1. What is the Prandtl Number?

The Prandtl Number (Pr) is a dimensionless number defined as the ratio of kinematic viscosity (ν) to thermal diffusivity (α). It relates the relative thickness of the velocity boundary layer to the thermal boundary layer in fluid flow.

2. How Does the Calculator Work?

The calculator uses the Prandtl Number equation:

Where:

• \( \nu \) — Kinematic viscosity (m²/s)
• \( \alpha \) — Thermal diffusivity (m²/s)
• \( Pr \) — Dimensionless Prandtl number

Explanation: The Prandtl number compares momentum diffusivity (viscosity) to thermal diffusivity, indicating how quickly momentum diffuses relative to heat in a fluid.

3. Importance of Prandtl Number

Details: The Prandtl number is crucial in heat transfer calculations, determining whether heat or momentum diffuses faster in a fluid. It affects convection patterns and boundary layer development.

4. Using the Calculator

Tips: Enter both kinematic viscosity and thermal diffusivity in m²/s. Both values must be positive numbers. The result is dimensionless.

5. Frequently Asked Questions (FAQ)

Q1: What are typical Prandtl number values?
A: For gases, Pr ≈ 0.7-1.0; for water at 20°C, Pr ≈ 7; for oils, Pr ≈ 100-40,000.

Q2: How does Pr affect heat transfer?
A: Fluids with Pr ≪ 1 (liquid metals) have thermal boundary layers thicker than velocity boundary layers. Fluids with Pr ≫ 1 (oils) have thinner thermal boundary layers.

Q3: What's the difference between Pr and Re numbers?
A: Reynolds number (Re) relates inertial to viscous forces, while Pr relates momentum diffusivity to thermal diffusivity.

Q4: Can Pr be less than 1?
A: Yes, for liquid metals and some gases, Pr can be much less than 1.

Q5: How does temperature affect Pr?
A: Pr generally decreases with temperature for liquids (as viscosity decreases faster than thermal conductivity increases) and increases slightly for gases.