Nusselt Number for Forced Convection

Heat Transfer Engineering
Thermodynamics
Engineering Physics

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
Cylinder
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
Tube
-
4.36
Square
-
3.61
Rectangle
a/b
1
2
3
4
6
8

3.61
4.12
4.79
5.33
6.05
6.49
8.24
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