The GATE Grind

GATE 2024 CH – Question 27

Heat Transfer · Convection, boundary layers and heat transfer coefficients · 1 mark · Multiple select

If the Prandtl number Pr = 0.01, which of the following statements is/are correct?

  1. The momentum diffusivity is much larger than the thermal diffusivity.
  2. The thickness of the momentum boundary layer is much smaller than that of the thermal boundary layer.
  3. The thickness of the momentum boundary layer is much larger than that of the thermal boundary layer.
  4. The momentum diffusivity is much smaller than the thermal diffusivity.

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Show answer and explanation

Correct answer: (B) The thickness of the momentum boundary layer is much smaller than that of the thermal boundary layer.; (D) The momentum diffusivity is much smaller than the thermal diffusivity.

Explanation

$Pr = \frac{\nu}{\alpha}$ is the ratio of momentum diffusivity to thermal diffusivity. With $Pr = 0.01$ the momentum diffusivity is much smaller (D). Heat spreads faster than momentum, so the thermal boundary layer is much thicker than the momentum boundary layer (B).