Project ForgeThe ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids P and Q on a flat plate are 1/2 and 2 respectively. The Reynolds number based on the plate length for both flows is 10⁴. The Prandtl and Nusselt numbers for P are 1/8 and 35 respectively. The Prandtl and Nusselt numbers for Q are respectively
- 8 and 140
- B8 and 70
- C4 and 70
- D4 and 35
Explanation
Pr ≈ (δ/δt)³ for laminar flat-plate flow. Checking P: (1/2)³=1/8, matches given PrP=1/8. For Q: (2)³=8, so PrQ=8. Using Nu=C·Re^0.5·Pr^(1/3) (same C and Re for both fluids): from P, 35=C×100×(1/8)^(1/3)=C×100×0.5=50C ⟹ C=0.7. Then NuQ=0.7×100×(8)^(1/3)=0.7×100×2=140.
Source: GATE ME 2011 (2011)
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