The Prandtl number is a dimensionless number, named after its inventor, a German engineer Ludwig Prandtl, who also identified the boundary layer. The Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity. The momentum diffusivity, or as it is normally called, kinematic viscosity, tells us the material’s resistance to shear-flows (different layers of the flow travel with different velocities due to e.g. different speeds of adjacent walls) in relation to density. That is, the Prandtl number formula is given as:
ν is momentum diffusivity (kinematic viscosity) [m2/s]
α is thermal diffusivity [m2/s]
μ is dynamic viscosity [N.s/m2]
k is thermal conductivity [W/m.K]
cp is specific heat [J/kg.K]
ρ is density [kg/m3]
Small values of the Prandtl number, Pr << 1, means the thermal diffusivity dominates. Whereas with large values, Pr >> 1, the momentum diffusivity dominates the behavior. For example, the typical value for liquid mercury, which is about 0.025, indicates that the heat conduction is more significant compared to convection, so thermal diffusivity is dominant. When Pr is small, it means that the heat diffuses quickly compared to the velocity.
In comparison to Reynolds number, the Prandtl number is not dependent on geometry of an object involved in the problem, but is dependent solely on the fluid and the fluid state. As such, the Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity.
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