⋅K) at 0 °C) melts to form liquid water (thermal conductivity of 0.56 W/(m⋅K) at 0 °C).[5]
Thermal anisotropy[edit]
Some substances, such as non-cubic crystals, can exhibit 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, with 35 W/(m⋅K) along the C-axis and 32 W/(m⋅K) along the A-axis.[6]Wood generally conducts better along the grain than across it. Other examples of materials where the thermal conductivity varies with direction are metals that have undergone heavy cold pressing, laminated materials, cables, the materials used for the Space Shuttle thermal protection system, and fiber-reinforced composite structures.[7]
When anisotropy is present, the direction of heat flow may not be exactly the same as the direction of the thermal gradient.
Electrical conductivity[edit]
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. Highly electrically conductive silver is less thermally conductive than diamond, which is an electrical insulator, but due to its orderly array of atoms it is conductive of heat via phonons.
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, as well as warm clothes. Natural, biological insulators such as fur and feathers achieve similar effects by dramatically inhibiting convection of air or water near an animal’s skin.
Light gases, such as hydrogen and helium typically have high thermal conductivity. Dense gases such as xenon and dichlorodifluoromethanehave low thermal conductivity. An exception, sulfur hexafluoride, a dense gas, has a relatively high thermal conductivity due to its high heat capacity. Argon and krypton, gases denser than air, are often used in insulated glazing (double paned windows) to improve their insulation characteristics
