# d10

* Chris Nkinthorn $\texttt{20190805}$

**Prompt:** Please discuss the effects of substances with different Prandtl Numbers in terms of expected momentum and thermal boundary layer heights and what are velocity profile consequences in boundary-layer analysis.

**Discussion:** As the Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity, this dimensionless value can be used to scale a known boundary layer to the other using analogous solutions. The Nusslet number, which describes the heat transfer coefficient can be correlated to the product of the Prandtl and Reynolds number raised to their respective powers. This number will vary linearly with the square root of the Reynolds number along the length of a flat plate in all cases. The effect of the fluid substance is seen as the Prandtl number varies from unity. In the case where Pr is much greater than 1, thermal boundary layer is much smaller than the velocity boundary layer. In the case where Pr is much smaller, then the reverse is true.

**Response to:** Emily De Stefanis

Thanks for giving examples of the variation of different fluids for the limiting cases of Prandtl number. Liquid metals and oils are key and classic examples for very small and very large Pr numbers, respectively.


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