Question Bank • QB_DFE_HMT_016 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 mass transfer theories predict that the convective mass transfer coefficient ($k_c$) is proportional to the square root of molecular diffusivity ($k_c \propto \sqrt{D_{AB}}$)?

Options:

  • (A) Higbie's penetration theory
  • (B) Danckwerts' surface renewal theory
  • (C) Whitman's two-film steady-state theory
  • (D) Reynolds analogy for turbulent pipe flow

Answer Key:

A, B

Step-by-Step Solution & Explanation

Higbie's penetration model ($k_c = 2 \sqrt{D_{AB}/(\pi t_e)}$) and Danckwerts' surface renewal model ($k_c = \sqrt{D_{AB} s}$) both predict $k_c \propto D_{AB}^{0.5}$. Whitman's two-film theory predicts $k_c \propto D_{AB}^{1.0}$.
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