Convective “film” coefficient concept The film coefficient (convective heat-transfer coefficient, h) can be interpreted as the ratio of:

Introduction / Context:
In many correlations and simple resistive analogies, convection is modeled as if a thin, stagnant “film” of fluid were conducting heat. This leads to an intuitive definition of the convective coefficient.

Given Data / Assumptions:

• Equivalent conductive film model adjacent to a surface.
• Uniform properties within the film: thermal conductivity k and notional thickness δ.
• Linear temperature drop across the film.

Concept / Approach:
Using the analogy q″ = k (ΔT/δ) and q″ = h (ΔT), the two forms give h = k/δ. While real convection involves velocity and temperature fields, this equivalence provides a useful way to visualize h and connect with thermal resistance R_conv = 1/(hA).

Step-by-Step Solution:
Write conductive form for a thin layer: q″ = k * (T_s − T_∞) / δ.Write Newton’s law of cooling: q″ = h * (T_s − T_∞).Equate and solve: h = k / δ → option A.

Verification / Alternative check:
Dimensional check: k has W/m·K, dividing by δ (m) gives W/m^2·K, which matches units of h.

Why Other Options Are Wrong:
(B), (C), and (D) mix ratios but do not yield the correct units for h; (E) is unrelated to convection.

Common Pitfalls:
Taking the film model too literally; δ is not a physical constant but a conceptual parameter that varies with flow conditions.

Final Answer:
thermal conductivity to the equivalent thickness of the fluid film (h = k/δ).