LMTD comparison for evaporators/condensers For the same terminal temperatures and capacity duty, how does the logarithmic mean temperature difference (LMTD) for parallel flow compare with that for counter flow?

Introduction / Context:
The logarithmic mean temperature difference (LMTD) is the primary temperature driving force used in sizing heat exchangers. For a fixed set of inlet and outlet temperatures, the LMTD depends on how the two fluids are arranged. Understanding which arrangement yields a larger LMTD helps designers choose more compact or efficient exchangers.

Given Data / Assumptions:

• Two-stream heat exchanger (evaporator or condenser) with specified terminal temperatures.
• Steady-state heat transfer with negligible heat loss to surroundings.
• Comparison strictly between parallel flow and counter flow arrangements.

Concept / Approach:
For the same terminal temperatures, counter flow consistently provides a larger LMTD than parallel flow. This is because counter flow maintains a more uniform temperature driving force along the length of the exchanger. Parallel flow suffers from a high initial driving force that rapidly diminishes, reducing the logarithmic mean overall.

Step-by-Step Solution:

Verification / Alternative check:
Plotting temperature profiles along length shows a steeper drop in parallel flow with a small tailing driving force, versus a more even counter-flow profile. Integrating the local driving force along the length reproduces the LMTD inequality.

Why Other Options Are Wrong:

Greater or equal: contradicts textbook results for two-stream exchangers under the same terminal temperatures.“Unrelated to flow arrangement” is incorrect; flow arrangement directly affects ΔT1 and ΔT2.Fouling alters required area but does not overturn the fundamental LMTD ordering.

Common Pitfalls:
Mixing up effectiveness and LMTD. Effectiveness accounts for capacity rates; LMTD is set by terminal temperatures and arrangement. Also, ensure temperatures are absolute values when evaluating differences.

Final Answer:

Less than for counter flow