Question

Lewis number is the ratio of

• A. Thermal diffusivity to mass diffusivity
• B. Mass diffusivity to momentum diffusivity
• C. Mass diffusivity to thermal diffusivity
• D. Momentum diffusivity to thermal diffusivity

Hint:

The Lewis number (\( \text{Le} = \frac{\alpha}{D} \)) compares the rates of heat and mass diffusion, often used in combustion and drying processes.

Answer 1

The Correct Option is A

Step 1: Define the Lewis number.
The Lewis number (\( \text{Le} \)) is a dimensionless number used in heat and mass transfer, particularly in processes involving simultaneous heat and mass transfer (e.g., combustion, drying). It is defined as the ratio of thermal diffusivity to mass diffusivity: \[ \text{Le} = \frac{\alpha}{D}, \] where:
\( \alpha \): Thermal diffusivity (\( \alpha = \frac{k}{\rho c_p} \), where \( k \) is thermal conductivity, \( \rho \) is density, \( c_p \) is specific heat),
\( D \): Mass diffusivity (diffusion coefficient for mass transfer, m²/s).
The Lewis number compares the rate of heat diffusion to the rate of mass diffusion. Step 2: Define the diffusivities in the options.
Thermal diffusivity (\( \alpha \)): Measures the rate of heat diffusion (\( \alpha = \frac{k}{\rho c_p} \)).
Mass diffusivity (\( D \)): Measures the rate of mass diffusion (e.g., diffusion of a species in a mixture).
Momentum diffusivity (\( \nu \)): Also known as kinematic viscosity (\( \nu = \frac{\mu}{\rho} \), where \( \mu \) is viscosity), measures the rate of momentum diffusion. Step 3: Evaluate the options.
(1) Thermal diffusivity to mass diffusivity: Correct, as \( \text{Le} = \frac{\alpha}{D} \). Correct.
(2) Mass diffusivity to momentum diffusivity: Incorrect, as this is related to the Schmidt number (\( \text{Sc} = \frac{\nu}{D} \)). Incorrect.
(3) Mass diffusivity to thermal diffusivity: Incorrect, as this is the inverse of the Lewis number (\( \frac{D}{\alpha} = \frac{1}{\text{Le}} \)). Incorrect.
(4) Momentum diffusivity to thermal diffusivity: Incorrect, as this is related to the Prandtl number (\( \text{Pr} = \frac{\nu}{\alpha} \)). Incorrect.
Step 4: Select the correct answer.
The Lewis number is the ratio of thermal diffusivity to mass diffusivity, matching option (1).