The Prandtl Number is an intrinsic property of a fluid that describes which mechanism dominates heat transfer. Specifically, it is the ratio of momentum diffusivity (how quickly energy is dispersed by convection) to thermal diffusivity (how quickly energy is dispersed as heat). In the abstract, the Prandtl Number describes how quickly a “velocity wave” moves relative to the speed of the “thermal wave” in the fluid.

Pr =  \frac{c_{p}\mu}{k}

Here, Pr is the Prandtl Number, c_{p} is the specific heat, \mu is the dynamic viscosity, and k is the thermal conductivity.

For large Prandtl Numbers — convection dominates over conduction

Example: Earth’s mantle

For small Prandtl Numbers — conduction dominates over convection

Example: Liquid metal (e.g. Earth’s liquid outer core)

For Prandtl Number near unity — neither convection or conduction are dominant

Example: most gases (e.g. Earth’s atmosphere)

The Prandtl number varies dramatically through the Earth’s layers (largest in the mantle and smallest in liquid outer core and near unity in the atmosphere)