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What Nu is a ratio of
The calculator evaluates h × L ÷ k. That is h divided by k/L, the coefficient a stagnant fluid layer of thickness L would give by conduction alone, so the result says how many times stronger the actual convection is than pure conduction over the same length. Because the number depends on how L is chosen, compare only cases that define L the same way.
Variables and SI units
| Symbol | Meaning | SI unit | Example |
|---|---|---|---|
| h | Convective coefficient from measurement or a validated correlation | W/(m²·K) | 50 |
| L | Length defined for the geometry, such as pipe diameter, hydraulic diameter or plate length | m | 0.1 |
| k | Thermal conductivity of the fluid, not the wall | W/(m·K) | 0.6 |
Where does h come from?
h comes from measurements or from a correlation for the geometry and flow. Design work usually finds Nu from a correlation first and converts it with h = Nu·k/L. This calculator runs the other way: convert an h measured on a test rig, or a wall heat-transfer coefficient reported by CFD, into Nu, and it can be set against the laminar tube values 3.66 and 4.36 or a turbulent correlation on the same scale.
Units and length definitions
- h is in W/(m²·K) and k in W/(m·K); one metre of the m² cancels with L, leaving Nu dimensionless.
- Older data in kcal/(h·m²·°C) convert by multiplying by 1.163 (1 kcal/h = 1.163 W). A temperature difference in °C equals the same difference in K.
- Entering L in mm makes the result 1000 times too large; a 4 mm tube is 0.004.
- k is the fluid's conductivity. The number that uses the wall's conductivity is the Biot number.
Examples you can reproduce in the calculator
Example 1. Changing only k in the "Fill example values" case
Inputs: the button fills h = 50 W/(m²·K), L = 0.1 m and k = 0.6 W/(m·K), the last being a rounded room-temperature water conductivity.
Calculation: Nu = 50 × 0.1 ÷ 0.6 = 8.33. Changing L to 0.05 m halves it to 4.17.
Changing k: with the same h and L, 20 °C air at k = 0.0258 W/(m·K) (IAEA Table 3.1) gives Nu = 193.8, while mistakenly entering type 316 stainless steel at k = 14.0 W/(m·K) (IAEA Table 6.20, 300 K) gives 0.357.
Interpretation: the same h yields Nu values more than 500 times apart depending on the k. A result below 1 usually means a solid's k was entered instead of the fluid's, or L has the wrong unit.
Example 2. Converting a measured h to Nu and comparing with laminar values
Given: 20 °C water flows in a 10 mm tube, and a test is assumed to have given a mean h = 2000 W/(m²·K). Water k is 0.5995 W/(m·K) from IAEA Table 3.3.
Inputs and calculation: h = 2000, L = 0.01 and k = 0.5995 give Nu = 33.4.
Interpretation: that is 7.7 to 9.1 times the fully developed laminar values of 3.66 (constant wall temperature) and 4.36 (constant heat flux), so the test section is not in fully developed laminar flow. It is either turbulent or strongly affected by the entry region. Compute Re from the velocity and viscosity to tell which, and if turbulent compare with Dittus–Boelter or Gnielinski.
Example 3. The error from entering an h in kcal units
Given: an old design sheet is assumed to list h = 1000 kcal/(h·m²·°C) for a 25 mm pipe carrying 60 °C water (IAEA Table 3.3, k = 0.6510 W/(m·K)).
Unit conversion: h = 1000 × 1.163 = 1163 W/(m²·K).
Calculation: Nu = 1163 × 0.025 ÷ 0.6510 = 44.7. Entering 1000 unconverted gives 38.4, 14% low.
Interpretation: because the factor 1.163 is close to 1, the wrong result still looks plausible. Check the unit label on the data first.
The thermal and mass diffusion note computes Nu = 10 from h = 120 W/(m²·K), L = 0.05 m and k = 0.6 W/(m·K), then shows that a heat flux additionally needs a temperature difference.
Using the Nusselt number calculator
What do I enter for L in a non-circular duct?
The length the correlation defines; for duct flow this is usually the hydraulic diameter Dh = 4A/P, with A the cross-section and P the wetted perimeter. A 20 mm × 10 mm rectangular duct has Dh = 4 × 0.02 × 0.01 ÷ 0.06 = 0.0133 m.
Can I enter the wall heat-transfer coefficient reported by CFD?
First check the reference temperature behind it. Depending on the software, h may be defined from the difference between wall and bulk temperature or between the wall and a user-set reference temperature. Only an h defined the same way as in the correlation gives a comparable Nu.
Can I get the heat rate from Nu?
Not from Nu alone. Convert back to h, then multiply by area and temperature difference (Q = hAΔT). In pipe flow the fluid temperature changes along the pipe, so something like a log-mean temperature difference is also needed.
References
- Idaho National Laboratory: RELAP-7 Theory Manual, Rev. 2. Fully developed laminar tube values 4.36 and 3.66, h = Nu·k/Dh (eq 589), k evaluated at the fluid bulk temperature
- Michigan Technological University: CM3120 Module 2 Lecture IV. Warning that Nu and Bi have similar definitions but different meanings
- IAEA: Thermophysical Properties of Materials for Nuclear Engineering (2008). Conductivity of water (Table 3.3), air (Table 3.1) and type 316 stainless steel (Table 6.20)
Related guides and calculators
Guide
Calculation notes
- Thermal and mass diffusion: the distinct roles of Pr, Sc, Pe and Nu: How the Nu from this calculator differs from diffusion scales, and what else a heat flux needs.
Related calculators
- Prandtl number (Pr): Compute Pr from properties at the same temperature before using a Nu correlation.
- Péclet number (Pe): Gives the advection-to-diffusion ratio but no h, so do not use it in place of Nu.
- Schmidt number (Sc): Takes the place of Pr when a Sherwood number is used for mass-transfer coefficients.