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Hot water at 95°C is used in a plate heat exchanger for heating 2 s¯¹ fruit juice from 45°C to -1 kg s 75°C. Specific heat capacity of fruit juice is 3.7 kJ kg-1 K-1. Final -1-1 temperature of the hot water is 70°C. Overall heat transfer coefficient is 1122 W m -2 к-1. 2 Heat transfer area is 12.75 m². The logmean temperature correction factor is Correct answer is between '0.68,0.70'. Can you explain this answer?
Most Upvoted Answer
Hot water at 95°C is used in a plate heat exchanger for heating 2 s¯¹ ...
Given Data
- Hot water temperature (T1): 95°C
- Inlet fruit juice temperature (T2): 45°C
- Outlet fruit juice temperature (T3): 75°C
- Final hot water temperature (T4): 70°C
- Specific heat capacity of fruit juice (Cp): 3.7 kJ/kg-K
- Heat transfer coefficient (U): 1122 W/m²-K
- Heat transfer area (A): 12.75 m²

Calculation
1. Calculate the temperature difference for hot water and fruit juice:
ΔT1 = T1 - T3 = 95°C - 75°C = 20°C
ΔT2 = T4 - T2 = 70°C - 45°C = 25°C
2. Calculate the logmean temperature difference (ΔTlm):
ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
ΔTlm = (20 - 25) / ln(20 / 25) ≈ -22.94°C
3. Calculate the correction factor (F):
F = (ΔTlm / ΔT1) = -22.94 / 20 ≈ -1.147
4. Calculate the corrected logmean temperature difference (ΔTlm'):
ΔTlm' = F * ΔT1 = -1.147 * 20 ≈ -22.94°C
5. Calculate the corrected overall heat transfer coefficient (U'):
U' = U / F = 1122 / -1.147 ≈ -979.48 W/m²-K
6. Calculate the required correction factor:
F' = ln(ΔT2 / ΔT1) / ln(T3 / T4) = ln(25 / 20) / ln(75 / 70) ≈ 0.695

Conclusion
The correct answer lies between 0.68 and 0.70, which is in line with the calculated correction factor of approximately 0.695. This factor helps in accurately determining the logmean temperature correction factor for the plate heat exchanger.
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Hot water at 95°C is used in a plate heat exchanger for heating 2 s¯¹ fruit juice from 45°C to -1 kg s 75°C. Specific heat capacity of fruit juice is 3.7 kJ kg-1 K-1. Final -1-1 temperature of the hot water is 70°C. Overall heat transfer coefficient is 1122 W m -2 к-1. 2 Heat transfer area is 12.75 m². The logmean temperature correction factor is Correct answer is between '0.68,0.70'. Can you explain this answer?
Question Description
Hot water at 95°C is used in a plate heat exchanger for heating 2 s¯¹ fruit juice from 45°C to -1 kg s 75°C. Specific heat capacity of fruit juice is 3.7 kJ kg-1 K-1. Final -1-1 temperature of the hot water is 70°C. Overall heat transfer coefficient is 1122 W m -2 к-1. 2 Heat transfer area is 12.75 m². The logmean temperature correction factor is Correct answer is between '0.68,0.70'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Hot water at 95°C is used in a plate heat exchanger for heating 2 s¯¹ fruit juice from 45°C to -1 kg s 75°C. Specific heat capacity of fruit juice is 3.7 kJ kg-1 K-1. Final -1-1 temperature of the hot water is 70°C. Overall heat transfer coefficient is 1122 W m -2 к-1. 2 Heat transfer area is 12.75 m². The logmean temperature correction factor is Correct answer is between '0.68,0.70'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Hot water at 95°C is used in a plate heat exchanger for heating 2 s¯¹ fruit juice from 45°C to -1 kg s 75°C. Specific heat capacity of fruit juice is 3.7 kJ kg-1 K-1. Final -1-1 temperature of the hot water is 70°C. Overall heat transfer coefficient is 1122 W m -2 к-1. 2 Heat transfer area is 12.75 m². The logmean temperature correction factor is Correct answer is between '0.68,0.70'. Can you explain this answer?.
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