Nusselt Number Calculator
Find convective heat transfer coefficient from Nusselt correlations.
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Formulas
Nu = hL/kDittus-Boelter: Nu = 0.023 Re^0.8 Pr^0.4 (turbulent, heating). Valid for Re > 10,000.
Nusselt Number
Ratio of convective to conductive heat transfer. Nu = 1: pure conduction. Higher Nu = stronger convection. Prandtl numbers: Air 0.71, Water 7, Engine oil 100-1000. Used in heat exchanger and cooling system design.
What the Nusselt Number Means
The Nusselt number is a dimensionless measure of convective heat transfer relative to conduction across a fluid layer. It tells you how much convection enhances heat transfer:
Nu = hL/kNu is the Nusselt number, h is the convective heat transfer coefficient (W/m²·K), L is the characteristic length, and k is the fluid's thermal conductivity.
Nu = 1 means heat moves by pure conduction (as in a still fluid). Higher values mean convection dominates — turbulent flow over a surface can give Nusselt numbers in the hundreds.
Worked Example
If Nu = 50 for airflow (k = 0.026 W/m·K) over a 0.1 m plate, rearrange to find h:
h = Nu × k / L = 50 × 0.026 / 0.1 = 13 W/m²·K
Typical Nusselt Ranges
| Situation | Nu (order of magnitude) |
|---|---|
| Pure conduction (still fluid) | ~1 |
| Free (natural) convection | 1 – 10s |
| Forced convection, laminar | 10s |
| Forced convection, turbulent | 100s |
Frequently Asked Questions
How is the Nusselt number found?
From empirical correlations involving the Reynolds and Prandtl numbers, such as the Dittus-Boelter equation for turbulent pipe flow.
What is the characteristic length?
A representative dimension of the geometry — pipe diameter for internal flow, or plate length for flow over a surface. It must match the correlation used.
Why is it dimensionless?
Dimensionless numbers let results scale across different sizes and fluids, so a correlation derived from lab tests applies to full-size equipment.