When is an LMTD correction factor required in heat exchanger design?

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:

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.