E Use of the Asymptotic Results at Intermediate Pe or Sc

Before proceeding to other topics, it is worthwhile to reflect briefly on the results of Sections ll.C and ll.D. In particular, let us focus our attention on the two results in (11-53) and (11-91) for the local temperature gradient in the case of a horizontal flat plate, with x = 0. These correspond to correlations for the local dimensionless heat flux 

It may be noted that the functional dependence of the local heat flux onx is the same as the shear stress. This is a consequence of the fact that the thickness of the thermal boundary layer varies with x in the same way as the momentum boundary-layer thickness. Furthermore, the form of the correlations for large and small Prandtl numbers are also quite similar. However, this latter observation may be somewhat misleading. In the case Pr 1, the heat 

We see that the maximum difference between this exact result and the nearest of the two asymptotes is about 20% at the point where the two asymptotes intersect. 

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