Thermal diffusivity

In thermodynamics, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. ^[1] It is a measure of the rate of heat transfer inside a material and has SI units of m²/s. It is an intensive property. Thermal diffusivity is usually denoted by lowercase alpha (α), but a, h, κ (kappa), ^[2] K, ^[3] ,D, ${\displaystyle D_{T}}$ are also used.

The formula is: ^[4] $${\displaystyle \alpha ={\frac {k}{\rho c_{p}}}}$$ where

• k is thermal conductivity (W/(m·K))
• c_p is specific heat capacity (J/(kg·K))
• ρ is density (kg/m³)

Together, ρc_p can be considered the volumetric heat capacity (J/(m³·K)).

Thermal diffusivity is a positive coefficient 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 substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its energy storage capacity or 'thermal bulk'.

Thermal diffusivity and thermal effusivity are related concepts and quantities used to simulate non-equilibrium thermodynamics. Diffusivity is the more fundamental concept and describes the stochastic process of heat spread throughout some local volume of a substance. Effusivity describes the corresponding transient process of heat flow through some local area of interest. Upon reaching a steady state where the stored energy distribution stabilizes, the thermal conductivity (k) may be sufficient to describe heat transfers inside solid or rigid bodies by applying Fourier's law. ^{[6] [7]}

Thermal diffusivity is often measured with the flash method. ^{[8] [9]} 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. ^{[10] [11]}

Thermal diffusivity of selected materials and substances

Thermal diffusivity of selected materials and substances ^[12]

Material	Thermal diffusivity (mm2/s)	Refs.
Pyrolytic graphite, parallel to layers	1,220
Diamond	1,060–1,160
Carbon/carbon composite at 25 °C	216.5	[13]
Helium (300 K, 1 atm)	190	[14]
Silver, pure (99.9%)	165.63
Hydrogen (300 K, 1 atm)	160	[14]
Gold	127	[15]
Copper at 25 °C	111	[13]
Aluminium	97	[15]
Silicon	88	[15]
Al-10Si-Mn-Mg (Silafont 36) at 20 °C	74.2	[16]
Aluminium 6061-T6 Alloy	64	[15]
Molybdenum (99.95%) at 25 °C	54.3	[17]
Al-5Mg-2Si-Mn (Magsimal-59) at 20 °C	44.0	[18]
Tin	40	[15]
Water vapor (1 atm, 400 K)	23.38
Iron	23	[15]
Argon (300 K, 1 atm)	22	[14]
Nitrogen (300 K, 1 atm)	22	[14]
Air (300 K)	19	[15]
Steel, AISI 1010 (0.1% carbon)	18.8	[19]
Aluminium oxide (polycrystalline)	12.0
Steel, 1% carbon	11.72
Si3N4 with CNTs 26 °C	9.142	[20]
Si3N4 without CNTs 26 °C	8.605	[20]
Steel, stainless 304A at 27 °C	4.2	[15]
Pyrolytic graphite, normal to layers	3.6
Steel, stainless 310 at 25 °C	3.352	[21]
Inconel 600 at 25 °C	3.428	[22]
Quartz	1.4	[15]
Sandstone	1.15
Ice at 0 °C	1.02
Silicon dioxide (polycrystalline)	0.83	[15]
Brick, common	0.52
Glass, window	0.34
Brick, adobe	0.27
PC (polycarbonate) at 25 °C	0.144	[23]
Water at 25 °C	0.143	[23]
PTFE (Polytetrafluorethylene) at 25 °C	0.124	[24]
PP (polypropylene) at 25 °C	0.096	[23]
Nylon	0.09
Rubber	0.089–0.13	[3]
Wood (yellow pine)	0.082
Paraffin at 25 °C	0.081	[23]
PVC (polyvinyl chloride)	0.08	[15]
Oil, engine (saturated liquid, 100 °C)	0.0738
Alcohol	0.07	[15]

See also

• Diffusion
• List of thermodynamic properties

References

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