Discussion
Air, with a Prandtl number of 0.7, flows over a flat plate at a high Reynolds number. Which of the following statement is TRUE?
Answer: A
With Pr = 0.7, the thermal boundary layer is thicker than the velocity boundary layer.
The Prandtl number compares momentum diffusivity with thermal diffusivity. When Pr is below 1, heat diffuses faster than momentum, so the temperature disturbance spreads further from the wall than the velocity disturbance. For laminar flow over a flat plate the ratio is about \(\delta/\delta_{t} \approx Pr^{1/3}\), so \(\delta_{t}/\delta \approx 0.7^{-1/3} \approx 1.13\).
A thinner thermal layer would need Pr above 1, as in oils and water, and equal thicknesses need Pr = 1. The two thicknesses are linked through Pr, so 'no relationship' is wrong.
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