In a shell-and-tube exchanger, as the overall temperature drop between hot and cold streams increases (other conditions similar), how does the LMTD correction factor FT typically change?

Introduction / Context:
The log-mean temperature difference (LMTD) correction factor FT accounts for deviation from true countercurrent flow in multi-pass shell-and-tube exchangers. Its magnitude determines the effective temperature driving force used for sizing.

Given Data / Assumptions:

• Comparison at fixed flow arrangement (e.g., 1–2 exchanger) and similar flow rates.
• We vary the overall temperature drop (i.e., less “pinch” at one end).
• Interest is the qualitative trend in FT.

Concept / Approach:
FT approaches 1.0 for large terminal temperature differences and moves significantly below 1.0 as the exchanger approaches temperature cross (small approach temperatures). Therefore, increasing the overall temperature drop (making approaches less tight) reduces the severity of the departure from true countercurrent behavior, and FT increases toward unity—often rapidly as the approach “opens up.”

Step-by-Step Solution:
With small temperature differences at one end (near pinch), FT is low.As the available ΔT increases, the temperature profiles separate further.This reduces multipass penalties → FT rises, trending quickly toward 1.0.

Verification / Alternative check:
Charts of FT vs. the temperature ratio parameters (R and S) show FT climbing steeply away from the cross region.

Why Other Options Are Wrong:
Decrease rapidly: opposite of observed behavior away from pinch.Remain constant or linear increase: FT response is non-linear and strongly dependent on R and S.

Common Pitfalls:
Confusing FT with LMTD itself; overlooking that FT is a correction for configuration, not for area or fouling.

Final Answer:
Increases very rapidly