# What is Thermal Diffusivity?

Heat transfer occurs through a combination of three methods; conduction, convection, and radiation. In heat conduction, two material properties affect how well conduction takes place, namely thermal conductivity (K) and thermal diffusivity (D or \alpha).

Thermal conductivity is a well-known property, and it is common knowledge that metals are better conductors of heat than plastics, for example. Thermal diffusivity, on the other hand, is not so straight forward and even relatively unknown. Thermal diffusivity defines the rate of heat transfer through a medium.

The higher the thermal diffusivity is, the faster the rate of heat transfer is through that medium. So it is possible for materials of widely varying thermal conductivities to have very similar thermal diffusivities. For example, nickel and air have the same thermal diffusivities but very different thermal conductivities. Furthermore, especially in composite materials, the combination of two materials with high thermal diffusivities may produce one with a lower overall thermal diffusivity than each of the materials alone [1].

• What thermal diffusivity is
• The measurement of thermal diffusivity
• Thermal diffusivity of different materials
• Future materials and application

Figure 1. Heat sinks are made of materials with high thermal diffusivity.

## What is thermal diffusivity?

The thermal diffusivity of a material is the thermal conductivity divided by the product of its density and specific heat capacity with the pressure held constant. It tells us how fast the transfer of heat occurs within a material from the hotter side to the cooler side. Thermal diffusivity is a measure of how quickly a material reacts to temperature changes. It is measured in m2/s.

The thermal diffusivity of a material can be expressed as

\alpha=\frac{k}{( \rho c_{p})}

Where k is thermal conductivity, c_{p} is specific heat capacity and \rho is density. \rho c_{p} is also known as the volumetric heat capacity. Thermal diffusivity could also be described as the ratio of heat that passes through a material to the heat stored in it per unit volume. This means that a high value of thermal diffusivity doesn’t necessarily mean that the material dissipates heat better than a material with low thermal diffusivity because thermal diffusivity is a ratio between the thermal conductivity and the volumetric heat capacity at constant pressure. One could say it tells us about the balance between the passage of heat and the storage of heat.

## Measurement of thermal diffusivity

Thermal diffusivity measurement techniques are easier carried out than the measurement of thermal conductivity and as such, thermal diffusivity measurements are often a means to the end of measuring thermal conductivity according to the equation k=\alpha \rho c with density and specific heat capacity known values. The techniques for measuring thermal diffusivity in the past have primarily been photothermal and photoacoustic (which are limited to laboratories), but thanks to recent strides in infrared technology, new thermographic techniques have been developed which can be performed on-site [2]. Some techniques for measuring thermal diffusivity are the laser flash method, thermal wave interferometry, and infrared thermography.

### The laser flash method

This method involves heating a plane-parallel sample material with a short burst of energy on one side and evaluating the change in temperature from the other side of the sample. The parameters measured would include time, temperature rise and the thickness of the sample. The limitation of this method is that it requires a sample of specific geometry.

### Thermal wave interferometry

This technique is used for thermal diffusivity measurements of coatings and thin slabs. The technique involves heating a coated sample by a modulated laser, and the two-layer structure of the sample produces a change in the ac component (phase and amplitude) of the surface temperature when compared to the uncoated surface. This change is caused by reflection and transmission of thermal waves at the interface between the coated and uncoated surfaces of the sample and this is monitored by an infrared detector. All this information is combined to determine thermal diffusivity [3].

### Infrared thermography

This technique involves analysing the time evolution of the temperature distribution of the rear surface of a plate-like sample which has been heated from the front by an instantaneous circular Gaussian heat source. Thermal diffusivity can then be determined by analysing the spatial distribution or phase image of the temperature of any of the front or rear sample surfaces. There are three thermographic methods, namely spatially resolved diffusivity measurement, lateral thermal waves, and single-side flash method [2].

Table 1. Experimental and literature values of thermal diffusivity values for AISI304 stainless steel [2]

 Measurement method Diffusivity [cm2/s] Error [cm2/s] Literature value 0.04 ± 0.0006*10-4 Laser Flash 0.0399 ± 0.001*10-4 Thermal wave Interferometry 0.040 ± 0.006*10-4 Thermographic method I (spatially resolved diffusivity measurement) 0.040 ± 0.0006*10-4 Thermographic method II (lateral thermal waves) 0.0398 ± 0.0006*10-4 Thermographic method III (single-side flash method) 0.0401 ± 0.004*10-4

From the table above, it can be seen that all the measurement methods have a high degree of accuracy with minimal deviation.

## Thermal diffusivity of different materials

Below is a table of selected materials and their thermal conductivities, thermal diffusivities and specific heat capacities. It can be seen, for example, that nickel and lead have the same thermal diffusivity, but nickel has a higher thermal conductivity. That means nickel conducts heat faster than lead but the heat stored in it would still be higher than lead since it has a higher volumetric heat capacity. Similarly, potassium and cobalt would conduct heat at a similar rate, but cobalt would heat up significantly more while doing so than potassium since it has a lower thermal diffusivity.

Table 2. Thermal properties of selected materials

 Material Thermal conductivity k (Wm-1K-1) Thermal diffusivity (mm2s-1) Specific heat capacity (Jkg-1K-1) VDM® Alloy 601 (Nickel-Iron alloy) 11.3 2.97 472 CTF25E (Carbide) 98 34.4 14.15 Zytel® 101 NC010 (Polyamide 66) 0.24 0 1680 General Fused Silica Glass (Fused quartz) 1.1 – 1.4 0.75 – 0.85 670 – 750 EN 10088-1 Grade X2CrNiMo18-14-3 solution annealed (Stainless steel) 13.5 – 15 3.6 0.44

## Future materials and application

Thermal diffusivity is important in many industries to select the best materials that can provide optimal heat flow without getting heated up in the process. A heat sink, for example, takes advantage of high thermal diffusivity materials to carry out its purpose of quickly transporting heat from another body, whereas insulations use materials of low thermal diffusivity to ensure that heat is not lost from a body.

Heat sinks are applied in virtually all electrical equipment where increased electrical resistance in some components could lead to heat build-up. This fundamental idea is a material selection criterion in the refrigeration of food, heating/cooling, architecture, and machining.

In the manufacture of space shuttle thermal tiles, aerogel materials have been developed that are such poor conductors of heat that they can be picked up with bare hands moments after being heated up over 1000oC in an oven. Such a material would have extremely low values of both thermal conductivity and thermal diffusivity.

Figure 2. Aerogels are new materials made particularly to have low levels of thermal diffusivity and thermal conductivity. (Jon Collier, Flickr)