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 nondimensional 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
Crosssection 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 Re^{0.330}Pr^{1/3}
Nu = 0.911 Re^{0.385}Pr^{1/3} Nu = 0.683 Re^{0.466}Pr^{1/3} Nu = 0.193 Re^{0.618}Pr^{1/3} Nu = 0.027 Re^{0.805}Pr^{1/3} 
Square

Gas

5000  100,000

Nu = 0.102 Re^{0.675}Pr^{1/3}

Square Tiltes 45°

Gas

5000  100,000

Nu = 0.246 Re^{0.588}Pr^{1/3}

Flat plate

Gas or Liquid

0  5 5 x 10^{5}  10^{7} 
Nu = 0.664 Re^{1/2}Pr^{1/3} Nu = (0.037 Re^{4/5} 871)Pr^{1/3} 
Certical Plate

Gas

4000  15,000

Nu = 0.228 Re^{0.731}Pr^{1/3}

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 
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