# Prandtl number

The **Prandtl number** (**Pr**) is a dimensionless number defined as the ratio of momentum diffusivity to thermal diffusivity.

where:

- is the kinematic diffusivity,
- is the thermal diffusivity,
- is the dynamic viscosity
- is the thermal conductivity
- is the specific heat
- is the density

## Typical ranges

From lowest to highest, the typical ranges of Prandtl numbers are:

- Liquid metals: 0.001 - 0.03
- Gases: 0.7 - 1.0
- Water: 1 - 10
- Oils: 50 - 2000

In problems of heat transfer, values of the Prandtl number less than 1 signifies that heat conduction dominates over fluid motion, whereas values of the Prandtl number much greater than 1 signifies that fluid motion dominates heat conduction. So for example, thermal conduction dominates in liquid mercury and bulk flow most likely does not speed up heat flow. On the other hand, thermal conduction is quite poor in engine oils, and bulk flow is necessary to enhance heat transfer.

On the other hand, the Prandtl numbers of gases are about 1, which indicates that both bulk flow and conduction are equally responsible for heat transfer.

The mass transfer analog of the Prandtl number is the Schmidt number.