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]

Material	Thermal diffusivity (mm²/s)	Refs.
Pyrolytic graphite, parallel to layers	1220
Silver, pure (99.9%)	165.63
Gold	127	[12]
Copper at 25 °C	111	[13]
Aluminium	97	[12]
Al-10Si-Mn-Mg (Silafont 36) at 20 °C	74.2	[14]
Aluminium 6061-T6 Alloy	64	[12]
Al-5Mg-2Si-Mn (Magsimal-59) at 20 °C	44.0	[15]
Steel, AISI 1010 (0.1% carbon)	18.8	[16]
Steel, 1% carbon	11.72
Steel, stainless 304A at 27 °C	4.2	[12]
Steel, stainless 310 at 25 °C	3.352	[17]
Inconel 600 at 25 °C	3.428	[18]
Molybdenum (99.95%) at 25 °C	54.3	[19]
Iron	23	[12]
Silicon	88	[12]
Quartz	1.4	[12]
Carbon/carbon composite at 25 °C	216.5	[13]
Aluminium oxide (polycrystalline)	12.0
Silicon Dioxide (Polycrystalline)	0.83	[12]
Si3 N4 with CNTs 26 °C	9.142	[20]
Si3 N4 without CNTs 26 °C	8.605	[20]
PC (Polycarbonate) at 25 °C	0.144	[21]
PP (Polypropylene) at 25 °C	0.096	[21]
Paraffin at 25 °C	0.081	[21]
PVC (Polyvinyl Chloride)	0.08	[12]
PTFE (Polytetrafluorethylene) at 25 °C	0.124	[22]
Water at 25 °C	0.143	[21]
Ice at 0 °C	1.02
Alcohol	0.07	[12]
Water vapour (1 atm, 400 K)	23.38
Air (300 K)	19	[12]
Argon (300 K, 1 atm)	22	[23]
Helium (300 K, 1 atm)	190	[23]
Hydrogen (300 K, 1 atm)	160	[23]
Nitrogen (300 K, 1 atm)	22	[23]
Pyrolytic graphite, normal to layers	3.6
Sandstone	1.15
Tin	40	[12]
Brick, common	0.52
Brick, adobe	0.27
Glass, window	0.34
Rubber	0.089 - 0.13	[3]
Nylon	0.09
Wood (Yellow Pine)	0.082
Oil, engine (saturated liquid, 100 °C)	0.0738

See also

• Heat equation
• Laser flash analysis
• Thermodiffusion
• Thermal effusivity
• Thermal time constant

