Heat–mass transfer analogy — Which of the following is explicitly concerned with both heat and mass transfer by relating their coefficients?

Introduction:Analogies between heat and mass transfer enable engineers to estimate mass-transfer coefficients from heat-transfer data and vice versa. These analogies rely on similarities in transport equations and boundary-layer behavior.

Given Data / Assumptions:

• Boundary-layer flow with similar velocity fields.
• Comparable Schmidt and Prandtl number ranges where analogies hold.
• Negligible generation terms aside from diffusion and convection.

Concept / Approach:The Lewis relationship links heat and mass transfer through the Lewis number Le = Sc/Pr. For example, under certain conditions, h_g / (ρ * c_p * k_m) ≈ 1, relating convective heat-transfer coefficient h_g to mass-transfer coefficient k_m. This provides a bridge between the two transport processes.

Step-by-Step Solution:Identify the analogy tool that directly connects heat and mass transfer.Recognize “Lewis relationship” as the standard linkage via Le = Sc/Pr.Select it over dimensionless numbers focused on single phenomena.

Verification / Alternative check:Textbook correlations use Chilton–Colburn j-factors (j_H and j_D) with j_H ≈ j_D as an expression of the same analogy, reinforcing the Lewis relationship.

Why Other Options Are Wrong:

• Nusselt number quantifies heat transfer only.
• Kutateladze relates to boiling/critical heat flux phenomena.
• Froude number compares inertia and gravity; not a heat/mass link.
• Fourier number addresses transient conduction, not mass-transfer coupling.

Common Pitfalls:Applying the analogy outside its validity range (very different Pr and Sc, or strong property variations).

Final Answer:Lewis relationship