Classical thermodynamics, heat transfer Definition

Thermal diffusivity

Builds on Thermal conductivity Heat capacity Heat equation

Definition

Let a homogeneous material have thermal conductivity $k > 0$ , density $\rho > 0$ and specific heat capacity at constant pressure $c_p > 0$ . Its thermal diffusivity is $\alpha = \frac{k}{\rho \, c_p}.$ Its unit is $\mathrm{m^2 \, s^{-1}}$ .

Remarks

With constant $\alpha$ , conduction without heat sources obeys the heat equation $\partial_t T = \alpha \Delta T$ .

Example: for copper, $k \approx 400$ , $\rho \approx 8900$ and $c_p \approx 385$ in SI units. So $\alpha \approx 400 / (8900 \cdot 385) \approx 1.2 \cdot 10^{-4}$ square metres per second.

Non-example: the conductivity $k$ alone is not the diffusivity. Two materials with the same $k$ but different heat capacities warm at different rates.

The ratio $\nu / \alpha$ , where $\nu$ is the kinematic viscosity of a fluid, is the Prandtl number.

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Tag	`MB509A4TAG`
URI	`m2://MB509A4TAG`
Kind	definition
Writing	W0 stub
MSC	80A19, 35K05
Defines	Thermal diffusivity
Uses	Thermal conductivity, Heat capacity, Heat equation
Changed	3 November 2026

Thermal diffusivity

Definition

Remarks

Reading path

Further reading

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