When is an LMTD correction factor required in heat exchanger design?
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ADouble-pipe heat exchanger.
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BMultipass shell-and-tube heat exchanger.
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CWhen fluids are fouling.
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DSimple counterflow of hot and cold fluids.
Answer
Correct Answer: Multipass shell-and-tube heat exchanger.
Explanation
Introduction / Context:The Log-Mean Temperature Difference (LMTD) method is a cornerstone of exchanger sizing. For complex flow arrangements, a correction factor F modifies the ideal LMTD to account for departure from pure countercurrent or cocurrent flow.
Given Data / Assumptions:
- Design at steady state with no phase change (for simplicity).
- Shell-and-tube exchangers often use multiple shell or tube passes.
Concept / Approach:Pure counterflow or pure parallel-flow exchangers have known temperature profiles and require no correction (F = 1). Multipass or crossflow arrangements distort the temperature driving-force distribution; hence, a correction factor F (0 < F ≤ 1) must be applied with the LMTD to estimate true performance.
Step-by-Step Solution:
Identify flow pattern: multipass shell-and-tube → nonideal temperature profile.Use LMTD with correction: ΔT_lm,true = F * ΔT_lm,ideal.Obtain F from standard charts using P and R ratios (temperature effectiveness parameters).Verification / Alternative check:Compare with the ε–NTU method; both should yield consistent duties when properties and areas are aligned.
Why Other Options Are Wrong:
- Double-pipe in pure counterflow has F ≈ 1; no correction needed.
- Fouling affects U, not the LMTD correction directly.
- A simple counterflow also has F = 1 by definition.
Common Pitfalls:Forgetting to check F ≥ 0.75–0.8 (typical design guidance) to avoid thermally inefficient arrangements.
Final Answer:Multipass shell-and-tube heat exchanger.