Question

In a counter-current heat exchanger, compared to co-current flow:

• A. LMTD is lower
• B. LMTD is higher
• C. Heat transfer area required is larger
• D. Exit temperatures cannot cross

Hint:

Counter-current heat exchangers are thermodynamically superior because they yield a larger LMTD, resulting in a more compact and cost-effective design (smaller required heat transfer area).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks us to compare the Logarithmic Mean Temperature Difference (LMTD) and overall performance of a counter-current heat exchanger against a co-current (parallel) heat exchanger.
This is a standard design concept in heat exchanger analysis.

Step 2: Key Formula or Approach:
The rate of heat transfer in a heat exchanger is governed by:
\[ Q = U \cdot A \cdot \text{LMTD} \]
where \( U \) is the overall heat transfer coefficient, \( A \) is the heat transfer area, and LMTD is defined as:
\[ \text{LMTD} = \frac{\Delta T_1 - \Delta T_2}{\ln\left(\frac{\Delta T_1}{\Delta T_2}\right)} \]

Step 3: Detailed Explanation:

• Temperature Driving Force: In a co-current exchanger, the hot and cold fluids enter at the same end.
The temperature difference between the two fluids is large at the inlet but decreases rapidly along the length of the exchanger.
In a counter-current exchanger, the fluids enter at opposite ends.
The temperature difference remains relatively uniform and sustained throughout the length of the exchanger.

• LMTD Comparison: For the same inlet and outlet temperatures, the average driving force (LMTD) is always higher for counter-current flow than for co-current flow:
\[ \text{LMTD}_{\text{counter-current}} \gt \text{LMTD}_{\text{co-current}} \]

• Area Requirement: Because the driving force (LMTD) is larger in a counter-current arrangement, the required surface area \( A \) is smaller for a specified heat duty \( Q \):
\[ A = \frac{Q}{U \cdot \text{LMTD}} \]

• Temperature Crossing: In counter-current flow, the outlet temperature of the cold fluid can exceed the outlet temperature of the hot fluid, which is thermodynamically impossible in co-current flow.


Step 4: Final Answer:
Compared to co-current flow, the counter-current arrangement results in a higher LMTD.