Heat exchanger analysis: identify the WRONG statement among the following commonly cited facts about LMTD, phase change, and controlling resistance during condensation heating of air.
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AThe controlling resistance in case of heating of air by condensing steam is in the air film.
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BThe log mean temperature difference (LMTD) for counter flow and parallel flow can be theoretically same when any one of the fluids (hot or cold fluid) passes through the heat exchanger at constant temperature.
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CIn case of a 1 - 2 shell and tube heat exchanger, the LMTD correction factor value increases sharply, when a temperature cross occurs.
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DPhase change in case of a pure fluid at a given pressure from liquid to vapor or vice-versa occurs at saturation temperature.
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ENone of the above.
Answer
Correct Answer: In case of a 1 - 2 shell and tube heat exchanger, the LMTD correction factor value increases sharply, when a temperature cross occurs.
Explanation
Introduction:Thermal design relies on proper interpretation of temperature driving forces and resistances. Misunderstanding LMTD behavior or where the dominant resistance lies can lead to oversized or underperforming exchangers. This question probes common truths and one deliberate misconception.
Given Data / Assumptions:
- Condensing steam heating air: very high steam-side h, low air-side h.
- LMTD comparison for counterflow vs. parallel flow with one fluid at constant temperature (phase change).
- LMTD correction factor F behavior in 1–2 shell-and-tube units when temperature cross occurs.
Concept / Approach:(a) is correct: the air film usually controls because condensing steam has a very high film coefficient. (b) is correct: if one stream changes phase at constant temperature (e.g., saturated steam), the LMTD for parallel and counter arrangements can be identical for the same terminal temperatures. (d) is correct: pure-fluid phase change at fixed pressure occurs at the saturation temperature. The problematic statement is (c): when a temperature cross occurs, the correction factor F does not “increase sharply”; it typically drops, approaching zero as the temperature cross becomes severe, indicating an ineffective arrangement for the specified terminal temperatures.
Step-by-Step Solution:Assess each statement with standard heat transfer principles.Identify (c) as contrary to the known trend of F decreasing with temperature cross.Choose (c) as the wrong statement.
Verification / Alternative check:Design charts for F versus temperature ratios clearly show F decreasing when temperature cross is approached or exceeded.
Why Other Options Are Wrong:
- (a), (b), and (d) are standard and consistent with textbooks.
- (e) “None” is invalid because (c) is indeed wrong.
Common Pitfalls:Confusing large LMTD with high effectiveness; shell arrangements need both adequate F and feasible terminal temperatures.
Final Answer:In case of a 1 - 2 shell and tube heat exchanger, the LMTD correction factor value increases sharply, when a temperature cross occurs.