Nusselt number

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The Nusselt number is a dimensionless number that measures the enhancement of heat transfer from a surface that occurs in a 'real' situation, compared to the heat transferred if just conduction occurred. Typically it is used to measure the enhancement of heat transfer when convection takes place.

[\mathit_L = \frac]

where

L = characteristic length
k_f = thermal conductivity of the "fluid"
h = convection heat transfer coefficient

Selection of the significant length scale should be in the direction of growth of the boundary layer. A salient example in introductory engineering study of heat transfer would be that of a horizontal cylinder versus a vertical cylinder in natural convection.

For a local Nusselt number, one may evaluate the significant length scale at the point of interest. To obtain an average Nusselt number analytically one must integrate over the characteristic length. More commonly the average Nusselt number is obtained by the pertinent correlation equation, often of the form Nu = Nu(Re, Pr).

The Nusselt number can also be viewed as being a dimensionless temperature gradient at the surface.

The mass transfer analog of the Nusselt number is the Sherwood number.

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