Thermal Diffusivity and Thermal Conductivity

Thermal conductivity and diffusivity are the most important thermophysical material parameters for the description of the heat transport properties of a material or component.

Definition of Thermal Conductivity

Definition of Thermal Conductivity

Thermal conductivity (λ with the unit W/(m•K)) describes the transport of energy – in the form of heat – through a body of mass as the result of a temperature gradient (see fig. 1). According to the second law of thermodynamics, heat always flows in the direction of the lower temperature.The relationship between transported heat per unit of time (dQ/dt or heat flow Q) and the temperature gradient (ΔT/Δx) through Area A (the area through which the heat is flowing perpendicularly at a steady rate) is described by the thermal conductivity equation.

Fig. 1: Schematic describing the concept of thermal conductivity with T1 > T2Fig. 1: Schematic describing the concept of thermal conductivity with T1 > T2

Thermal conductivity is thus a material-specific property used for characterizing steady heat transport. It can be calculated using the following equation:

Where
a:  Thermal diffusivity         
cp: Specific heat capacity         
ρ:   Density

An overview of the thermal conductivity for various materials is shown in figure 2.

Fig. 2: Thermal conductivity – insulation materials are characterized by low values, metals by high values. Diamond has the highest thermal conductivity.Fig. 2: Thermal conductivity – insulation materials are characterized by low values, metals by high values. Diamond has the highest thermal conductivity.
Definition of Thermal Diffusivity

Definition of Thermal Diffusivity

Thermal diffusivity (a with the unit mm2/s) is a material-specific property for characterizing unsteady heat conduction. This value describes how quickly a material reacts to a change in temperature.

In order to predict cooling processes or to simulate temperature fields, the thermal diffusivity must be known; it is a requisite for solving the Fourier Differential Equation for unsteady heat conduction.

An overview of the thermal conductivity and thermal diffusivity values of selected materials is shown in table 1.

Table 1: Thermal conductivity and thermal diffusivity values for various materials

 

MaterialThermal Conductivity / W/(m•K)Thermal Diffusivity / mm2/s
Aluminum23798.8
Steel8122.8
Copper399117
Fused Silica1.400.87
Gypsum0.510.47
Polyethylene0.350.15
Marble2.81.35

Source: www.chemie.de/lexikonInformation about the thermal conductivity of further materials can be found in the “Thermal Properties of Elements", "Thermal Properties of Ceramics" and "Thermal Properties of Polymers” posters.

Which Method is the Best Suited to my Particular Sample?

The presented methods for thermal conductivity and thermal diffusivity differ from one another primarily with regard to the recommended sample geometry and the achievable thermal diffusivity and thermal conductivity ranges. An overview of suitable sample sizes is shown in table 1.

Table 1: Established sample geometries

 

LFAGHPHFM*TCT
Sample shapeRound or rectangularSquareRound or rectangularRectangular (cuboid)
Number of pieces per sample1212
Diameter and/or edge lengths6 mm to 25.4 mm300 mm x 300 mm150 mm x 150 mm to 300 mm x 300 mm (or 305 mm x 305 mm to 610 mm x 610 mmNo less than 200 mm x 100 mm (Standard: 230 mm x 114 mm)
Max. thickness6 mm100 mm100 mm (or 200 mm)76 mm
Min. thickness0.01 mm,  dependent upon sample propertiesApprox. 1 mm, dependent upon sampleApprox. 5 mm50 mm

* Two models of HFM are available for different sample sizes

Due to their relatively large sample capacities, HFMs (Heat Flow Meters), GHPs (Guarded Hot Plates) and TCTs (Thermal Conductivity Tester, hot wire technique) – the methods for direct determination of thermal conductivity – are those primarily used for inhomogeneous sample materials (insulation materials). The TCT 426 was specially developed for tests on refractory materials and ceramics.

The Laser or Light Flash Apparatuses (LFAs) are configured to handle only much smaller sample sizes. Standard samples have a size of 12.7 mm and a thickness of 2 to 3 mm.

An overview of the various thermal conductivities depending on the used method can be seen in figure 1 and for temperature ranges in figure 2.

Fig. 1: Thermal conductivity ranges for the various methods for determining thermal diffusivity and thermal conductivityFig. 1: Thermal conductivity ranges for the various methods for determining thermal diffusivity and thermal conductivity
Fig. 2: Temperature ranges of the various instruments for measuring thermal conductivity and thermal diffusivityFig. 2: Temperature ranges of the various instruments for measuring thermal conductivity and thermal diffusivity
Principle of the LFA Method

Principle of the LFA Method

The laser or light flash method dates back to studies by Parker et al. in 1961. 

In carrying out a measurement, the lower surface of a plane parallel sample (see fig. 1) is first heated by a short energy pulse. The resulting temperature change on the upper surface of the sample is then measured with an infrared detector. The typical course of the signals is presented in figure 2 (red curve). The higher the sample’s thermal diffusivity, the steeper the signal increase.

Fig. 1: LFA schemeFig. 1: LFA scheme
Fig. 2: Typical measuring curve with important supporting points for curve evaluationFig. 2: Typical measuring curve with important supporting points for curve evaluation

a: Thermal diffusivity
ρ: Density
cp: Specific heat capacity
λ: Thermal conductivity
T:  Temperature

Using the half time (t1/2, time value at half signal height) and sample thickness (d), the thermal diffusivity (a) and finally the thermal conductivity (λ) can be calculated by means of the formula in figure 2. Furthermore, the specific heat (cp) of solids can be determined using the signal height (ΔTmax) compared to the signal height of a reference material. 

LFA investigations generally take much less time than thermal conductivity measurements by means of GHP (Guarded Hot Plate), HFM (Heat Flow Meter) or TCT (Thermal Conductivity Tester).

Detailed Insight Into the World of Thermal Analysis

Detailed Insight Into the World of Thermal Analysis

For the precise measurement of thermal diffusivity a, the flash method has established itself as a rapid, versatile and precise direct measuring method. NETZSCH offers a total of three models (LFA 467 HyperFlash, LFA 457 MicroFlash® and LFA 427), which cover the total a broad spectrum of materials and temperature ranges.

The thermal conductivity (λ) of insulation materials can be determined directly with plate instrumentation (HFM = Heat Flow Meter or GHP = Guarded Hot Plate): Included here are the HFM 436 Lambda with its new, expanded measurement capabilities and the GHP 456 Titan® guarded hot plate, which is an absolute method and thus requires no calibration.

For determining the thermal conductivity of refractory materials, the hot wire method is best suited (TCT = Thermal Conductivity Tester).

The instruments listed above operate in accordance with relevant instrument and usage norms.

Specifically, these include:

For LFA: ASTM E1461, DIN EN 821-2, DIN 30905, ISO 22007-4, ISO 18755
For HFM: ASTM C518, ISO 8301, DIN EN 12667, JIS A 1412
For TCT: ISO 8894, ASTM C1113, EN 993-14/15, DIN 51046

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