Heat exchangers: Compared with parallel flow, a counter-current (counter-flow) heat exchanger can transfer ________ total heat between the same two fluids (all else equal).

Introduction / Context:
Flow arrangement strongly affects the temperature profiles and the log-mean temperature difference (LMTD) in a heat exchanger. Counter-current flow generally yields higher effectiveness than parallel flow given similar sizes and heat transfer coefficients.

Given Data / Assumptions:

• Two-fluid, steady-state heat exchanger.
• Same overall heat transfer coefficient and area for both arrangements.
• No phase change (for simplicity).

Concept / Approach:
Total heat transfer rate Q is computed using Q = U * A * LMTDCounter-current flow offers a larger LMTD for the same inlet temperatures, because the temperature difference is maintained more uniformly along the length.

Step-by-Step Solution:
Compute LMTD for parallel: DeltaT1_par = Th_in - Tc_in; DeltaT2_par = Th_out - Tc_out.Compute LMTD for counter: DeltaT1_cnt = Th_in - Tc_out; DeltaT2_cnt = Th_out - Tc_in.Typically, LMTD_counter > LMTD_parallel → higher Q for counter-current.

Verification / Alternative check:
Effectiveness–NTU relations show higher maximum temperature approach on the cold end for counter-current, enabling greater heat recovery.

Why Other Options Are Wrong:

• Less/same/zero: contradict LMTD and effectiveness analysis.
• Only latent heat: arrangement benefits both sensible and latent applications.

Common Pitfalls:
Assuming area or U can compensate equally; in design, counter-current is preferred when feasible for better performance and smaller area.

Final Answer:
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