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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 if 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 the heat transport 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 flux density and temperature gradient (equation 2). The example in (equation 3) serves to illustrate this.
λ = ρ * cp * α (1)
λ = thermal conductivity, ρ = density, cp = specific heat capacity, α = thermal diffusivity
λ = -q / ∆T (2)
λ = thermal conductivity, q = average heat flux density, ∆T = temperature gradient
If this definition is used to consider, for example, a cylindrical sample, the following calculations can be performed: If an ideal homogeneous cylinder of length l and constant cross-section A is considered, which is insulated on its side and can only have one temperature change at its two ends, the temperature gradient over 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.
If we consider the cross-section A, there is a heat flow Qwhich 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):
The measurement methods for determining thermal conductivity are varied, but can be divided into two basic groups for a better overview: transient and stationary measurement methods.
In our video, our two scientists explain the difference between these methods.
Stationary measuring methods
plate process, such as the “Guarded Hot Plate“, the “Heat Flow Meter“, or the “Thermal Interface Material Tester” belong to the stationary measuring methods.
The material sample is placed between a heated and a cooled plate. This results in a temperature gradient and consequently also a heat flow along the sample, which is monitored until it approaches a constant final value.
If the sample thickness and the measured heat flow are known, the thermal conductivity of the sample can be calculated. With the TIM tester, the thermal resistance can be measured under variable load or compression and the thermal conductivity and thermal contact resistance can be determined from this.
Transient measurement methods
A well-known example of transient processes is the laser flash process – a classic that has been around since 1975 and is still in use worldwide today. The reason: despite its high costs and technical complexity, it delivers extremely precise results, even under extreme conditions of up to 2,800 °C. The sample disk is heated on one side by a short, high-energy laser or light flash. An infrared detector then measures the temperature rise on the opposite side. In combination with the sample thickness, the thermal diffusivity can be calculated using a thermal conductivity model.
Heating wire and heating strip methods (e.g. the transient hot bridge method) also belong to the transient techniques. They are flexible, can be used in a wide variety of sensor configurations and therefore cover a large measuring range. A heating wire embedded in a substrate constantly emits heat. The resulting, time-dependent temperature distribution in the sample and sensor is recorded with an integrated thermometer – a direct indicator of the thermal transport properties of the material.
Special feature: Measurement of thermal conductivity on thin layers
A special case is the measurement of thermal conductivity in thin layers in the nanometer to micrometer range. Although these measurements are partly based on the same basic principles as for solid samples, the practical implementation differs significantly. Instead of the classic laser flash method, for example, time-domain thermoreflectance (TDTR) is used here, while the 3-omega method is a specialized form of the heating strip method. These adaptations are necessary in order to reliably capture the special boundary conditions of ultra-thin layers.
