Related Resources: heat transfer

Nusselt Number for Forced Convection

In heat transfer at a boundary (surface) within a fluid, the Nusselt number (Nu) is the ratio of convective to conductive heat transfer across (normal to) the boundary. In this context, convection includes both advection and diffusion. Named after Wilhelm Nusselt, it is a dimensionless number. The conductive component is measured under the same conditions as the heat convection but with a (hypothetically) stagnant (or motionless) fluid. A similar non-dimensional parameter is Biot Number, with the difference that the thermal conductivity is of the solid body and not the fluid.

A Nusselt number close to one, namely convection and conduction of similar magnitude, is characteristic of "slug flow" or laminar flow. A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range.

The convection and conduction heat flows are parallel to each other and to the surface normal of the boundary surface, and are all perpendicular to the mean fluid flow in the simple case.

Empirical correlations for the average Nusselt number for forced convection over a flat plate and circular and noncircular cylinders in cross flow

 Cross-section of the Cylinder Fluid Range of Re Nusselt number Circle Gas or Liquid 0.4 – 4 4 - 40 40 - 4000 4000 - 40,000 40,000 - 400,000 Nu = 0.989 Re0.330Pr1/3 Nu = 0.911 Re0.385Pr1/3 Nu = 0.683 Re0.466Pr1/3 Nu = 0.193 Re0.618Pr1/3 Nu = 0.027 Re0.805Pr1/3 Square Gas 5000 - 100,000 Nu = 0.102 Re0.675Pr1/3 Square Tiltes 45° Gas 5000 - 100,000 Nu = 0.246 Re0.588Pr1/3 Flat plate Gas or Liquid 0 - 5 5 x 105 - 107 Nu = 0.664 Re1/2Pr1/3 Nu = (0.037 Re4/5  871)Pr1/3 Certical Plate Gas 4000 - 15,000 Nu = 0.228 Re0.731Pr1/3

Nusselt number of fully developed laminar flow in circular tubes and rectangular channels

 Cross Section of Tube Aspect Ratio Nusset Number - 4.36 - 3.61 a/b 1 2 3 4 6 8 ∞ 3.61 4.12 4.79 5.33 6.05 6.49 8.24