Heat exchanger theory: the LMTD correction factor (FT) is defined as which ratio when accounting for departures from pure countercurrent or cocurrent flow?

Difficulty: Easy

Correct Answer: Ratio of true temperature difference to the LMTD

Explanation:


Introduction / Context:
Log-mean temperature difference (LMTD) is central to sizing heat exchangers. Real exchangers often have multipass or crossflow arrangements that deviate from ideal countercurrent or cocurrent flow. The LMTD correction factor, FT, adjusts the ideal LMTD to reflect the true effective temperature driving force.



Given Data / Assumptions:

  • Steady-state exchanger; no phase change restrictions beyond standard assumptions.
  • Two-stream service with known inlet and outlet temperatures.
  • Configuration requires FT (e.g., 1–2, 2–4 shell-and-tube, crossflow with bypassing).


Concept / Approach:
For an ideal countercurrent exchanger, the temperature driving force is exactly the LMTD. For more complex flow patterns, the true mean temperature difference is smaller. The correction factor FT relates these by: true ΔT_mean = FT * LMTD. Rearranging gives the definition of FT as a ratio.



Step-by-Step Solution:

Start from the relation: ΔT_true = FT * LMTD.Solve for FT: FT = ΔT_true / LMTD.Interpretation: FT ≤ 1, with FT approaching 1 for near-ideal countercurrent operation.


Verification / Alternative check:
Standard FT charts (based on temperature effectiveness parameters R and P) show FT values below unity except for idealized limits; these confirm the ratio definition.



Why Other Options Are Wrong:

  • “LMTD / true ΔT” inverts the definition.
  • Difference or geometric mean have no basis in the governing derivation.


Common Pitfalls:
Applying FT above 1; using FT outside recommended ranges (e.g., FT < 0.75 often suggests reconsidering configuration); mixing temperature levels or units inconsistently.



Final Answer:
Ratio of true temperature difference to the LMTD

More Questions from Process Equipment and Plant Design

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion