Physical Interpretation of the Nu, Pr, Sh and Sc Numbers

This section will present one of the possible physical interpretations of these important dimensionless numbers. First, to show the meaning of Nusselt number, we consider the heat transfer flux in the x direction in the case of a pure molecular mechanism compared with the heat transfer characterizing the process when convection is important. The corresponding fluxes are then written as  

The result shows that the physical significance of the Nusselt number is quantity of heat transferred by the convective mechanism 

As for the Prandtl number, we consider the heat transfer flux which can be written with the use of the fluid enthalpy (Eq. (6.164)) and the molecular momentum flux given by Eq. (6.165)  

The ratio between both fluxes shows that the Prandtl number is an index giving the relative quantity of the momentum transported by the molecular mechanism and of the heat transported by the same mechanism at the interface  

As for the significance of the Sherwood number, the following mass transfer fluxes for species A are used  

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