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Prandtl Number

Heat Transfer Engineering and Design

Prandtl Number

The relative thickness of the velocity and the thermal boundary layers is best described by the dimensionless parameter Prandtl number, defined as:

Pr = v / α

Pr = µ C_p / k

Pr = Molecular diffusivity of momentum / Molecular diffusivity of heat

Prandtl Number are unit-less.

The Prandtl numbers of fluids range from less than 0.01 for liquid metals to more than 100,000 for heavy oils (Table below). Note that the Prandtl number is in the order of 10 for water.

The Prandtl numbers of gases are about 1, which indicates that both momentum and heat dissipate through the fluid at about the same rate. Heat diffuses very quickly in liquid metals (Pr < 1) and very slowly in oils (Pr > 1) relative to momentum. Consequently the thermal boundary layer is much thicker for liquid metals and much thinner for oils relative to the velocity boundary layer.

Typical ranges of Prandtl numbers for common fluids
Fluid	Pr
Liquid metals	0.004–0.030
Gases	0.7–1.0
Water	1.7–13.7
Light Organic Fluids	5–50
Oils	50–100,000
Glycerin	2000–100,000