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How It Works
The Nusselt number compares convective heat transfer at a surface to pure conduction through the fluid. A Nu of 1 means convection adds nothing beyond what conduction alone would provide. In practice, turbulent flows over heated surfaces produce Nu values of 100 or more, meaning convection is far more effective than conduction.
Engineers use Nusselt correlations (functions of Reynolds and Prandtl numbers) to determine the convection coefficient h without costly experiments, enabling quick sizing of heat exchangers, cooling fins, and pipe insulation.
Example Problem
Water (k = 0.6 W/(m·K)) flows through a 0.02 m diameter pipe with a convection coefficient h = 3,000 W/(m²·K). What is the Nusselt number?
- Nu = hL / k = 3,000 × 0.02 / 0.6
- Nu = 60 / 0.6 = 100
A Nusselt number of 100 means convection transfers heat 100 times faster than conduction alone across the same fluid layer, typical for turbulent water flow in a pipe.
Frequently Asked Questions
What is the Nusselt number used for in heat exchanger design?
Engineers use Nusselt correlations to calculate the convection coefficient h without experiments. From h, they determine the overall heat transfer coefficient U and then size the heat exchanger area needed to achieve the required duty. Common correlations include Dittus-Boelter for turbulent pipe flow and Sieder-Tate for viscous fluids.
What is the Nusselt number for laminar flow in a pipe?
For fully developed laminar flow with constant wall heat flux, Nu = 4.36. With constant wall temperature, Nu = 3.66. These are exact analytical values and do not depend on Reynolds or Prandtl numbers, unlike turbulent flow correlations.
How does the Nusselt number relate to the Sherwood number?
The Sherwood number is the mass-transfer analogue of the Nusselt number. Nu describes convective heat transfer relative to conduction, while Sh describes convective mass transfer relative to diffusion. In systems where heat and mass transfer analogies apply, their correlations have the same functional form.
Why does the Nusselt number increase with turbulence?
Turbulent eddies mix hot and cold fluid far more efficiently than molecular conduction. This enhanced mixing dramatically increases the effective heat transfer coefficient. In turbulent pipe flow, Nu scales roughly as Re⁰⋅⁸ Pr⁰⋅⁴, so doubling the flow velocity can increase Nu by about 70%.
Related Calculators
- Prandtl Number Calculator — momentum vs. thermal diffusivity, a key input to Nusselt correlations.
- Sherwood Number Calculator — the mass-transfer analogue of the Nusselt number.
- Peclet Number Calculator — advective vs. diffusive heat transport in a flowing fluid.
- Reynolds Number Calculator — determine flow regime needed for Nusselt correlations.
- Thermal Conductivity Calculator — find the conductive heat transfer coefficient in the Nusselt ratio.