The thermal conductivity is a physical size characterizing the behavior of materials at the time of the Transfer of heat by conduction. This constant appears for example in the Fourier analysis (see the thermal article Conduction). It represents the quantity of Chaleur transferred per unit of area and a unit from time under a Gradient from Température.

General information

In the international System of units, thermal conductivity is expressed in Watt S by Mètre - Kelvin, (W·m^-1·K^-1) where:

• Watt is the unit of power
• the meter is the unit of Length
• the Kelvin is the unit of Température

Conductivity depends mainly on:

*La natural of material,

*la temperature.

• Of other parameters like moisture, the pressure also intervene.

In general, thermal conductivity goes hand in hand with the electric Conductivité. For example, metals, good conducting of electricity are also of good thermal drivers. There are exceptions, most exceptional is that of the Diamant which has a raised thermal conductivity, between 1000 and 2600 W·m^-1·K^-1, whereas its electric conductivity is low.

From an atomic point of view, thermal conductivity is related to two types of behaviors:

* the movement of the charge carriers, electrons or holes.

* the oscillation of the Atom S around their position of balance.

In the metals, the movement of the free electrons is dominating whereas in the case of the non-metals, the vibration of the ions is most important.

Thermal conductivity is thus related on the one hand on the electric Conductivité (movement of the charge carriers) and to the structure even of the material (vibrations of the atoms). Indeed in a solid, the vibrations of the atoms are not random and independent from/to each other, but correspond to clean modes of vibration, such called “Phonon S” (one can make for example the analogy with a pendulum or a cord of guitar, whose frequency of vibration is fixed. These clean modes of vibration correspond to Onde S which can be propagated in material, if its structure is periodic (organized). This contribution will be thus more important in a Cristal, ordered, than in a Verre, disordered (from where for example the difference in conductivity thermal between the Diamant above and the Verre in the table).

Mathematically, thermal conductivity λ can of which to be written as the sum of two contributions:

$\backslash \; lambda=\; \backslash \; lambda\_e\; +\; \backslash \; lambda\_p\; \backslash ,$

where

* λ_e is the contribution of the charge carriers (electrons or holes)

* λ_p is the contribution of the vibrations of the atoms (Phonon S)

The contribution of the charge carriers is related to the electric Conductivité σ of material by the relation of Wiedemann-Franz:

$\backslash \; lambda\_e=LT\; \backslash \; sigma\; \backslash ,$

where L is called “Factor of Lorentz”. This number L depends on the processes of diffusion of the charge carriers (what corresponds more or less to the way in which they are obstructed by obstacles during their displacements, of also seeing Diffusion of the waves) as well as position of the Niveau of Fermi. In metals, it is equal to the number of Lorentz L₀, with:

$L\_0=\; \backslash \; frac\; \{\backslash \; pi^2\}\; \{3\}\; \backslash \; left\; (\backslash \; frac\; \{K\}\; \{E\}\; \backslash \; right)\; ^2=2,45.10^\; \{-\; 8\}\; V^2K^\; \{-\; 2\}\; \backslash ,$

where

*k is the Boltzmann constant

*e is the electron charge.

Orders of magnitude of thermal conductivities of some materials

If the Diamant has a very high thermal conductivity, that of natural blue diamond is even more. One can thus examine gems to determine if they are genuine diamonds by using a testing device of thermal conductivity, one of the standard instruments used in Gemmologie. Diamonds of any size appear always very cold with the touch because of their high thermal conductivity.

With equal density and moisture, coniferous timber is more conducting than broad leaved timber. The denser one wood is and the wetter it is, the more it is conducting.

Evolution with the temperature

Thermal conductivity evolves/moves with the temperature.

For the solids, she answers the following law:

$\backslash \; lambda=\; \backslash \; lambda\_0\; (1+\; have\; \backslash \; theta)\; \backslash ,$

where

*λ₀ is the thermal conductivity of material with 0°K

*a is a coefficient characteristic of each material

*θ is the temperature in Degree Celsius.

has is positive for heat insulators and negative for the thermal drivers.

When the temperature increases, an insulator loses its capacity of insulation and conversely a driver loses its capacity of conduction.

