In convective heat transfer across a composite resistance (e.g., a hot fluid–wall–cold fluid system), the “controlling” heat transfer film coefficient is associated with the layer that offers the greatest hindrance.\r Which film or side is referred to as controlling in terms of its resistance to heat transfer?

Introduction:
Whenever heat flows through several resistances in series (for example, a hot fluid film, a wall, and a cold fluid film), the overall rate is governed by the largest resistance in the path. In heat exchanger design this idea helps engineers focus on the “controlling” side for enhancement efforts such as adding fins, increasing velocity, or changing flow regimes.

Given Data / Assumptions:

• Multiple resistances exist in series: hot-side film, wall conduction, and cold-side film.
• Film coefficients are inversely related to film resistances.
• We are identifying the controlling resistance and its qualitative magnitude.

Concept / Approach:
Overall heat transfer coefficient U for series resistances is determined by 1/U = R_total = R_hot film + R_wall + R_cold film. The largest of these dominates the total. A “controlling film coefficient” means the film with the lowest h (largest 1/h) and hence the greatest resistance, which throttles the heat flow.

Step-by-Step Solution:
Write total resistance: R_total = 1/h_hot + (δ/k) + 1/h_cold.Identify which term is largest; that term controls R_total and thus U.Translate to wording: the controlling film offers the largest resistance.

Verification / Alternative check:
Electrical analogy (series resistors) shows current is limited by the largest resistor; likewise, heat flow is limited by the largest thermal resistance.

Why Other Options Are Wrong:

• No / negligible / lower / least: These imply small resistance, which would not control the overall process.

Common Pitfalls:
Confusing “largest coefficient” with “largest resistance.” Remember resistance is 1/h; a small h means a large resistance and hence controlling.

Final Answer:
the largest