Table of Contents
What Is the Nusselt Number?
The Nusselt number (Nu) is a dimensionless number that characterizes the ratio of convective to conductive heat transfer at a boundary. A Nusselt number of 1 means heat transfer is purely by conduction; higher values indicate enhanced heat transfer due to convection. It is one of the most important parameters in thermal engineering and heat exchanger design.
Named after Wilhelm Nusselt, this number depends on flow conditions (laminar or turbulent), geometry, and fluid properties. Engineers use empirical correlations involving Reynolds, Prandtl, and Grashof numbers to predict the Nusselt number for various configurations. Once known, it directly gives the heat transfer coefficient.
Formula
Where h is the convective heat transfer coefficient (W/m²K), L is the characteristic length (m), and k is the thermal conductivity of the fluid (W/mK).
Common Correlations
| Configuration | Correlation | Conditions |
|---|---|---|
| Flat plate (laminar) | Nu = 0.332 Re^0.5 Pr^0.33 | Re < 5×10⁵ |
| Flat plate (turbulent) | Nu = 0.0296 Re^0.8 Pr^0.33 | Re > 5×10⁵ |
| Pipe (turbulent) | Nu = 0.023 Re^0.8 Pr^0.4 | Dittus-Boelter |
| Natural convection (vertical) | Nu = 0.59 (GrPr)^0.25 | 10⁴ < GrPr < 10⁹ |
Frequently Asked Questions
What does a high Nusselt number mean?
A high Nusselt number indicates that convection is much more effective than conduction alone at transferring heat. Turbulent flows, high velocities, and rough surfaces all increase the Nusselt number. For forced convection in pipes, Nu can range from 10 to over 1000.
How do I choose the characteristic length?
The characteristic length depends on geometry: for pipes it is the diameter, for flat plates it is the plate length in the flow direction, and for spheres it is the diameter. Using the correct length is essential for applying correlations properly.