Prandtl Number (Pr)

It is the dimensionless parameter which gives the relation between the relative thickness of the velocity boundary layer and thermal boundary layer.

It is denoted by Pr.

Pr =  (Momentum diffusivity)/(Thermal diffusivity)

     = V/α

     = (µ x ρ x Cp )/(ρ x k )

Pr = (µ x Cp )/( k )

Here,

V - Kinematic viscosity, Stroke

μ - Dynamic Viscosity, kg/m-s

α - Thermal diffusivity, k/(ρ x Cp)

Cp - Specific Heat, J/kg K

k - Thermal conductivity, W/mK

Its value is more than 100,000 for heavy oils and less than 0.01 for liquid metals.

It is in the order of 10 for water. 

For gases, it varies from 0.004 to 1, which depicts that both momentum and heat dissipate through the fluid medium at same rate.

It is clear that, heat diffuses very quickly in liquid metals (Pr < 1) relative to momentum transfer. At the same time, as in case of oils, it is very slow. (Pr > 1)

Also, the thermal boundary layer is thicker for liquid metals and thinner for oils comparative to velocity boundary layer.





Note :

The dimensionless number is named after Ludwig Prandtl , who initially set up the concept of boundary layer in  1904 and give major contributions to boundary layer theory.