Nusselt Number
Nusselt number formula Nu = hL/k for convective heat transfer.
Includes correlations for common geometries and worked examples.
The Formula
The Nusselt number is a dimensionless quantity that measures the ratio of convective to conductive heat transfer at a surface. A Nusselt number of 1 means heat is transferred purely by conduction through a stagnant fluid layer. Higher values indicate that convection is significantly enhancing heat transfer beyond what conduction alone would provide.
Named after Wilhelm Nusselt, who introduced the concept in 1915, this number is central to thermal engineering. When designing heat exchangers, cooling systems, or any device where heat must be transferred between a solid surface and a flowing fluid, engineers rely on Nusselt number correlations to predict performance.
The Nusselt number depends on the flow conditions and geometry. For forced convection over a flat plate in turbulent flow, a common correlation is Nu = 0.037 Re0.8 Pr1/3, where Re is the Reynolds number and Pr is the Prandtl number. For natural convection from a vertical plate, the correlation involves the Rayleigh number instead. Dozens of correlations exist for different geometries such as pipes, spheres, cylinders, and channels.
Once you know the Nusselt number, you can solve for the convective heat transfer coefficient h, which directly tells you how fast heat moves between the surface and the fluid. This coefficient is essential for calculating total heat transfer rates in real engineering systems.
Variables
| Symbol | Meaning |
|---|---|
| Nu | Nusselt number (dimensionless) |
| h | Convective heat transfer coefficient (W/m²·K) |
| L | Characteristic length (m) |
| k | Thermal conductivity of the fluid (W/m·K) |
Example 1
Air flows over a flat plate. The convective coefficient is h = 25 W/m²·K, plate length L = 0.5 m, and air conductivity k = 0.026 W/m·K. Find Nu.
Nu = hL / k = 25 × 0.5 / 0.026
Nu = 12.5 / 0.026
Nu ≈ 481 (strong convective enhancement over conduction)
Example 2
Water flows through a pipe with Nu = 120, pipe diameter L = 0.02 m, and water conductivity k = 0.6 W/m·K. Find h.
h = Nu × k / L = 120 × 0.6 / 0.02
h = 72 / 0.02
h = 3,600 W/m²·K
When to Use It
The Nusselt number is used whenever convective heat transfer must be quantified.
- Designing heat exchangers for industrial processes
- Sizing cooling systems for electronics and machinery
- HVAC engineering for building climate control
- Automotive engineering for engine and brake cooling
- Aerospace engineering for thermal management of spacecraft and aircraft