# Thermal Conductivity / Thermal Diffusivity

**Explanation**

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.

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.

**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 methods or Thin Film LASER FLASH methods. Therefore the sample thickness and especially the specific heat capacity of the sample has to be determined which is mostly done by Differential Scanning Caloirmetry - 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.

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