Evolution with moisture

For construction materials, it is current to use the following relation:

$\backslash \; lambda=\; \backslash \; lambda\_0\; e^\; \{0,08H\}\; \backslash ,$

where

* λ₀ is the thermal conductivity of dry material

* H is the relative humidity expressed as a percentage.

Measure thermal conductivity

Measure with the stationary state

The principle of the determination of the thermal conductivity of a material rests on the bond between the heat flow which crosses this material and the Gradient of temperature that it generates. It is illustrated on the following figure:

One of the ends of the sample of section has is fixed at a cold finger (thermal bath) whose role is to evacuate the heat flux crossing the sample, and the end opposed to a foot-warmer dissipating in the sample a electric output Q obtained by Joule effect, so as to produce a heat gradient according to the length of the sample. thermocouples separated by a distance L measure the difference in temperature dT along the sample. A third thermocouple, gauged, is also fixed at the sample to determine its average temperature (the temperature of measurement). Thermal conductivity is then given by:

$\backslash \; lambda=\; \backslash \; frac\; \{Q.L\}\; \{A.dT\}\; \backslash ,$

If dT is not too important (about 1°C), measured thermal conductivity is that corresponding to the average temperature measured by the third thermocouple. The principle of measurement rests then on the assumption that the totality of the heat flow passes by the sample. The measuring accuracy thus depends on the capacity to eliminate the thermal losses, that it is by thermal Conduction by wire, Convection by residual gas, Radiation by surfaces of the sample or losses in the foot-warmer: measurement is thus carried out under conditions Adiabatique S. To ensure the best possible precision, the sample which one wishes to measure thermal conductivity is thus placed in a vacuum measuring chamber (to minimize the convection). This room itself is wrapped in several heatshields whose temperature is controlled (in order to minimize the radiative effects). Lastly, the wire of the thermocouples are selected so as to conduct the least possible the heat.

Being given that it is all the more difficult to minimize the thermal losses that the temperature increases, this technique allows the measurement of thermal conductivity only temperatures lower than the room temperature (of 2 Kelvin S with 200 Kelvins without difficulties, and up to 300 Kelvins (27°C) for the best measuring devices).

Measure by the method known as “Laser Flash”

For the higher temperatures with the room temperature, it becomes increasingly difficult to eliminate or take account of the thermal losses by radiation (adiabatic conditions ), and the use of the technique to the stationary state presented above is not recommended. A solution is to measure the thermal Diffusivité instead of thermal conductivity. These two sizes are indeed bound by the relation:

$\backslash \; lambda\; (T)\; =a\; (T)\; D\; (T)\; C\_p\; (T)\; \backslash ,$

where

* λ (T) is thermal conductivity in mW.cm ^-1.K^-1

* has (T) is the thermal Diffusivité in cm².s^-1

* D (T) is the specific mass in g.cm ^-3

* C_p (T) is the specific heat in J.g^-1.K^-1

If it is supposed that the specific mass does not vary with the temperature, it is enough to measure thermal diffusivity and the specific heat to obtain a measurement of thermal conductivity at high temperature.

The following figure schematizes the equipment used for the thermal measurement of conductivity by the method known as “laser flash”:

A cylindrical sample of which the thickness D is definitely lower than its diameter is placed in a carry-sample which is inside a maintained furnace at constant temperature. One of its faces is illuminated by pulsate (about the millisecond) emitted by a Laser, which ensures a uniform heating of the front face. The temperature of the back face is measured, according to time, using a Capteur of measurement Infrarouge. In the absence of thermal losses of the sample, the temperature should increase in a monotonous way. In a real situation, the recorder will measure a peak of temperature followed by one return to the temperature of the furnace. Time T necessary so that the back face reaches half of the temperature of peak (compared to the temperature of the furnace), makes it possible to determine thermal diffusivity according to:

$\backslash \; mathfrak\; \{has\}\; =\; \backslash \; frac\; \{1,37.d^2\}\; \{T.\; \backslash \; pi^2\}\; \backslash ,$

It is then possible to calculate thermal conductivity thanks to the specific mass and the specific heat.

The difficulty of this technique lies in the choice of the optimum parameters of measurement (power of the laser and thickness of the sample).

Standards and payments

In France, were promulgated successive standards to encourage the builders with a maximum thermo isolation of the buildings. For example the standard RT 2000 then the standard RT 2005.

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