# Thermal diffusivity

In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.[1] It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI derived unit of m²/s. Thermal diffusivity is usually denoted α but a,h,κ,[2] K,[3] and D are also used. The formula is:

${\displaystyle \alpha ={\frac {k}{\rho c_{p}}}}$[4]

where

• ${\displaystyle k}$ is thermal conductivity (W/(m·K))
• ${\displaystyle c_{p}}$ is specific heat capacity (J/(kg·K))
• ${\displaystyle \rho }$ is density (kg/m³)

Together, ${\displaystyle \rho c_{p}\,}$ can be considered the volumetric heat capacity (J/(m³·K)).

As seen in the heat equation,[5]

${\displaystyle {\frac {\partial T}{\partial t}}=\alpha \nabla ^{2}T}$,

one way to view thermal diffusivity is as the ratio of the time derivative of temperature to its curvature, quantifying the rate at which temperature concavity is "smoothed out". In a sense, thermal diffusivity is the measure of thermal inertia.[6] In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'.

Thermal diffusivity is often measured with the flash method.[7][8] It involves heating a strip or cylindrical sample with a short energy pulse at one end and analyzing the temperature change (reduction in amplitude and phase shift of the pulse) a short distance away.[9][10]

Thermal diffusivity of selected materials and substances[11]
MaterialThermal diffusivity
(m²/s)
Thermal diffusivity
(mm²/s)
Pyrolytic graphite, parallel to layers1.22 × 10−31220
Silver, pure (99.9%)1.6563 × 10−4165.63
Gold1.27 × 10−4 [12]127
Copper at 25 °C1.11 × 10−4 [13]111
Aluminium9.7 × 10−5 [12]97
Al-10Si-Mn-Mg (Silafont 36) at 20 °C74.2 × 10−6 [14]74.2
Aluminium 6061-T6 Alloy6.4 × 10−5 [12]64
Al-5Mg-2Si-Mn (Magsimal-59) at 20 °C4.4 × 10−5 [15]44.0
Steel, AISI 1010 (0.1% carbon)1.88 x 10−5 [16]18.8
Steel, 1% carbon1.172 × 10−511.72
Steel, stainless 304A at 27 °C4.2 × 10−6 [12]4.2
Steel, stainless 310 at 25 °C3.352 × 10−6 [17]3.352
Inconel 600 at 25 °C3.428 × 10−6 [18]3.428
Molybdenum (99.95%) at 25 °C54.3 × 10−6 [19]54.3
Iron2.3 × 10−5 [12]23
Silicon8.8 × 10−5 [12]88
Quartz1.4 × 10−6 [12]1.4
Carbon/carbon composite at 25 °C2.165 × 10−4 [13]216.5
Aluminium oxide (polycrystalline)1.20 × 10−512.0
Silicon Dioxide (Polycrystalline)8.3 × 10−7 [12]0.83
Si3 N4 with CNTs 26 °C9.142 × 10−6 [20]9.142
Si3 N4 without CNTs 26 °C8.605 × 10−6 [20]8.605
PC (Polycarbonate) at 25 °C1.44 × 10−7 [21]0.144
PP (Polypropylene) at 25 °C9.6 × 10−8 [21]0.096
Paraffin at 25 °C8.1 × 10−8 [21]0.081
PVC (Polyvinyl Chloride)8 × 10−8 [12]0.08
PTFE (Polytetrafluorethylene) at 25 °C0.124 × 10−6 [22]0.124
Water at 25 °C1.43 × 10−7 [21]0.143
Alcohol7 × 10−8 [12]0.07
Water vapour (1 atm, 400 K)2.338 × 10−523.38
Air (300 K)1.9 × 10−5 [12]19
Argon (300 K, 1 atm)2.2×10−5[23]22
Helium (300 K, 1 atm)1.9×10−4[23]190
Hydrogen (300 K, 1 atm)1.6×10−4[23]160
Nitrogen (300 K, 1 atm)2.2×10−5[23]22
Pyrolytic graphite, normal to layers3.6 × 10−63.6
Sandstone1.12–1.19 × 10−61.15
Tin4.0 × 10−5 [12]40
Brick, common5.2 × 10−70.52
Glass, window3.4 × 10−70.34
Rubber0.89 [3] - 1.3 × 10−70.089 - 0.13
Nylon9 × 10−80.09
Wood (Yellow Pine)8.2 × 10−80.082
Oil, engine (saturated liquid, 100 °C)7.38 × 10−80.0738

## References

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