Le = α/DAB = Sc/Pr — ratio of thermal to mass diffusivity. Governs the coupling between heat and mass transfer; Le = 1 is the foundation of the Lewis analogy used in evaporation, drying, and combustion problems.
Heat & Mass Transfer · Dimensionless NumberSolve for:
Fluid pair preset (fills α, DAB, ν):
α = k / (ρ cp) · Air ≈ 2×10⁻⁵ · Water ≈ 1.4×10⁻⁷ m²/s
Gas pairs ≈ 10⁻⁵ · Solutes in water ≈ 10⁻⁹ m²/s
Definition — three equivalent forms:
Boundary layer thickness ratio:
When Le = 1 (most gases), the thermal and concentration boundary layers are identical — this is the basis of the Lewis analogy that simplifies combined heat-mass transfer analysis.
Relationship between Pr, Sc, and Le:
Any one of Pr, Sc, Le can be derived from the other two plus ν, making this a self-consistent set of three diffusivity ratios.
Typical Le values:
| System | Le | Regime |
|---|---|---|
| H₂ in air at 20 °C | 0.30 | Le < 1 — mass diffuses fast |
| H₂O vapour in air at 20 °C | 0.82 | Le ≈ 1 (gas) |
| O₂ in air at 20 °C | 1.18 | Le ≈ 1 (gas) |
| CO₂ in air at 20 °C | 1.33 | Le ≈ 1 (gas) |
| O₂ in water at 25 °C | ≈ 68 | Le >> 1 (liquid) |
| NaCl in water at 25 °C | ≈ 89 | Le >> 1 (liquid) |
| Sucrose in water at 25 °C | ≈ 274 | Le >> 1 (liquid) |
Lewis analogy in engineering: