Editing Prandtl number (section)

== Physical interpretation ==
Small values of the Prandtl number, {{math|Pr ≪ 1}}, means the thermal diffusivity dominates. Whereas with large values, {{math|Pr ≫ 1}}, the momentum diffusivity dominates the behavior.
For example, the listed value for liquid mercury indicates that the [[heat conduction]] is more significant compared to [[convection]], so thermal diffusivity is dominant.
However, engine oil with its high viscosity and low heat conductivity, has a higher momentum diffusivity as compared to thermal diffusivity.<ref>{{Cite book|last=Çengel|first=Yunus A.|title=Heat transfer : a practical approach|date=2003|publisher=McGraw-Hill|isbn=0072458933|edition=2nd|location=Boston|oclc=50192222}}</ref>

The Prandtl numbers of gases are about 1, which indicates that both [[momentum]] and [[heat]] dissipate through the fluid at about the same rate. Heat diffuses very quickly in liquid metals ({{math|Pr ≪ 1}}) and very slowly in oils ({{math|Pr ≫ 1}}) relative to momentum. Consequently [[Thermal boundary layer thickness and shape|thermal boundary layer]] is much thicker for liquid metals and much thinner for oils relative to the [[Boundary layer thickness|velocity boundary layer]].

In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal [[boundary layers]]. When {{math|Pr}} is small, it means that the heat diffuses quickly compared to the velocity (momentum). This means that for liquid metals the thermal boundary layer is much thicker than the velocity boundary layer.

In laminar boundary layers, the ratio of the thermal to momentum boundary layer thickness over a flat plate is well approximated by<ref name="A Heat Transfer Textbook">{{Cite book|last1=Lienhard IV|first1=John Henry|last2=Lienhard V|first2=John Henry|title=A Heat Transfer Textbook|date=2017|publisher=Phlogiston Press|edition=4th|location=Cambridge, MA}}</ref>
: <math>\frac{\delta_t}{\delta} = \mathrm{Pr}^{-\frac13}, \quad 0.6 \leq \mathrm{Pr} \leq 50,</math>
where <math>\delta_t</math> is the thermal boundary layer thickness and <math>\delta</math> is the momentum boundary layer thickness.

For incompressible flow over a flat plate, the two [[Nusselt number]] correlations are asymptotically correct:<ref name="A Heat Transfer Textbook"/>
: <math>\mathrm{Nu}_x = 0.339 \mathrm{Re}_x^{\frac12} \mathrm{Pr}^{\frac13}, \quad \mathrm{Pr} \to \infty,</math>
: <math>\mathrm{Nu}_x = 0.565 \mathrm{Re}_x^{\frac12} \mathrm{Pr}^{\frac12}, \quad \mathrm{Pr} \to 0,</math>

where <math>\mathrm{Re}</math> is the [[Reynolds number]]. These two asymptotic solutions can be blended together using the concept of the [[Norm (mathematics)]]:<ref name="A Heat Transfer Textbook"/>
: <math>\mathrm{Nu}_x = \frac{0.3387 \mathrm{Re}_x^{\frac12} \mathrm{Pr}^{\frac13}}{\left( 1 + \left( \frac{0.0468}\mathrm{Pr} \right)^{\frac23} \right)^{\frac14}}, \quad \mathrm{Re} \mathrm{Pr} > 100.</math>