Nusselt Number

What is the Nusselt Number (Nu)?

The Nusselt Number (Nu) is a dimensionless parameter widely used in heat transfer analysis. It represents the ratio of convective heat transfer to conductive heat transfer across a boundary layer in a fluid.

Specifically:

• A Nusselt number of 1 indicates that heat transfer is entirely by pure conduction (fluid is stationary).
• A higher Nusselt number indicates that convective heat transfer (due to fluid movement/flow) is enhancing the rate of heat transfer.

The Nusselt Number Formula

The formula is:

Where:

• h is the convective heat transfer coefficient (W/m²·K)
• L is the characteristic length (meters), such as pipe diameter or plate length
• k is the thermal conductivity of the fluid (W/m·K)

Common Correlations

In engineering practice, the Nusselt number is rarely calculated from first principles. Instead, it is estimated using empirical correlations. Some of the most famous include:

• Dittus-Boelter Equation: Used for fully developed turbulent flow in circular tubes.
• Sieder-Tate Correlation: Accounts for large variations in fluid viscosity due to temperature gradients.
• Churchill-Bernstein Correlation: Applies to crossflow over cylinders over a wide range of Reynolds numbers.