Counter-current (counter-flow) heat exchanger — inlet/exit temperature states In a counter-current flow heat exchanger, which inlet condition best describes the relative hot/cold states of the two fluids?

Introduction / Context:
Flow arrangement dictates temperature profiles and log-mean temperature difference (LMTD). Counter-flow generally achieves larger LMTD than parallel flow for the same terminal temperatures, improving effectiveness.

Given Data / Assumptions:

• Two-stream heat exchanger with one hot stream and one cold stream.
• Counter-flow means the streams move in opposite directions.

Concept / Approach:
In counter-flow, the hot fluid enters where the cold fluid exits, and vice versa. Therefore, at the common inlet station of each stream, one is at its hottest while the other (coming from the cold end) is at its coldest. This large temperature difference at both ends enhances driving force.

Step-by-Step Solution:

Verification / Alternative check:
Plot temperature vs. length: counter-flow lines cross from high to low in opposite directions, showing maximal approach at the cold end and hot end.

Why Other Options Are Wrong:

Both hottest or both coldest at inlet describes parallel flow.“Both hottest at exit” is unphysical for simultaneous heat exchange.Identical states at inlet/exit contradict heat transfer.

Common Pitfalls:
Confusing “inlet of exchanger” with “inlet of each stream.” Consider each stream’s own inlet boundary.

Final Answer:

one fluid is coldest and the other is hottest at inlet