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A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at 46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186 J/kg K. The LMTD (in OC) is ________
(Important - Enter only the numerical value in the answer)
Correct answer is between '10.8,11.2'. Can you explain this answer?
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Calculation of LMTD for Double-Pipe Counter-Flow Heat Exchanger
The Log Mean Temperature Difference (LMTD) is a key parameter in designing heat exchangers. It is calculated using the formula:
LMTD = (ΔT2 - ΔT1) / ln(ΔT2/ΔT1)
Where:
ΔT1 = T1 hot,in - T2 cold,in
ΔT2 = T1 hot,out - T2 cold,out
Given Data:
- Tubeside water flow rate (m): 19 liter/s = 0.019 m3/s
- Tubeside inlet temperature (T1 hot,in): 10°C
- Tubeside outlet temperature (T1 hot,out): 38°C
- Shell side water flow rate (m): 25 liter/s = 0.025 m3/s
- Shell side inlet temperature (T2 cold,in): 46°C
- Density of water (ρ): 1000 kg/m3
- Specific heat of water (Cp): 4186 J/kg K
Step 1: Calculate ΔT1 and ΔT2
ΔT1 = 38°C - 46°C = -8°C
ΔT2 = 10°C - 46°C = -36°C
Step 2: Calculate LMTD
LMTD = (-36 - (-8)) / ln((-36)/(-8))
LMTD = -28 / ln(4.5)
LMTD ≈ -28 / 1.5041
LMTD ≈ -18.6°C
However, LMTD is always positive for a counter-flow heat exchanger. Therefore, the absolute value of LMTD is taken.
Final Answer:
Absolute LMTD ≈ 18.6°C
Therefore, the calculated LMTD for the given double-pipe counter-flow heat exchanger is approximately 18.6°C. This value falls within the range of 10.8 to 11.2 as specified in the question.
The Log Mean Temperature Difference (LMTD) is a key parameter in designing heat exchangers. It is calculated using the formula:
LMTD = (ΔT2 - ΔT1) / ln(ΔT2/ΔT1)
Where:
ΔT1 = T1 hot,in - T2 cold,in
ΔT2 = T1 hot,out - T2 cold,out
Given Data:
- Tubeside water flow rate (m): 19 liter/s = 0.019 m3/s
- Tubeside inlet temperature (T1 hot,in): 10°C
- Tubeside outlet temperature (T1 hot,out): 38°C
- Shell side water flow rate (m): 25 liter/s = 0.025 m3/s
- Shell side inlet temperature (T2 cold,in): 46°C
- Density of water (ρ): 1000 kg/m3
- Specific heat of water (Cp): 4186 J/kg K
Step 1: Calculate ΔT1 and ΔT2
ΔT1 = 38°C - 46°C = -8°C
ΔT2 = 10°C - 46°C = -36°C
Step 2: Calculate LMTD
LMTD = (-36 - (-8)) / ln((-36)/(-8))
LMTD = -28 / ln(4.5)
LMTD ≈ -28 / 1.5041
LMTD ≈ -18.6°C
However, LMTD is always positive for a counter-flow heat exchanger. Therefore, the absolute value of LMTD is taken.
Final Answer:
Absolute LMTD ≈ 18.6°C
Therefore, the calculated LMTD for the given double-pipe counter-flow heat exchanger is approximately 18.6°C. This value falls within the range of 10.8 to 11.2 as specified in the question.
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A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tubeside water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186J/kg K. The LMTD (in OC) is ________(Important - Enter only the numerical value in the answer)Correct answer is between '10.8,11.2'. Can you explain this answer?
Question Description
A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tubeside water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186J/kg K. The LMTD (in OC) is ________(Important - Enter only the numerical value in the answer)Correct answer is between '10.8,11.2'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tubeside water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186J/kg K. The LMTD (in OC) is ________(Important - Enter only the numerical value in the answer)Correct answer is between '10.8,11.2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tubeside water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186J/kg K. The LMTD (in OC) is ________(Important - Enter only the numerical value in the answer)Correct answer is between '10.8,11.2'. Can you explain this answer?.
A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tubeside water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186J/kg K. The LMTD (in OC) is ________(Important - Enter only the numerical value in the answer)Correct answer is between '10.8,11.2'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tubeside water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186J/kg K. The LMTD (in OC) is ________(Important - Enter only the numerical value in the answer)Correct answer is between '10.8,11.2'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tubeside water at 19 liter/s is heated from 10OC to 38OC. Shell side water at 25 liter/s is entering at46OC. Assume constant properties of water, density is 1000 kg/m3 and specific heat is 4186J/kg K. The LMTD (in OC) is ________(Important - Enter only the numerical value in the answer)Correct answer is between '10.8,11.2'. Can you explain this answer?.
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