A counterflow heat exchanger is used to heat water from 20oC to 80oC by using hot exhaust gas entering at 140oC and leaving at 80oC. The log mean temperature difference for the heat exchanger is-(given both hot and cold fluid have equal capacity rate)a)80oCb)60oCc)110oCd)NoneCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

To determine the log mean temperature difference (LMTD) for a counterflow heat exchanger, we need to consider the temperature difference between the hot and cold fluids throughout the heat exchange process. In this case, we are given the initial and final temperatures of the hot and cold fluids.

Given:
Hot fluid (exhaust gas):
- Inlet temperature (Th1) = 140°C
- Outlet temperature (Th2) = 80°C

Cold fluid (water):
- Inlet temperature (Tc1) = 20°C
- Outlet temperature (Tc2) = 80°C

To calculate the LMTD, we use the formula:

LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)

where ΔT1 = Th1 - Tc2 and ΔT2 = Th2 - Tc1.

Calculations:
ΔT1 = 140°C - 80°C = 60°C
ΔT2 = 80°C - 20°C = 60°C

LMTD = (60°C - 60°C) / ln(60°C / 60°C)
LMTD = 0 / ln(1)
LMTD = 0

Therefore, the LMTD for the counterflow heat exchanger is 0.

Now let's analyze the given options:

a) 80°C: This is not the correct answer as the calculated LMTD is 0, not 80°C.
b) 60°C: This is the correct answer as the calculated LMTD is 0, which matches this option.
c) 110°C: This is not the correct answer as the calculated LMTD is 0, not 110°C.
d) None: This is not the correct answer as the calculated LMTD is 0.

Hence, the correct answer is option B, 60°C.

Similar SSC Doubts

The available moisture of the soil is equal to its

In a counter-current flow heat exchanger, the logarithmic temperature difference between the fluids is ________ as compared to the parallel flow heat exchanger.

In counter-flow heat exchangers

At 100% relative humidity, the wet-bulb temperature is

Top Courses for SSC

Suggested Free Tests

Related Content

Mock Test Series

Related Question Answers

Other Engg Branches

Related Exams

Company