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Mass Transfer
Diffusion
GATE 2010
Hard

A liquid flows over a flat naphthalene plate of length L, at ReL=1500. The surface concentration of naphthalene is CAs>CA∞, and surface temperature Ts>T∞. Assume Pr=Sc=1. If at x=L, the dimensionless concentration gradient at the wall ∂C*A/∂y*|y*=0=10, then the Nusselt number and the friction coefficient at x=L, are

  • 10, 1/75
  • B10, 10
  • C20, 10
  • D1/75, 5

Explanation

The dimensionless wall concentration gradient directly gives the local Sherwood number: Shx=10. Since Pr=Sc=1, the Reynolds/Chilton-Colburn analogy gives Nux=Shx=10 (identical momentum, heat, and mass transfer profiles). Also Cf/2=Nux/Rex (with Pr=1): Cf=2×10/1500=1/75.

Source: GATE CH 2010 (2010)

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