Lewis Number Calculator

What is the Lewis Number?

The Lewis number (Le) is a dimensionless quantity that compares the rate of thermal diffusion to the rate of mass diffusion in a fluid system. It is defined as the ratio of thermal diffusivity to mass diffusivity: Le = α / Dᴄ. When Le = 1, thermal and concentration boundary layers grow at the same rate. When Le > 1, heat spreads faster than chemical species; when Le < 1, species diffuse faster than heat.

Named after Warren K. Lewis, this number is central to the analysis of simultaneous heat and mass transfer processes. It is particularly important in combustion engineering, drying technology, evaporative cooling, and atmospheric science. The Lewis number is related to the Prandtl number (Pr) and Schmidt number (Sc) through the identity Le = Sc / Pr.

Lewis Number Formula

The Lewis number is defined as:

Le = α / Dᴄ

Where:

• Le is the Lewis number (dimensionless)
• α is the thermal diffusivity (m²/s) - measures how fast heat conducts through a material
• Dᴄ is the mass diffusivity (m²/s) - measures how fast a chemical species spreads through a medium

How to Use the Lewis Number Calculator

Using the calculator is simple. Select what you want to solve for, then enter the known values:

• Solve for Lewis Number: Enter thermal diffusivity and mass diffusivity to determine the ratio of heat to mass diffusion rates
• Solve for Thermal Diffusivity: Enter the Lewis number and mass diffusivity to find the thermal diffusivity
• Solve for Mass Diffusivity: Enter the thermal diffusivity and Lewis number to find the mass diffusivity

Lewis Number Values and Interpretation

The Lewis number tells you which diffusion process dominates in a combined heat and mass transfer problem:

• Le = 1: Heat and mass diffuse at the same rate. This is a common assumption in combustion textbooks that simplifies theoretical analysis significantly.
• Le > 1: Heat diffuses faster than mass. The thermal boundary layer is thicker than the concentration boundary layer. This provides increased flame stability.
• Le < 1: Mass diffuses faster than heat. The concentration boundary layer is thicker. This can lead to cellular flame instabilities.

Applications of the Lewis Number

• Combustion Engineering: Predicting flame stability, cellular instabilities, and extinction limits for different fuels. Hydrogen flames (Le ≈ 0.3) are far more unstable than heavier-fuel flames.
• Drying Processes: Modeling simultaneous heat and moisture transfer in food, textile, and wood drying applications.
• Evaporative Cooling: Designing cooling towers and performing wet-bulb psychrometric calculations.
• Atmospheric Science: Analyzing cloud droplet growth where heat and vapor diffusion compete.
• Chemical Engineering: Designing reactors and separation processes with coupled heat and mass transfer.

Example Calculation

Air at 25 C has a thermal diffusivity of 2.2 x 10^-5 m²/s and the mass diffusivity of water vapor in air is 2.5 x 10^-5 m²/s. What is the Lewis number?

1. Identify: α = 2.2 x 10^-5 m²/s, Dᴄ = 2.5 x 10^-5 m²/s
2. Use Le = α / Dᴄ = 2.2 x 10^-5 / 2.5 x 10^-5 = 0.88
3. Interpret: Le slightly below 1 means water vapor diffuses a little faster than heat in air, which is typical for the air-water system