References

1. Lide, David R., ed. (2009). CRC Handbook of Chemistry and Physics (90th ed.). Boca Raton, Florida: CRC Press. p. 2-65. ISBN 978-1-4200-9084-0.
2. Gladwell, Richard B. Hetnarski, M. Reza Eslami ; edited by G.M.L. (2009). Thermal Stresses - Advanced Theory and Applications (Online-Ausg. ed.). Dordrecht: Springer Netherlands. p. 170. ISBN 978-1-4020-9247-3.
3. Unsworth, J.; Duarte, F. J. (1979), "Heat diffusion in a solid sphere and Fourier Theory", Am. J. Phys., 47 (11): 891–893, Bibcode:1979AmJPh..47..981U, doi:10.1119/1.11601
4. Lightfoot, R. Byron Bird, Warren E. Stewart, Edwin N. (1960). Transport Phenomena. John Wiley and Sons, Inc. Eq. 8.1-7. ISBN 978-0-471-07392-5.
5. Carslaw, H. S.; Jaeger, J. C. (1959), Conduction of Heat in Solids (2nd ed.), Oxford University Press, ISBN 978-0-19-853368-9
6. Venkanna, B.K. (2010). Fundamentals of Heat and Mass Transfer. New Delhi: PHI Learning. p. 38. ISBN 978-81-203-4031-2. Retrieved 1 December 2011.
7. "NETZSCH-Gerätebau, Germany". Archived from the original on 2012-03-11. Retrieved 2012-03-12.
8. W.J. Parker; R.J. Jenkins; C.P. Butler; G.L. Abbott (1961). "Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity". Journal of Applied Physics. 32 (9): 1679. Bibcode:1961JAP....32.1679P. doi:10.1063/1.1728417.
9. J. Blumm; J. Opfermann (2002). "Improvement of the mathematical modeling of flash measurements". High Temperatures – High Pressures. 34 (5): 515. doi:10.1068/htjr061.
10. Thermitus, M.-A. (October 2010). "New Beam Size Correction for Thermal Diffusivity Measurement with the Flash Method". In Gaal, Daniela S.; Gaal, Peter S. (eds.). Thermal Conductivity 30/Thermal Expansion 18. 30th International Thermal Conductivity Conference/18th International Thermal Expansion Symposium. Lancaster, PA: DEStech Publications. p. 217. ISBN 978-1-60595-015-0. Retrieved 1 December 2011.
11. Brown; Marco (1958). Introduction to Heat Transfer (3rd ed.). McGraw-Hill. and Eckert; Drake (1959). Heat and Mass Transfer. McGraw-Hill. ISBN 978-0-89116-553-8. cited in Holman, J.P. (2002). Heat Transfer (9th ed.). McGraw-Hill. ISBN 978-0-07-029639-8.
12. Jim Wilson (August 2007). "Materials Data". Cite journal requires |journal= (help)
13. V. Casalegno; P. Vavassori; M. Valle; M. Ferraris; M. Salvo; G. Pintsuk (2010). "Measurement of thermal properties of a ceramic/metal joint by laser flash method". Journal of Nuclear Materials. 407 (2): 83. Bibcode:2010JNuM..407...83C. doi:10.1016/j.jnucmat.2010.09.032.
14. P. Hofer; E. Kaschnitz (2011). "Thermal diffusivity of the aluminium alloy Al-10Si-Mn-Mg (Silafont 36) in the solid and liquid states". High Temperatures – High Pressures. 40 (3–4): 311.
15. E. Kaschnitz; M. Küblböck (2008). "Thermal diffusivity of the aluminium alloy Al-5Mg-2Si-Mn (Magsimal-59) in the solid and liquid states". High Temperatures – High Pressures. 37 (3): 221.
16. Lienhard, John H. Lienhard, John H. (2019). A Heat Transfer Textbook (5th ed.). Dover Pub. p. 715.
17. J. Blumm; A. Lindemann; B. Niedrig; R. Campbell (2007). "Measurement of Selected Thermophysical Properties of the NPL Certified Reference Material Stainless Steel 310". International Journal of Thermophysics. 28 (2): 674. Bibcode:2007IJT....28..674B. doi:10.1007/s10765-007-0177-z.
18. J. Blumm; A. Lindemann; B. Niedrig (2003–2007). "Measurement of the thermophysical properties of an NPL thermal conductivity standard Inconel 600". High Temperatures – High Pressures. 35/36 (6): 621. doi:10.1068/htjr145.
19. A. Lindemann; J. Blumm (2009). Measurement of the Thermophysical Properties of Pure Molybdenum. 17th Plansee Seminar. 3.
20. O. Koszor; A. Lindemann; F. Davin; C. Balázsi (2009). "Observation of thermophysical and tribological properties of CNT reinforced Si₃ N₄". Key Engineering Materials. 409: 354. doi:10.4028/www.scientific.net/KEM.409.354.
21. J. Blumm; A. Lindemann (2003–2007). "Characterization of the thermophysical properties of molten polymers and liquids using the flash technique". High Temperatures – High Pressures. 35/36 (6): 627. doi:10.1068/htjr144.
22. J. Blumm; A. Lindemann; M. Meyer; C. Strasser (2011). "Characterization of PTFE Using Advanced Thermal Analysis Technique". International Journal of Thermophysics. 40 (3–4): 311. Bibcode:2010IJT....31.1919B. doi:10.1007/s10765-008-0512-z.
23. Lide, David R., ed. (1992). CDC Handbook of Chemistry and Physics (71st ed.). Boston: Chemical Rubber Publishing Company. cited in Baierlein, Ralph (1999). Thermal Physics. Cambridge, UK: Cambridge University Press. p. 372. ISBN 978-0-521-59082-2. Retrieved 1 December 2011.