Heat exchangers — minimum surface area with phase change In a heat exchanger where one of the fluids is undergoing evaporation or condensation (approximately constant temperature on that side), which flow arrangement generally requires the least heat transfer area for a given duty and terminal temperatures?

Introduction / Context:
Exchanger area depends on the required heat duty, overall heat transfer coefficient, and the logarithmic mean temperature difference (LMTD). When one stream changes phase, its temperature is nearly constant, which changes LMTD behavior across flow arrangements.

Given Data / Assumptions:

• One side evaporating or condensing, so its bulk temperature stays essentially constant.
• Uniform overall heat transfer coefficient for comparison.
• Same inlet/outlet temperatures targeted.

Concept / Approach:
Counter flow maximizes the temperature driving force at each location, producing the highest LMTD among the common arrangements (for the same terminal temperatures). A higher LMTD means, for a fixed duty and U, the necessary area A = Q/(U*LMTD) is minimized.

Step-by-Step Solution:
For parallel flow, hot and cold streams enter from the same end; temperature driving force decays quickly, lowering LMTD.For counter flow, streams move oppositely; the local temperature difference stays higher, increasing LMTD.With a phase-changing side, counter flow further avoids “pinch” at the cold end, giving the largest LMTD → smallest area.

Verification / Alternative check:
Worked examples with typical terminal temperatures show counter flow LMTD exceeds parallel/cross, hence smaller area.

Why Other Options Are Wrong:
(a) Parallel has lower LMTD → larger area. (c) Cross flow lies between parallel and counter depending on mixing; seldom beats pure counter flow. (d) Not true because LMTD differs. (e) Not a conventional recuperative exchanger arrangement.

Common Pitfalls:
Assuming “phase change means infinite U so area is minimal anyway.” U may be high, but LMTD still governs area for a specified Q.

Final Answer:
Counter flow