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For evaporators and condensers, for the given conditions, the logarithmic mean temperature difference for parallel flow is
  • a)
    Does not depend on counter flow
  • b)
    Smaller than counter flow
  • c)
    Greater than counter flow
  • d)
    Equal to counter flow
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For evaporators and condensers, for the given conditions, the logarith...
The temperature of one of the fluid remains constant during the flow passage.
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For evaporators and condensers, for the given conditions, the logarith...
Logarithmic Mean Temperature Difference (LMTD)

The logarithmic mean temperature difference (LMTD) is a key parameter used in the design and analysis of heat exchangers, particularly evaporators and condensers. It represents the average temperature difference between the hot and cold fluids over the length of the heat exchanger.

Parallel Flow and Counter Flow

In a parallel flow heat exchanger, the two fluids flow in the same direction, entering at the same end and exiting at the other end. On the other hand, in a counter flow heat exchanger, the two fluids flow in opposite directions, entering at opposite ends and exiting at the same end.

Calculation of LMTD

The LMTD is calculated using the formula:

LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)

where ΔT1 is the temperature difference at one end of the heat exchanger and ΔT2 is the temperature difference at the other end.

Comparison between LMTD in Parallel Flow and Counter Flow

In parallel flow, the temperature difference remains constant throughout the length of the heat exchanger, as the two fluids are moving in the same direction. Therefore, ΔT1 and ΔT2 are equal, resulting in a logarithmic mean temperature difference of zero.

On the other hand, in counter flow, the temperature difference changes along the length of the heat exchanger. Initially, the temperature difference is high, but it decreases as the hot and cold fluids approach each other. As a result, ΔT1 is greater than ΔT2, leading to a positive LMTD.

Conclusion

From the above discussion, it is clear that the logarithmic mean temperature difference for parallel flow is zero, while for counter flow it is positive. Therefore, the correct answer is option 'D', which states that the LMTD for parallel flow is equal to counter flow.
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For evaporators and condensers, for the given conditions, the logarithmic mean temperature difference for parallel flow isa)Does not depend on counter flowb)Smaller than counter flowc)Greater than counter flowd)Equal to counter flowCorrect answer is option 'D'. Can you explain this answer?
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