Nusselt Number Calculator
Calculate the Nusselt number (Nu), the key dimensionless parameter characterising convective heat transfer. Choose between the fundamental definition Nu = hL/k, the flat-plate empirical correlation, or the Dittus-Boelter equation for internal pipe flow.
Method
W/(m²·K)
m
W/(m·K)
Ratio of convective to conductive heat transfer
h = 200 W/(m²·K)
L = 0.5 m
k = 0.6 W/(m·K)
Nu = hL/k
- 1
h × L
200 × 0.5 = 100 - 2
Nusselt number Nu = (h × L) ÷ k
100 ÷ 0.6 = 166.6667
How does this calculator work?
The Nusselt number Nu = hL/k quantifies convective vs conductive heat transfer. For flat plate laminar flow use Nu = 0.664 Re^½ Pr^⅓; for turbulent pipe flow use the Dittus-Boelter equation Nu = 0.023 Re^0.8 Pr^n (n=0.4 heating, 0.3 cooling). Nu = 1 is pure conduction; larger values mean stronger convection.
Formula
How this is calculated
The Nusselt number compares convective to conductive heat transfer across a fluid layer: Nu = hL/k, where h is the convective heat transfer coefficient (W/(m²·K)), L is a characteristic length (m), and k is the fluid thermal conductivity (W/(m·K)). A Nusselt number of 1 means pure conduction; values much greater than 1 indicate strong convection relative to conduction.
For external flow over a flat plate, the average Nusselt number is given by empirical correlations from Incropera (7th ed.). In the laminar regime (Re ≤ 5×10⁵, Pr > 0.6): Nu_avg = 0.664 Re^(1/2) Pr^(1/3). For mixed laminar-turbulent boundary layers at higher Reynolds numbers: Nu_avg = (0.037 Re^(4/5) − 871) Pr^(1/3) using a critical Reynolds number of 5×10⁵.
For fully developed turbulent flow inside smooth circular pipes (Re > 10,000; 0.7 < Pr < 160; L/D > 10), the Dittus-Boelter equation applies: Nu = 0.023 Re^(4/5) Pr^n, where n = 0.4 when the fluid is being heated and n = 0.3 when cooled. These correlations are engineering approximations; they assume constant fluid properties and can disagree with experimental data by ±25% outside their stated validity ranges.
Frequently asked questions
A high Nusselt number means convection is much more effective than conduction for transferring heat. Nu = 1 would be pure conduction; Nu = 100 means convection transfers 100 times more heat than conduction alone would across the same fluid layer.
The Prandtl number Pr = ν/α is the ratio of kinematic viscosity to thermal diffusivity. Typical values at ~20 °C: air ≈ 0.71, water ≈ 7, engine oil ≈ 100–1000. Look up fluid property tables at your operating temperature.
It is valid for turbulent, fully developed flow in smooth circular tubes with Re > 10,000, Prandtl number between 0.7 and 160, and length-to-diameter ratio L/D > 10. Outside these ranges use more specialised correlations such as Gnielinski.
Also known as
TG we-Calculate Editorial Team. (2026). Nusselt Number Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/nusselt-number-calculator
TG we-Calculate Editorial Team. "Nusselt Number Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/nusselt-number-calculator.
TG we-Calculate Editorial Team, "Nusselt Number Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/nusselt-number-calculator
@misc{wecalculate_nusselt_number_calculator, title = {Nusselt Number Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/nusselt-number-calculator}}, year = {2026}, note = {TG we-Calculate} }
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