Formula & Calculator
Nusselt Number
Dimensionless ratio of convective to conductive heat transfer across a fluid boundary layer.
Interpretation
Nusselt number: Nu = h·L/k, ratio of convective to conductive heat transfer. Example: h=50, L=0.1, k=0.6 → Nu=8.33.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Nu | Nusselt number | |
| h | Convective heat transfer coefficient | W/m2.K |
| L | Characteristic length | m |
| k | Fluid thermal conductivity | W/m.K |
What it means
The Nusselt number is a dimensionless parameter that represents the enhancement of heat transfer due to convection compared to conduction alone. It is defined as Nu = h L / k, where h is the convective heat transfer coefficient, L is a characteristic length (e.g., pipe diameter or plate length), and k is the thermal conductivity of the fluid. In forced convection, Nu is often correlated with Re and Pr via empirical equations (e.g., Dittus‑Boelter). A higher Nu indicates more effective convective heat transfer. This number is used in the design of heat exchangers, cooling of electronic components, and many thermal engineering applications. It allows engineers to scale up from experimental data to full‑scale equipment. The Nusselt number is named after Wilhelm Nusselt, who made significant contributions to heat transfer theory. It is a central concept in convective heat transfer analysis.
Worked example
Nusselt Number – Two Examples
Real‑World| Parameter | Value |
|---|---|
| h | 500 W/m²K |
| L | 0.05 m |
| k | 0.6 W/mK |
| Parameter | Value |
|---|---|
| h | 1000 |
| L | 0.1 |
| k | 0.6 |
Common mistakes
- Characteristic length L: Depends on geometry (e.g., D for a pipe, L for a flat plate). Choose the correct one.
- Heat transfer coefficient h: The average coefficient over the surface, not local.
- Thermal conductivity k: At the film temperature (average of surface and fluid temperatures).
- Units: h in W/(m²·K), L in m, k in W/(m·K) → Nu is dimensionless.
- Physical meaning: Nu = 1 means pure conduction; larger Nu indicates convection enhancement.
Applications
The Nusselt number, Nu = h·L/k, is the ratio of convective to conductive heat transfer across a fluid boundary layer. It is a key dimensionless parameter in convective heat transfer correlations. Engineers use Nu to calculate the convective heat transfer coefficient h from empirical correlations for different geometries (e.g., flow inside pipes, over flat plates, around spheres). Accurate h values are essential for sizing heat exchangers, cooling systems, and electronic devices. The Nusselt number depends on Reynolds and Prandtl numbers, and its relationship is determined experimentally or via numerical simulations. By applying Nu correlations, engineers can predict heat transfer rates, design effective cooling systems, and ensure thermal management in a wide range of applications.
- Calculation of convective heat transfer coefficients in pipes, ducts, and external flows
- Design of heat exchangers and cooling systems
- Thermal analysis of electronics and power electronics
- HVAC system design and comfort analysis
- Natural and forced convection studies in buildings and equipment
Frequently Asked Questions
The Nusselt number is a dimensionless parameter that represents the ratio of convective to conductive heat transfer across a boundary: Nu = h·L / k, where h is the convective heat transfer coefficient, L is the characteristic length, and k is the thermal conductivity of the fluid. It is used to correlate heat transfer data.
- For laminar flow in a pipe: Nu ≈ 3.66 (constant wall temperature) or 4.36 (constant heat flux).
- For turbulent flow in a pipe: Nu ranges from 50 to several hundred.
- For natural convection, Nu depends on Ra and is often < 10 for gases.
- Using the wrong characteristic length – L must match the correlation (e.g., diameter for pipe, length for plate).
- Using a correlation outside its range of Re, Pr, or Ra.
- Assuming Nu is constant – it varies with flow conditions.
- Using the wrong definition (e.g., using Nu based on diameter vs length).
Once Nu is known from a correlation, h = Nu·k / L. This is the key step in calculating the overall heat transfer coefficient U.
The local Nu varies along the surface; the average Nu is the integrated value over the length. Correlations often give the average Nu for the whole surface.
For forced convection, Nu typically increases with Re (turbulent mixing) and Pr (fluid properties). A common correlation for turbulent pipe flow is Dittus‑Boelter: Nu = 0.023·Re^0.8·Pr^n, where n = 0.4 for heating, 0.3 for cooling.
When Nu = 1, the heat transfer is purely by conduction (no convection enhancement). This is the case for a stagnant fluid film.
Nu is used to predict h, which is needed to calculate U and then the required area. It is also used in calculating the effectiveness and NTU of heat exchangers.