Question

Given below are two statements:
Statement I: In parallel flow heat exchanger the exit temperature of cold fluid can exceed that of hot fluid.
Statement II: In counter flow heat exchanger the exit temperature of cold fluid cannot be higher than that of hot fluid.
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Hint:

Remember:
- Parallel Flow: \( T_{c,out} < T_{h,out} \) always.
- Counter Flow: \( T_{c,out} > T_{h,out} \) is highly possible and represents a major thermodynamic advantage.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In heat exchangers, two fluids of different initial temperatures flow through the system to exchange thermal energy.
In a parallel-flow arrangement, both the hot and cold fluids enter at the same end, flow in the exact same direction, and leave at the same end.
In a counter-flow arrangement, the fluids enter at opposite ends and flow in opposite directions.
The limits of the exit temperatures of both fluids are determined by the laws of thermodynamics and the flow configuration.

Step 2: Detailed Explanation:
Let us analyze both statements in detail:
- Statement I: In a parallel-flow heat exchanger, as the fluids flow along the length of the exchanger, their temperatures asymptotically approach each other.
The temperature of the hot fluid decreases while the temperature of the cold fluid increases.
The maximum possible heat transfer is achieved when both fluids reach the exact same outlet temperature.
Therefore, the outlet temperature of the cold fluid (\( T_{c,out} \)) can never exceed the outlet temperature of the hot fluid (\( T_{h,out} \)).
This makes Statement I false.
- Statement II: In a counter-flow heat exchanger, because the fluids flow in opposite directions, the cold fluid leaves near the entrance of the hot fluid.
This configuration allows the outlet temperature of the cold fluid (\( T_{c,out} \)) to exceed the outlet temperature of the hot fluid (\( T_{h,out} \)).
In fact, under ideal conditions with an infinitely large surface area, the cold fluid can be heated almost to the inlet temperature of the hot fluid.
This makes Statement II false, as it states that the exit temperature of the cold fluid cannot be higher than that of the hot fluid.
Since both statements are thermodynamically incorrect, option (B) is the correct choice.

Step 3: Final Answer:
Both Statement I and Statement II are incorrect.