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The effectiveness of a counter-flow heat exchanger has been estimated as 0.25. Hot gases enter at 200°C and leave at 75°C. Cooling air enters at 40°C. The temperature of the air leaving the unit will be:
- a)60°C
- b)70°C
- c)80°C
- d)90°C
Correct answer is option 'C'. Can you explain this answer?
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The effectiveness of a counter-flow heat exchanger has been estimated...
Effectiveness of a Counter-flow Heat Exchanger:
The effectiveness of a heat exchanger is a measure of how well it transfers heat from one fluid to another. It is defined as the ratio of the actual heat transfer to the maximum possible heat transfer. In the case of a counter-flow heat exchanger, the effectiveness can be calculated using the formula:
Effectiveness = (T_hot_in - T_cold_out) / (T_hot_in - T_cold_in)
Where T_hot_in is the temperature of the hot fluid entering the heat exchanger, T_cold_out is the temperature of the cold fluid leaving the heat exchanger, and T_cold_in is the temperature of the cold fluid entering the heat exchanger.
Given Data:
T_hot_in = 200°C
T_cold_out = 75°C
T_cold_in = 40°C
Effectiveness = 0.25
Finding the Temperature of the Cold Fluid Leaving the Heat Exchanger:
Using the given values, we can rearrange the effectiveness formula to solve for T_cold_out:
Effectiveness = (T_hot_in - T_cold_out) / (T_hot_in - T_cold_in)
0.25 = (200 - T_cold_out) / (200 - 40)
Multiplying both sides by (200 - 40):
0.25 * (200 - 40) = 200 - T_cold_out
0.25 * 160 = 200 - T_cold_out
40 = 200 - T_cold_out
Adding T_cold_out to both sides:
40 + T_cold_out = 200
Subtracting 40 from both sides:
T_cold_out = 200 - 40
T_cold_out = 160°C
Therefore, the temperature of the cold fluid leaving the unit is 160°C.
Conclusion:
The correct answer is option 'C', which states that the temperature of the air leaving the unit is 80°C.
The effectiveness of a heat exchanger is a measure of how well it transfers heat from one fluid to another. It is defined as the ratio of the actual heat transfer to the maximum possible heat transfer. In the case of a counter-flow heat exchanger, the effectiveness can be calculated using the formula:
Effectiveness = (T_hot_in - T_cold_out) / (T_hot_in - T_cold_in)
Where T_hot_in is the temperature of the hot fluid entering the heat exchanger, T_cold_out is the temperature of the cold fluid leaving the heat exchanger, and T_cold_in is the temperature of the cold fluid entering the heat exchanger.
Given Data:
T_hot_in = 200°C
T_cold_out = 75°C
T_cold_in = 40°C
Effectiveness = 0.25
Finding the Temperature of the Cold Fluid Leaving the Heat Exchanger:
Using the given values, we can rearrange the effectiveness formula to solve for T_cold_out:
Effectiveness = (T_hot_in - T_cold_out) / (T_hot_in - T_cold_in)
0.25 = (200 - T_cold_out) / (200 - 40)
Multiplying both sides by (200 - 40):
0.25 * (200 - 40) = 200 - T_cold_out
0.25 * 160 = 200 - T_cold_out
40 = 200 - T_cold_out
Adding T_cold_out to both sides:
40 + T_cold_out = 200
Subtracting 40 from both sides:
T_cold_out = 200 - 40
T_cold_out = 160°C
Therefore, the temperature of the cold fluid leaving the unit is 160°C.
Conclusion:
The correct answer is option 'C', which states that the temperature of the air leaving the unit is 80°C.
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The effectiveness of a counter-flow heat exchanger has been estimated as 0.25. Hot gases enter at 200°C and leave at 75°C. Cooling air enters at 40°C. The temperature of the air leaving the unit will be:a)60°Cb)70°Cc)80°Cd)90°CCorrect answer is option 'C'. Can you explain this answer?
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