Nusselt Number Calculator

Calculation method

Use direct definition when you already know h. Use correlations when you only know Reynolds and Prandtl numbers.

Heat transfer coefficient, h (W/m²·K)

Thermal conductivity, k (W/m·K)

Characteristic length, L

Boundary condition

Applies to fully developed laminar flow in a circular tube.

Reynolds number, Re

Prandtl number, Pr

Thermal condition

Reynolds number based on length, Re_L

Computed from Re_L = ρ·V·L / μ, if needed.

Prandtl number, Pr

Decimal places

Formula used

The Nusselt number (Nu) is a dimensionless ratio that compares convection to pure conduction across a fluid layer near a surface.

Nu = h·L / k (direct definition)
Nu = 0.023·Re^0.8·Pr^n (Dittus–Boelter, turbulent internal flow)
Nu_L = 0.664·Re_L^0.5·Pr^(1/3) (average laminar flat plate)
Nu_L = (0.037·Re_L^0.8 − 871)·Pr^(1/3) (average turbulent flat plate)
Nu = 3.66 or Nu = 4.36 (fully developed laminar tube, idealized)

Correlations are approximations; apply them within their typical ranges and assumptions.

How to use this calculator

Select a calculation method that matches your scenario.
Enter the required inputs (numbers only; units where provided).
Click Calculate to display results above the form.
Review the details table to confirm the formula and assumptions.
Use Download CSV or Download PDF for documentation.

Example data table

Scenario	Method	Inputs (sample)	Output
Water over a small surface	Direct	h=120 W/m²·K, L=0.05 m, k=0.60 W/m·K	Nu ≈ 10.0
Turbulent pipe flow	Dittus–Boelter	Re=80,000, Pr=6.9, heating	Nu ≈ 333
Air over flat plate	Laminar plate	Re_L=200,000, Pr=0.71	Nu_L ≈ 248

Values are illustrative. Your results depend on your inputs and chosen method.

Nusselt number guide for practical heat-transfer work

1) Meaning of the Nusselt number

The Nusselt number (Nu) compares convection to pure conduction across a fluid layer. Nu = 1 indicates conduction-dominated transfer, while larger Nu signals stronger convection. It links directly to the heat-transfer coefficient using h = Nu·k/L.

2) Typical values by regime

In fully developed laminar tube flow, Nu is commonly 3.66 (constant wall temperature) or 4.36 (constant heat flux). Turbulent internal flows often produce Nu in the tens to hundreds as Reynolds number rises. External forced convection varies widely with geometry and surface conditions.

3) Internal laminar options included here

This calculator provides fully developed laminar cases and a developing-flow correction when you enter tube length. Entrance effects become important when the thermal entrance length is not small compared with the heated length. Use consistent units for diameter, length, and properties.

4) Internal turbulent correlations

The Dittus–Boelter form Nu = 0.023·Re^0.8·Prⁿ is common for smooth tubes. Typical exponents are n = 0.4 for heating and n = 0.3 for cooling. A Gnielinski-style option is also provided for broader accuracy in many applications.

5) External convection over a flat plate

Flat-plate correlations depend on whether the boundary layer is laminar or turbulent. Laminar averages scale roughly with Re_L^1/2, while turbulent averages scale closer to Re_L^0.8, both with a mild Pr dependence. Always use plate length along the flow as L.

6) Why Prandtl number matters

Prandtl number (Pr) reflects how fast momentum diffuses compared with heat. Many gases are near 0.7, water near room temperature is about 7, and oils can be much higher. Evaluate properties near a representative film temperature when temperature differences are large.

7) Validity checks before trusting Nu

Confirm your Reynolds number falls within the intended range for the selected correlation. Ensure the geometry assumption matches your case (smooth tube, flat plate, uniform properties). For pipes, laminar is often Re < 2300 and turbulent above about 4000. For flat plates, transition may begin near Re_L ≈ 5×10^5. If flow is transitional or roughness is significant, use a more specialized model.

8) Turning Nu into engineering outputs

After Nu, compute h and then estimate heat transfer with Q = h·A·ΔT. Combine convection with wall conduction and fouling in an overall resistance network. Record the chosen method and inputs so designs remain auditable and repeatable.

FAQs

1) What does Nu = 1 physically mean?

Nu = 1 means convection is no stronger than conduction across the fluid layer. Heat transfer behaves like a stagnant film, so the convective coefficient h equals k/L for the chosen length scale.

2) Which characteristic length should I use?

Use hydraulic diameter for internal duct or pipe flow. For a flat plate, use the plate length in the flow direction. For other shapes, use the length definition specified by the chosen correlation.

3) When is Dittus–Boelter not recommended?

Avoid it for laminar flow, strong property variation, very rough tubes, low Prandtl numbers, or short entrance-length situations. In those cases, a correlation with friction factor or developing-flow treatment is safer.

4) What Prandtl number range is typical?

Many gases are around 0.7, water near room temperature is about 7, and many oils are much higher. Always use properties at a representative temperature because Pr changes with temperature.

5) Why does turbulent flow give much larger Nu?

Turbulence increases mixing and reduces the effective thermal boundary-layer thickness. That increases the temperature gradient at the wall, which raises the convective heat transfer coefficient and therefore Nu.

6) Can I use Nu to compute heat-transfer coefficient directly?

Yes. Once Nu is known, compute h = Nu·k/L. Use the same k and length scale used for Nu. Then combine h with area and temperature difference for heat-rate estimates.

7) What inputs most strongly affect the result?

Reynolds number and Prandtl number usually dominate because correlations often scale like Re^0.5–0.8 and Pr^0.3–0.4. Geometry choices (diameter, length) and regime selection also matter.