# What does thermal conductivity mean?

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

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

## Scientific definition

The scientific definition of thermal conductivity claims it as the material property that describes heat transport within a sample. For any given 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 flux density and temperature gradient (Equation 2). The example in (equation 3) serves as an illustration.

λ = ρ * cp * α (1)

λ = thermal conductivity, ρ = density, cp = spec. heat capacity, α = thermal diffusivity.

λ = -q / ∆T (2)

λ = thermal conductivity, q = mean heat flux density, ∆T = temperature gradient.

If this definition is used to consider, for example, a cylindrical sample, the following calculations can be made: If an ideal homogeneous cylinder of length l and constant cross-section A is considered, which is insulated at its side and can have only one temperature change at its two ends, the temperature gradient along its length is (∆T) / l. The density of the heat flow with the direction from the hot to the cold side is λ * (∆T) / l.

Considering the cross section A, there is a heat flux Q which can be calculated with (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):

The measurement methods for determining thermal conductivity are many and varied, but can be divided into two basic groups for a better overview: **transient and steady-state measurement methods**.

In our video, our two scientists explain the difference between these methods.

If a material is heated locally, the temperature distribution within the body changes until it is evenly distributed and stable after a certain time. The phase shortly after the start of the heat input, in which the temperature distribution is still changing, is called the transient phase. When the temperature distribution is stable, it is called a steady state.

## Stationary measuring methods

Plate methods such as the “Guarded Hot Plate“, the “Heat Flow Meter“, or the “Thermal Interface Material Tester” belong to the stationary measurement methods.

The material sample is placed between a heated and a cooled plate. This results in a temperature gradient and consequently a heat flow along the sample, which is monitored until it approaches a constant final value.

Knowing the sample thickness and the measured heat flux, the thermal conductivity of the sample can be calculated. With the TIM tester, the thermal resistance under variable load or compression can be measured and from this the thermal conductivity and the thermal contact resistance can be determined.

## Transient measuring methods

The laser flash method is one of the transient measurement methods and is based on a patent from 1975. Despite its high cost and complexity, it is still widely used today. And for good reason! With the laser flash method, materials can be tested fully automatically even at the most extreme temperatures of up to 2,800 degrees Celsius. For the measurement, the sample disk is exposed on one side to a short, high-energy heat pulse from a laser or flash lamp. The resulting temperature rise on the opposite side is recorded with an infrared detector. In relation to the sample thickness, this allows the thermal diffusivity to be calculated using a thermal conductivity model.

**Heating wire and heating strip methods** are widely used, for example in the form of the Transient Hot Bridge method, and also belong to the transient measurement methods.

They can be found in a wide variety of sensor configurations, can be used flexibly and offer the widest possible range of applications and measurements. Embedded in a carrier substrate, the heating wire emits a constant heat flux during the measurement, which causes a time-varying temperature distribution in the sample as well as the sensor itself. The temperature rise over time is measured by an integrated thermometer and serves as a measure of the thermal transport properties of the material.

## Special feature: Measurement of thermal conductivity on thin layers

The measurement of thermal conductivity on thin films in the nm to μm range is a special case. Although some of the same measurement principles can be used for this purpose, the implementation forms – time-domain thermoreflectance instead of LaserFlash and the 3 Omega method as a special form of the heating strip method – differ considerably in order to meet the changed boundary conditions.