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Thermal properties of materials

Which value is closest to the thermal diffusivity α = κ/(ρc) of aluminum (thermal conductivity 237 W/(m·K), density 2700 kg/m³, specific heat 900 J/(kg·K))?

  1. AAbout 9.8×10⁻⁵ m²/s
  2. BAbout 9.8×10⁻² m²/s
  3. CAbout 0.26 m²/s
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Answer: A. About 9.8×10⁻⁵ m²/s

α = 237/(2700×900) = 237/(2.43×10⁶) ≈ 9.75×10⁻⁵ m²/s, about 9.8×10⁻⁵ m²/s. Thermal diffusivity expresses how quickly a change in temperature spreads through a material, and it appears in the transient heat conduction equation ∂T/∂t = α∇²T. A rough time for the temperature to change through a material of thickness L is L²/α, which for aluminum 10 mm thick is about 1 s. About 9.8×10⁻² m²/s uses the specific heat as 0.9 in J/(g·K), shifting the result by a factor of 1000. About 0.26 m²/s forgets to multiply by the density, giving κ/c, which does not even have units of m²/s.

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