Lewis Number Calculator

Lewis number equals thermal diffusivity divided by mass diffusivity

Solution

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How It Works

The Lewis number tells you whether heat or mass diffuses faster in a given system. 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.

This ratio is central to combustion analysis because it determines flame shape, stability, and extinction behavior. It also matters in drying, evaporative cooling, and any process where heat and mass transfer occur simultaneously.

Example Problem

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

  1. Le = α / Dᴄ = 2.2 × 10⁻⁵ / 2.5 × 10⁻⁵
  2. Le = 0.88

A Lewis number slightly below 1 means water vapor diffuses a little faster than heat in air, which is typical for the air-water system and influences evaporative cooling calculations.

Frequently Asked Questions

What is a typical Lewis number for air?

For common gas-phase species diffusing in air, the Lewis number ranges from about 0.8 to 1.2. Hydrogen in air has Le ≈ 0.3 because hydrogen diffuses much faster than heat, while heavier hydrocarbons can have Le above 1.5.

How does the Lewis number affect flame stability?

When Le < 1, fuel diffuses into the flame faster than heat diffuses away, which can make flames more unstable and prone to cellular patterns. When Le > 1, heat loss stabilizes the flame. This is why hydrogen flames (Le ≈ 0.3) are much more prone to instabilities than heavier-fuel flames.

How is the Lewis number related to Prandtl and Schmidt numbers?

Le = Sc / Pr, where Sc is the Schmidt number and Pr is the Prandtl number. This relationship lets you compute the Lewis number from commonly tabulated fluid properties without needing thermal and mass diffusivities directly.

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