In Sec. 14.4, we introduced the notion of a laminar boundary layer by analyzing flow past a thin plate. Now suppose that this same plate is maintained at a different temperature from the free flow. A thermal boundary layer will form, in addition to the viscous boundary layer, which we presume to be laminar. These two boundary layers both extend outward from the wall but (usually) have different thicknesses.

(a) Explain why their relative thicknesses depend on the Prandtl number.

(b) Using Eq. (18.4), show that in order of magnitude the thickness δ_T of the thermal boundary layer is given by

where v(δ_T) is the fluid velocity parallel to the plate at the outer edge of the thermal boundary layer, and ℓ is the distance down stream from the leading edge.

(c) Let V be the free-stream fluid velocity and △T be the temperature difference between the plate and the body of the flow. Estimate δ_T in the limits of large and small Prandtl numbers.

(d) What will be the boundary layer’s temperature profile when the Prandtl number is exactly unity?

Eq. (18.4)

Transcribed Image Text:

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