Dimensionless groups in coupled transport: In simultaneous heat and mass transfer problems, which dimensionless number most directly links thermal and mass diffusivities and is widely used to correlate coupled phenomena?

Introduction / Context:
When heat and mass transfer occur together—such as in drying, humidification, evaporative cooling, or combustion—the relative rates of thermal and species diffusion strongly influence boundary-layer behavior and overall transfer rates. A key dimensionless group captures this relationship.

Given Data / Assumptions:

• Single-phase flows with coupled heat and mass transfer.
• No chemical reaction, or reaction effects considered separately.
• Continuum mechanics and boundary-layer concepts apply.

Concept / Approach:
The Lewis number is defined as Le = α / D = (k / ρcp) / D, where α is thermal diffusivity and D is mass diffusivity. Le directly compares the relative thickness and development of thermal and concentration boundary layers. Schmidt number Sc = ν / D and Prandtl number Pr = ν / α are also important, but Le explicitly couples heat and mass transfer by the ratio of diffusivities. Sherwood number Sh = k_c L / D is a mass-transfer analog of Nusselt number and is used for correlations, not for comparing α and D directly.

Step-by-Step Solution:
Write Le = α / D.Interpretation: Le > 1 → heat diffuses faster than mass; Le < 1 → species diffuse faster than heat.Coupled-transfer analogies (e.g., Chilton–Colburn) often invoke Le ≈ 1 to simplify correlations.Hence, the dimensionless number of interest is the Lewis number.

Verification / Alternative check:
In air–water systems at ambient conditions, Le ≈ 1, which supports simplified j-factor analogies linking heat and mass transfer coefficients.

Why Other Options Are Wrong:
Schmidt and Prandtl compare momentum with mass/heat diffusion separately; they do not directly relate mass to heat diffusion.

Sherwood is a transfer coefficient correlation parameter, not a ratio of diffusivities.

Common Pitfalls:

• Using Sc or Pr when a direct heat–mass coupling metric (Le) is required.
• Assuming Le = 1 universally; it varies with fluid and conditions.

Final Answer:
Lewis number