Subtopic: Simultaneous heat and mass transfer in agricultural processing operations
Question Statement:
During convective air drying of sliced fruits, the thermal diffusivity of drying air is $\alpha = 2.2e-05\text{ m}^2\text{/s}$. If the dimensionless Lewis number is $Le = 0.9$, calculate the mass diffusivity of water vapor in air, $D_{AB}$ (in $10^{-5}\text{ m}^2\text{/s}$, rounded to 2 decimal places):
Answer Key:
2.44
Step-by-Step Solution & Explanation
The Lewis number $Le$ characterizes fluid flows where there is simultaneous heat and mass transfer by convection:
$Le = \frac{\alpha}{D_{AB}} = \frac{Sc}{Pr}$
Rearranging for mass diffusivity $D_{AB}$:
$D_{AB} = \frac{\alpha}{Le} = \frac{2.2e-05}{0.9} = 0.0000244\text{ m}^2\text{/s} = 2.44 \times 10^{-5}\text{ m}^2\text{/s}$