Nusselt Number Calculator

Nu = hL/k — dimensionless convective heat transfer. Relates the convective heat transfer coefficient to fluid thermal conductivity over a characteristic length.

Heat Transfer · Dimensionless Number

Inputs

Solve for:

Characteristic length L (m)

Heat transfer coefficient h (W/(m²·K))

Typical: forced air 25–250, water 500–10 000, boiling 2 500–100 000

Fluid thermal conductivity k (W/(m·K))

Theory

Definition:

Nu = h × L / k [dimensionless]

h = Nu × k / L [W/(m²·K)]

k = h × L / Nu [W/(m·K)]

Nu compares convective to conductive heat transfer across the same thickness. Nu = 1 means convection provides no enhancement over pure conduction; Nu = 100 means convection is 100× more effective than conduction alone.

Physical interpretation of Nu values:

Nu = 1 — pure conduction (stagnant fluid layer, no bulk motion)
Nu = 2 — theoretical minimum for a sphere in an infinite medium
Nu = 3.66 — fully developed laminar pipe flow, constant wall temperature
Nu = 4.36 — fully developed laminar pipe flow, constant heat flux
Nu ~ 10–100 — typical forced convection in liquids or gases
Nu ~ 100–10 000 — boiling and condensation

Common Nu correlations:

Geometry / regime	Correlation	Validity
Laminar pipe, const-T	Nu = 3.66	Fully developed, Re < 2300
Laminar pipe, const-q	Nu = 4.36	Fully developed, Re < 2300
Turbulent pipe (Dittus-Boelter)	Nu = 0.023 Re⁰·⁸ Prⁿ	Re > 10 000, 0.6 < Pr < 160
Flat plate, laminar avg	Nu = 0.664 Re^½ Pr^⅓	Re < 5×10⁵, Pr > 0.6
Sphere (Ranz-Marshall)	Nu = 2 + 0.6 Re^½ Pr^⅓	1 < Re < 2×10⁵
Cylinder crossflow	Nu = C Re^m Pr^⅓ (Hilpert)	Re > 0.4

Nu vs Biot number — a common source of confusion:

Nu = h × L / k_fluid (uses fluid thermal conductivity)

Bi = h × L / k_solid (uses solid thermal conductivity)

Both share the same algebraic form but describe different physics. Nu is a convective parameter; Bi describes conductive resistance inside a solid relative to its surface convective resistance.