LMTD correction in multi–shell-pass exchangers In a shell-and-tube heat exchanger, how does the LMTD correction factor FT change when the number of shell passes is increased (for the same terminal temperatures and number of tube passes)?

Introduction / Context:
The log-mean temperature difference (LMTD) method is widely used to size heat exchangers. For non-ideal flow arrangements (not purely counter-current), a correction factor FT is applied to the LMTD of an equivalent counter-current exchanger. Understanding how FT varies with flow arrangement—especially the number of shell passes—is vital for practical design and debottlenecking.

Given Data / Assumptions:

• Same inlet and outlet temperatures of hot and cold streams (same terminal temperature differences).
• Tube pass configuration is held fixed while increasing the number of shell passes.
• No phase change; sensible heat exchange context.

Concept / Approach:
FT quantifies departure from ideal counter-current behavior. Increasing shell passes tends to distribute temperature driving force more effectively along the exchanger, making the arrangement closer to counter-current. As a result, FT moves upward toward 1.0. Designers often prefer 1–2 or 2–4 arrangements precisely because they achieve higher FT than a single-pass 1–1 cross-flow–like pattern.

Step-by-Step Solution:

Verification / Alternative check:
TEMA charts of FT versus temperature effectiveness and heat capacity rate ratio show higher FT values for multi–shell-pass arrangements at the same operating points.

Why Other Options Are Wrong:

• Decreases/remains same: Contradicts FT charts and the counter-current approximation.
• “Remains same, only if tube passes do not change”: Even at fixed tube passes, FT rises with more shell passes.

Common Pitfalls:
Confusing FT with overall U or with LMTD itself; FT is a dimensionless multiplier tied to flow arrangement and terminal temperatures.

Final Answer:
increases