Question Bank • QB_DFE_020 MSQ • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Diffusive and convective mass transfer

Question Statement:

Which of the following dimensionless numbers correctly represent the stated physical ratios in convective heat and mass transfer operations?

Options:

  • (A) Sherwood number ($Sh = \frac{k_c L}{D_{AB}}$) represents the ratio of convective mass transfer to molecular diffusion rate.
  • (B) Schmidt number ($Sc = \frac{\mu}{\rho D_{AB}} = \frac{\nu}{D_{AB}}$) represents the ratio of momentum diffusivity to molecular mass diffusivity.
  • (C) Lewis number ($Le = \frac{\alpha}{D_{AB}}$) represents the ratio of thermal diffusivity to mass diffusivity.
  • (D) Prandtl number ($Pr = \frac{k}{\mu c_p}$) represents the ratio of convective heat flux to radiative heat flux.

Answer Key:

A, B, C

Step-by-Step Solution & Explanation

• A, B, and C are canonical definitions of transport phenomena dimensionless numbers. • D is incorrect: Prandtl number is the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity: $Pr = \frac{\nu}{\alpha} = \frac{\mu c_p}{k}$.
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