Summary

The Prandtl number is a dimensionless number named after the German physicist Ludwig Prandtl. It represents the ratio of molecular diffusivity of momentum to the molecular diffusivity of heat.

Definitions

$C_{p}$	:	Specific heat (J/kg.K)
$k$	:	Thermal conductivity of the fluid (W/m.K)
$\text{Pr}$	:	Prandtl number
$\mu$	:	Dynamic viscosity of the fluid (kg/m.s)

Introduction

The Prandtl number is the ratio of molecular diffusivity of momentum to the molecular diffusivity of heat. It may be calculated as follows:

$$ \displaystyle \text{Pr} = \frac{\text{ viscous diffusion rate }}{\text{ thermal diffusion rate }} = \frac{\mu C_{p}}{k} $$

Small values of the Prandtl number (less than 1) in a given fluid indicates that thermal diffusion occurs at a greater rate than momentum diffusion and therefore heat conduction is more effective than convection. Conversely if the Prandtl number is large (greater than 1), momentum diffuses at a greater rate than heat and convection is more effective than conduction.

Typical Values of Prandtl Number

The tables below contain some typical Prandtl numbers for air, water and R32gas.

Air at 1 bar

Temperature (K)	Prandtl Number
200	0.738
240	0.724
280	0.710
300	0.705

Water at 1 bar

Temperature (K)	Prandtl Number
280	10.3
300	5.69
320	3.65
340	2.60
380	1.59

Difluoromethane (R32) Gas at 1 bar

Temperature (K)	Prandtl Number
250	0.908
280	0.860
300	0.842
320	0.836
350	0.831

Variations of the Prandtl Number

Turbulent Prandtl Number

The turbulent Prandtl number is the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity and characterises the relationship between shear stress and heat flux in turbulent flow.