When water (Prandtl number roughly 6) flows over a flat plate heated across its entire span, how does thermal boundary layer thickness compare to hydrodynamic boundary layer thickness?
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Answer: A. Less
Explanation
The Prandtl number represents the ratio of momentum diffusivity to thermal diffusivity in fluids. For water, the Prandtl number is approximately six, meaning momentum diffuses faster than heat. Consequently, the hydrodynamic boundary layer grows faster and thicker than the thermal boundary layer. Thermal boundary layer thickness defines the region where fluid temperature changes near a heated plate. Hydrodynamic boundary layer thickness measures velocity gradient development across solid surfaces. Prandtl number links fluid viscosity and thermal conductivity properties into a single ratio.
Heat exchanger design for liquid water systems requires accounting for different boundary layer thicknesses. Cooling electronic components with liquid coolants depends on accurate thermal boundary layer analysis. Convective heat transfer coefficients are calculated using dimensionless correlations involving Prandtl numbers. Option A correctly identifies that the thermal boundary layer is thinner when Prandtl exceeds one. More would occur if the Prandtl number were less than one, where heat diffuses faster than momentum. Equal boundary layer thicknesses occur only when the Prandtl number equals exactly one.
- Subject
- Engineering
- Category
- Chemical Engineering
- Topic
- —
- Difficulty
- medium
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