square meter per second
Diffusivityexact by definition
The square metre per second is the SI coherent unit for every quantity with dimensions of area over time: thermal diffusivity, mass diffusivity, kinematic viscosity, momentum diffusivity and hydraulic diffusivity. Its relation to the base units is exact by definition. It answers how fast a disturbance spreads by diffusion rather than by bulk flow.
Watch out: Three different physical properties share these units and are easy to interchange by accident. Thermal diffusivity \(\alpha = k/(\rho c_p)\) governs temperature spreading, kinematic viscosity \(\nu = \mu/\rho\) governs momentum spreading, and mass diffusivity \(D\) governs species spreading. Their ratios are the Prandtl, Schmidt and Lewis numbers.
| 1 m²/s | 1,000,000 mm²/s |
About the square meter per second
Anything that spreads by random molecular wandering rather than by being carried along has a diffusivity, and diffusivity always carries units of area per time. That is not a coincidence: the diffusion equation \(\partial T/\partial t = \alpha \nabla^2 T\) needs \(\alpha\) to reconcile a second spatial derivative with a first time derivative. The practical consequence is the square-root rule. A diffusive front travels a distance of roughly \(\sqrt{\alpha t}\), so covering twice the distance takes four times as long. This is why a thick steel plate takes disproportionately longer to heat through than a thin one, and why diffusion is hopeless as a transport mechanism over any large distance.
Some values for scale, all in m²/s: copper's thermal diffusivity is about 1.1 × 10⁻⁴, air about 2.2 × 10⁻⁵, water about 1.4 × 10⁻⁷, and brick or concrete around 5 × 10⁻⁷. Copper spreads heat nearly a thousand times faster than water, which is why saucepans have copper bases and why thermal mass in a building is measured in hours of lag rather than seconds. Note that high conductivity and high diffusivity are not the same thing: diffusivity is conductivity divided by volumetric heat capacity, so a material can conduct well and still respond slowly if it stores a lot of heat per degree.