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 unitless.
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

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