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How It Works
The Prandtl number tells you which boundary layer grows faster: the velocity layer or the thermal layer. When Pr < 1, heat diffuses faster than momentum, producing a thick thermal boundary layer (typical of liquid metals). When Pr > 1, momentum diffuses faster, so the velocity boundary layer is thicker (typical of oils and water).
Pr is a pure fluid property -- it depends only on temperature and the substance, not on flow geometry or speed. It appears in nearly every Nusselt-number correlation, making it one of the most referenced dimensionless numbers in heat-transfer engineering.
Example Problem
Engine oil at 60 °C has kinematic viscosity ν = 8.4 × 10⁻⁵ m²/s and thermal diffusivity α = 8.6 × 10⁻⁸ m²/s. What is the Prandtl number?
- Pr = ν / α = 8.4 × 10⁻⁵ / 8.6 × 10⁻⁸
- Pr = 977
An extremely high Prandtl number means the thermal boundary layer in oil is very thin compared to the velocity boundary layer, which is why oil requires large heat-exchanger surfaces.
Frequently Asked Questions
What is the Prandtl number of air and water?
At 20 °C, air has Pr ≈ 0.71 and water has Pr ≈ 7.0. As water heats to 100 °C, Pr drops to about 1.75 because viscosity decreases faster than thermal diffusivity. Liquid metals like mercury have Pr ≈ 0.025.
Why does the Prandtl number matter for heat transfer correlations?
Most Nusselt-number correlations (like Dittus-Boelter: Nu = 0.023 Re⁰⋅⁸ Pr⁰⋅⁴) include Pr because the relative thickness of boundary layers directly affects how efficiently heat is transferred. A fluid with higher Pr needs more surface area or higher velocity to achieve the same heat-transfer rate.
How is the Prandtl number related to the Lewis and Schmidt numbers?
The Lewis number equals Sc / Pr, linking all three. Pr compares momentum to thermal diffusivity, Sc compares momentum to mass diffusivity, and Le compares thermal to mass diffusivity. Together they fully characterize the relative rates of momentum, heat, and mass transport.
Can the Prandtl number change with temperature?
Yes, significantly. Water's Pr drops from about 13 at 0 °C to 1.75 at 100 °C because viscosity is strongly temperature-dependent. For gases, Pr is relatively stable (air stays near 0.71 from 0 to 300 °C).
Related Calculators
- Nusselt Number Calculator — convective heat transfer ratio that depends on Pr.
- Schmidt Number Calculator — the mass-transfer analogue of the Prandtl number.
- Lewis Number Calculator — ratio of thermal to mass diffusivity (Sc/Pr).
- Peclet Number Calculator — advective vs. diffusive transport, using Pe = Re × Pr.
- Reynolds Number Calculator — determine the flow regime paired with Prandtl number correlations.
- Thermal Diffusivity Calculator — find thermal diffusivity, the denominator in the Prandtl ratio.