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:

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

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

Fluid	Pressure (bar)	Temperature (K)	Prandtl Number
Air	1	200	0.738
Air	1	240	0.724
Air	1	280	0.710
Air	1	300	0.705
Water	1	280	10.3
Water	1	300	5.69
Water	1	320	3.65
Water	1	340	2.60
Water	1	380	1.59
Difluoromethane (R32)	1	250	0.908
Difluoromethane (R32)	1	280	0.860
Difluoromethane (R32)	1	300	0.842
Difluoromethane (R32)	1	320	0.836
Difluoromethane (R32)	1	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.

Magnetic Prandtl Number

The magnetic Prandtl number used in magnetohydrodynamics and is the ratio of momentum diffusivity (kinematic viscosity) to the magnetic diffusivity.