# What does thermal conductivity mean?

**Thermal conductivity is one kind of heat transfer. Heat can be tranferred by three mechanisms:**

- Radiation
- Convection
- Thermal conductivity

## Radiation

One mechanism of heat transfer is by radiation which is by transmitting electromagnetic waves. This mechanism is well know „feeling“ the heat of a radiator or during sunshine. Radiation does not need the presence of any material due to tha fact that electromagnetic waves can propagate in vacuum.

Radiation emitted by a black body is described by Boltzmann’s law :

## Convection

The second mechanism of heat transfer is convection. Convection is related to a bulk movement of particles and thus related to fluids (gases and liquids). It’s a major driving force in meteorology: wind beeing a convection of air masses in the atmosphere.

## Thermal conductivity

Thermal conductivity describes the ability to conduct heat without the transport of particles or electromagnetic waves. It needs the presence of a material and is the predominant mechanism in solids. Heat is transmitted by vibrations of molecules, atoms or ions and their random collisions (Brownian motion ; lattice vibrations = phononic contribution) and by freely moving electrons (electronic contribution). In thermally and electrically isolating materials the phononic contribution, in conducting materials like metals the electronic contribution is predominant.

In metals electric conductivity and thermal conductivity are both dominated by the electronic contribution so that Wiedemann-Franz law is followed, saying that thermal conductivity diveded by electrial conductivity is propartional to the absolute temperature, Lorenz number beeing the proportionality constant:

In general parlance thermal conductivity is the amount of heat that flows within 1 second through a 1x1x1m cube of a material if there is a temperature gradient of exactly 1 K between two opposite sides.

## Thermal diffusivity

Sometimes there is some confusion about thermal diffusivity and thermal conductivit. Thermal conductivity describes the propagation of heat in a material while thermal diffusivity describes the propagation of a temperature difference. Both properties are related by the following formula:

This makes thermal conductivity become a characteristic material property with its own symbol (λ – „lambda“) and its own SI-unit W/mK. Its reciprocal value is the specific heat resistance.

**Some figures :**

Gases and isolating materials have low thermal conductivities in the range of 0 to 1 W/mK (air : 0.026 W/mK ; EPS (expanded polystryrene) : 0.035-0.050 W/mK ; polymers like PE, PP, PMMA etc : 0.1 – 0.2 W/mK).

Most liquids have thermal conductivities in the range of 0.1 to 0.6 W/mK (polar liquids having higher conductivities than apolar ones; water : 0.6 W/mK).

Metals have high thermal (and electrical conductivities) varying from some W/mK to some hundreds W /mK, silver and copper having the highest conductivities (> 400 W/mK).

The highest published thermal conductivities are those of diamond and graphene with values of >> 1000 W/mK (some papers metionning > 5000 W/mK for graphene).

**Scientific Definition**

The scientific definition of thermal conductivity claims it as the material property that describes the transport of heat within a sample. For each sample temperature it is obtained from the product of density, thermal diffusivity and specific heat capacity at that temperature (equation 1) and can be described as the negative quotient of heat flow density and temperature gradient (equation 2). The example in (Equation 3) is for illustration.

λ= ρ* c_{p}*α (1)

λ = thermal conductivity, ρ = density, c

_{p}= spez. heat capacity, α = thermal diffusivity

λ=-q/∆T (2)λ = thermal conductivity, q = average heat flow density, ∆T = temperature gradient

If this definition is used to consider for example a cylindrical sample, the following calculations can be done: If an ideal, homogeneous cylinder with the length l and the constant cross section A is considered which is isolated at its side and can only have a temperature change at its two ends, the temperature gradient over its length is (∆T )/l. The density of the heat flow with direction from hot to cold side is λ*(∆T )/l. So considering the cross section A, there is a heat flow Q that can be calculated using (equation 3):

Q = (A*λ*∆T)/l (3)λ = thermal conductivity, Q = heat flow, ∆T = temperature gradient, A = cross section, l = length

**Thermal conductivity measurement (methods):**

Due to these facts, there are several direct and indirect methods to determine the thermal conductivity. The most established procedures are on the one hand the measurement of thermal diffusivity using Laser Flash method or Thin Film Laser Flash method. Therefore the sample thickness and especially the specific heat capacity of the sample has to be determined which is mostly done by Differential Scanning Calorimetry – DSC.

From these results the thermal conductivity can be calculated. On the other hand there are direct methods like hot wire methods, for example the THB measurement that detects the power of a heating element over sample thickness and length which is equivalent to the heat flow. There is also the hot plate method, which is used for example in the HFM. This method uses a constant temperature gradient that is attached to a sample from top and bottom side and directly measures the heat flow.

Several measurment methods in order to measure thermal conductivity and/or thermal conductivity are known. They can be devided in two groups:

**Stationary methods****Transient or time dependent methods**

Stationary methods (like the heat flux meters, guarded hotplates, some hot wire techniques, 3 omega method etc.) do the measurement of a heat flux while a (dynamic) equilibrium is installed in the tested material. It’s put in contact with a hot plate on one side and a cold plate on the other side of the sample. After installation ofthermal equilibrium a stationnary (no more time dependent) temperature gradient is present and from the heat flux the thermal conductivity can be calculated the theory beeing quite simple.

Transient methods (like laser flash method and some hot wire techniques) create a state out of equilibrium and its levelling-out during time is analysed. The theory to be used depend on the method and is more complicated as for the stationary methods.