# 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 ability of a material to conduct thermal energy relative to its ability to store thermal energy. It has the SI unit of m²/s. Thermal diffusivity is usually denoted α but a, κ,[2] K,[3] and D are also used. The formula is:

$\alpha = {k \over {\rho c_p}}$

where

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

Together, $\rho c_p\,$ can be considered the volumetric heat capacity (J/(m³·K)).

As seen in the heat equation,[4]

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

thermal diffusivity is 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.[5] 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.[6][7] 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.[8][9]

Thermal diffusivity of selected materials and substances[10]
Material Thermal diffusivity
(m²/s)
Thermal diffusivity
(mm²/s)
Pyrolytic graphite, parallel to layers 1.22 × 10−3 1220
Silver, pure (99.9%) 1.6563 × 10−4 165.63
Gold 1.27 × 10−4 [11] 127
Copper at 25 °C 1.11 × 10−4 [12] 111
Aluminium 8.418 × 10−5 84.18
Al-10Si-Mn-Mg (Silafont 36) at 20 °C 74.2 × 10−6 [13] 74.2
Aluminum 6061-T6 Alloy 6.4 × 10−5 [11] 64
Al-5Mg-2Si-Mn (Magsimal-59) at 20 °C 44.0 × 10−6 [14] 44.0
Steel, 1% carbon 1.172 × 10−5 11.72
Steel, stainless 304A at 27 °C 4.2 × 10−6 [11] 4.2
Steel, stainless 310 at 25 °C 3.352 × 10−6 [15] 3.352
Inconel 600 at 25 °C 3.428 × 10−6 [16] 3.428
Molybdenum (99.95%) at 25 °C 54.3 × 10−6 [17] 54.3
Iron 2.3 × 10−5 [11] 23
Silicon 8.8 × 10−5 [11] 88
Quartz 1.4 × 10−6 [11] 1.4
Carbon/carbon composite at 25 °C 216.5 × 10−6 [12] 216.5
Aluminium oxide (polycrystalline) 1.20 × 10−5 12.0
Silicon Dioxide (Polycrystalline) 8.3 × 10−7 [11] 0.83
Si3 N4 with CNTs 26 °C 9.142 × 10−6 [18] 9.142
Si3 N4 without CNTs 26 °C 8.605 × 10−6 [18] 8.605
PC (Polycarbonate) at 25 °C 0.144 × 10−6 [19] 0.144
PP (Polypropylene) at 25 °C 0.096 × 10−6 [19] 0.096
Paraffin at 25 °C 0.081 × 10−6 [19] 0.081
PVC (Polyvinyl Chloride) 8 × 10−8 [11] 0.08
PTFE (Polytetrafluorethylene) at 25 °C 0.124 × 10−6 [20] 0.124
Water at 25 °C 0.143 × 10−6 [19] 0.143
Alcohol 7 × 10−8 [11] 0.07
Water vapour (1 atm, 400 K) 2.338 × 10−5 23.38
Air (300 K) 1.9 × 10−5 [11] 19
Argon (300 K, 1 atm) 2.2×10−5[21] 22
Helium (300 K, 1 atm) 1.9×10−4[21] 190
Hydrogen (300 K, 1 atm) 1.6×10−4[21] 160
Nitrogen (300 K, 1 atm) 2.2×10−5[21] 22
Pyrolytic graphite, normal to layers 3.6 × 10−6 3.6
Sandstone 1.12–1.19 × 10−6 1.15
Tin 4.0 × 10−5 [11] 40
Brick, common 5.2 × 10−7 0.52
Brick, adobe 2.7 × 10−7 0.27
Glass, window 3.4 × 10−7 0.34
Rubber 0.89 [3] - 1.3[citation needed] × 10−7 0.089 - 0.13
Nylon 9 × 10−8 0.09
Wood (Yellow Pine) 8.2 × 10−8 0.082
Oil, engine (saturated liquid, 100 °C) 7.38 × 10−8 0.0738

## 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. ^ a b 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. ^ Carslaw, H. S.; Jaeger, J. C. (1959), Conduction of Heat in Solids (2nd ed.), Oxford University Press, ISBN 978-0-19-853368-9
5. ^ 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.
6. ^ NETZSCH-Gerätebau, Germany
7. ^ 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.
8. ^ J. Blumm, J. Opfermann (2002). "Improvement of the mathematical modeling of flash measurements". High Temperatures – High Pressures 34: 515. doi:10.1068/htjr061.
9. ^ 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.
10. ^ Brown; Marco (1958). Introduction to Heat Transfer (3rd ed.). McGraw-Hill. and Eckert; Drake (1959). Heat and Mass Transfer. McGraw-Hill. ISBN 0-89116-553-3. cited in Holman, J.P. (2002). Heat Transfer (9th ed.). McGraw-Hill. ISBN 0-07-029639-1.
11. Jim Wilson (August 2007). "Materials Data".
12. ^ a b 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" 407 (2). p. 83. Bibcode:2010JNuM..407...83C. doi:10.1016/j.jnucmat.2010.09.032.
13. ^ 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.
14. ^ 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.
15. ^ 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.
16. ^ 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. Check date values in: |date= (help)
17. ^ A. Lindemann, J. Blumm (2009). "Measurement of the Thermophysical Properties of Pure Molybdenum". 17th Plansee Seminar 3.
18. ^ a b 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.
19. ^ a b c d 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. Check date values in: |date= (help)
20. ^ 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.
21. ^ a b c d 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 0-521-59082-5. Retrieved 1 December 2011.