Nusselt Number Calculator (Nu = hL / k)

Method and variables

Definition: Nu = hL/k. Dittus–Boelter: Nu = 0.023Re^0.8Prⁿ, where n = 0.4 for a fluid being heated and 0.3 for a fluid being cooled.

h — convection heat-transfer coefficient
L — characteristic length; hydraulic diameter for the internal-pipe correlation
k — fluid thermal conductivity
Re and Pr — Reynolds and Prandtl numbers evaluated at a consistent reference state

Worked example

For a fluid being heated in a circular pipe with Re = 50,000 and Pr = 7, Dittus–Boelter gives Nu = 0.023 × 50,000^0.8 × 7^0.4 ≈ 330. With k = 0.598 W/(m·K) and D = 0.05 m, h is about 3,947 W/(m²·K).

Correlation scope

The Dittus–Boelter mode screens Re ≥ 10,000, 0.6 ≤ Pr ≤ 160 and L/D ≥ 10. It assumes fully developed, single-phase turbulent flow in a smooth circular tube and modest property variation. Outside that scope, select a correlation that actually matches the geometry and condition.

Important limits

This is not for laminar, transition, strongly developing, rough, non-circular, multiphase, boiling/condensing, large-property-variation or gas-compressibility cases. Passing the built-in screening limits is not final design validation.

References

Frequently asked questions

What does Nusselt number represent?
Nusselt number is the dimensionless ratio represented by Nu = hL/k. It connects a convection coefficient to a characteristic length and fluid thermal conductivity.

When can I use Dittus–Boelter?
This page screens the commonly stated conditions for fully developed turbulent flow in a smooth circular tube: Re at least 10,000, Pr between roughly 0.6 and 160, and heated length to diameter ratio at least 10. It remains an estimate, not a universal rule.

Why does the exponent change for heating and cooling?
The usual Dittus–Boelter form uses Pr to the power 0.4 when the fluid is heated and 0.3 when it is cooled.