Nusselt Number Calculator
The Nusselt number calculator determines the dimensionless convective heat transfer coefficient for flow over flat plates and through pipes. The Nusselt number links fluid mechanics (Reynolds number, Prandtl number) to heat transfer (convection coefficient h), making it the cornerstone of convective heat transfer analysis. Chemical process engineers use Nu to design heat exchangers and reactors. HVAC engineers use it to calculate cooling effectiveness of air over surfaces and through ducts. Electronics cooling engineers use it to determine how effectively air or liquid removes heat from chips and circuit boards. Select the geometry and flow regime, enter the dimensionless numbers, and the tool returns Nu and the convection coefficient.
Nusselt number correlations
Flat plate laminar (Re less than 5e5): Nu = 0.664 * Re^0.5 * Pr^(1/3)
Flat plate turbulent (Re greater than 5e5): Nu = 0.037 * Re^0.8 * Pr^(1/3)
Pipe turbulent (Dittus-Boelter): Nu = 0.023 * Re^0.8 * Pr^n
Pipe laminar (Re less than 2300): Nu = 3.66
h = Nu * k / L
Typical Prandtl numbers
- Air at 25 degC: Pr = 0.71
- Water at 20 degC: Pr = 7.0
- Water at 100 degC: Pr = 1.76
- Engine oil at 25 degC: Pr = 1,600
- Mercury at 25 degC: Pr = 0.025
Nusselt number: frequently asked questions
What is the Nusselt number?
The Nusselt number (Nu) is a dimensionless number representing the ratio of convective to conductive heat transfer at a fluid-solid boundary. Nu = h * L / k_fluid. A higher Nusselt number means convection is much more effective than pure conduction. Nu = 1 means pure conduction; Nu values of 100 to 1000 are typical for forced convection.
How is Nu calculated for flow over a flat plate?
For laminar flow over a flat plate (Re less than 5e5): Nu = 0.664 * Re^(0.5) * Pr^(1/3). For turbulent flow (Re greater than 5e5): Nu = 0.037 * Re^(0.8) * Pr^(1/3). These are the Pohlhausen and Colburn correlations. Re = u*L/nu and Pr = mu*Cp/k for the fluid.
How is Nu calculated for flow inside a pipe?
For fully developed turbulent pipe flow (Re greater than 10,000), the Dittus-Boelter equation gives: Nu = 0.023 * Re^0.8 * Pr^n, where n = 0.4 for heating and n = 0.3 for cooling. For laminar pipe flow (Re less than 2300), Nu = 3.66 (constant wall temperature) or 4.36 (constant heat flux).
What is Prandtl number?
Prandtl number (Pr) is the ratio of momentum diffusivity (viscosity) to thermal diffusivity: Pr = Cp * mu / k. For gases Pr is around 0.7. For water Pr is 7 at 20 degC. For engine oil Pr is 1000 to 10000. Pr tells you whether velocity or temperature boundary layers are thicker.
How do I find h from the Nusselt number?
Once Nu is calculated from a correlation, the convective heat transfer coefficient is h = Nu * k_fluid / L, where k_fluid is the thermal conductivity of the fluid and L is the characteristic length (plate length or pipe diameter). h has units of W/(m^2*K).
Official sources
- NIST: NIST Reference Fluid Thermodynamic Properties.
- ASHRAE: ASHRAE Handbook of Fundamentals - Heat Transfer.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.