Formula and Method for the Nusselt Number
The Nusselt number (Nu) is a dimensionless quantity used in heat transfer to compare convective heat transfer to conductive heat transfer across a fluid boundary. Named after German engineer Wilhelm Nusselt, it is defined as Nu = hL / k, where h is the convective heat transfer coefficient, L is the characteristic length of the surface, and k is the thermal conductivity of the fluid. This calculator computes Nu directly from those three quantities, along with the conduction-only coefficient (k / L) and how much convection improves heat transfer over conduction alone.
What the Nusselt number tells you
Nu is the ratio of convective heat transfer to the heat transfer that conduction alone would produce across a fluid layer of thickness L. A Nusselt number of 1 means the fluid layer transfers heat exactly as if it were a stagnant, purely conducting layer — convection is adding nothing. As Nu rises above 1, convection becomes increasingly effective relative to conduction: natural convection in air typically gives Nu in the range of a few units to a few tens, while turbulent forced convection in pipes or over surfaces can push Nu into the hundreds or thousands.
Choosing h, L, and k correctly
Getting Nu right depends on matching the three inputs to the same geometry and conditions. The characteristic length L is not arbitrary — it follows convention for the geometry: use the internal diameter for flow inside a pipe, the plate length in the direction of flow for a flat plate, or the diameter for flow over a cylinder or sphere. The thermal conductivity k belongs to the fluid, not the solid surface, and should be evaluated at the fluid's film temperature (the average of the surface and bulk fluid temperatures). The heat transfer coefficient h is usually the least certain of the three — in practice it is either measured directly or backed out after first estimating Nu from an empirical correlation.
Knowing the limits
This calculator performs the direct algebraic step Nu = hL / k; it does not derive h from flow conditions on its own. Predicting h from scratch requires choosing the correct empirical correlation for your geometry and flow regime — for example, the Dittus-Boelter equation (Nu = 0.023 Re0.8 Prn) applies only to turbulent flow in smooth pipes with Re above roughly 10,000, while natural-convection correlations use the Rayleigh number instead of the Reynolds number. Always confirm a correlation's valid Reynolds, Prandtl, or Rayleigh range before using the Nu it produces.