Heat exchangers: For the same terminal temperatures, the logarithmic mean temperature difference (LMTD) of a counter-current flow heat exchanger is __________ than that of a parallel-flow heat exchanger.

Introduction / Context:
The LMTD method is a cornerstone of heat-exchanger sizing. Understanding how flow arrangement influences the temperature driving force helps engineers select compact and efficient configurations.

Given Data / Assumptions:

• Terminal temperatures (hot in/out, cold in/out) are fixed and identical for both arrangements.
• Steady state, negligible heat losses to surroundings.
• Fluids have sensible heat exchange (no phase change) for this comparison.

Concept / Approach:
For given terminal temperatures, counter-current flow maintains a more uniform temperature difference along the length. This results in a larger logarithmic mean of the end temperature differences than parallel flow, where the temperature driving force decays more rapidly.

Step-by-Step Solution:

Verification / Alternative check:
Test a numeric example: hot 100→60°C, cold 30→70°C. Counter: ΔT_1 = 100−70 = 30, ΔT_2 = 60−30 = 30 ⇒ LMTD = 30. Parallel: ΔT_1 = 100−30 = 70, ΔT_2 = 60−70 = −10 (sign handled via magnitudes) ⇒ effective LMTD smaller. This illustrates the advantage.

Why Other Options Are Wrong:

• “Same” is incorrect; textbook results show counter-current advantage.
• “Less” contradicts the fundamental LMTD comparison.
• “Indeterminate” is unnecessary when terminal temperatures are specified.

Common Pitfalls:
Confusing LMTD with effectiveness (ε) or assuming phase change without noting terminal conditions.

Final Answer:
greater