Nusselt Number

Wilhelm Nusselt's 1915 paper on the similarity theory of heat transfer, and his 1916 analysis of laminar film condensation — still the standard result a century later — gave engineering its habit of expressing convection dimensionlessly. Nu is the convective coefficient measured against the conduction that would occur through a stagnant fluid layer of the same thickness: Nu = 1 means the fluid may as well be motionless, Nu = 100 means convection is doing a hundred times better. Nearly every convection correlation ever published has the form Nu = f(Re, Pr), and this equation is how you cash one in.

The workflow is always the same. Compute Re and Pr from the fluid and the flow, look up or apply a correlation to get Nu, then convert to a physical h using h = Nu·k/L. A Nusselt number of 20.8 in water (k = 0.6 W/(m·K)) inside a 50 mm tube means h = 20.8 × 0.6/0.05 = 250 W/(m²·K). The trap is L. It is whatever the correlation's author used — internal-flow correlations use the tube inside diameter, flat-plate correlations the distance from the leading edge, and non-circular ducts the hydraulic diameter 4A/P — and it must be the same L on both sides of the calculation. The k is the fluid's, never the wall's; using the metal's conductivity here is the most common error in the whole subject.