Thermal Diffusivity

Thermal diffusivity (symbol α) is a material property that measures how quickly heat spreads through a substance relative to its capacity to store thermal energy. It is defined as the ratio of thermal conductivity to the product of density and specific heat capacity: α = k/(ρcₚ). A material with high thermal diffusivity — like copper — conducts heat rapidly and equilibrates quickly. A material with low thermal diffusivity — like wood — stores heat locally and resists temperature change.

The significance of thermal diffusivity is not merely practical. It is the single parameter that controls the dynamics of the heat equation, determining the timescale on which a temperature perturbation spreads and the spatial scale of thermal gradients. In fluid dynamics, the analogous quantity is kinematic viscosity ν — the ratio of viscosity to density — and the comparison between thermal and momentum diffusivity gives the Prandtl number, a dimensionless ratio that controls whether heat or momentum diffuses faster in a flowing fluid.

Thermal diffusivity is the reason that some materials feel cold to the touch while others feel warm at the same ambient temperature. It is not the temperature that matters to your nerves, but the rate at which heat is conducted away from your skin. The sensory experience of temperature is, in this sense, a direct measurement of thermal diffusivity.