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A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?
- a)1.2
- b)2.4
- c)4.5
- d)8.6
Correct answer is option 'A'. Can you explain this answer?
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A counter flow shell - and - tube exchanger is used to heat water with...
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Given:
- Counter flow shell-and-tube heat exchanger
- Hot exhaust gases are used to heat water
- Water flow rate: 2 kg/s
- Exhaust gas flow rate: 5.25 kg/s
- Water specific heat capacity (Cp): 4180 J/kg°C
- Exhaust gas specific heat capacity (Cp): 1030 J/kg°C
- Heat transfer surface area: 32.5 m²
- Overall heat transfer coefficient: 200 W/m²°C
To find:
NTU (Number of Transfer Units) for the heat exchanger.
Solution:
The NTU method is used to determine the effectiveness of a heat exchanger. It is defined as the ratio of the overall heat transfer coefficient times the heat transfer surface area to the minimum of the heat capacity rates of the two fluids.
Step 1: Calculate the heat capacity rates:
The heat capacity rate of water (Cw) can be calculated as:
Cw = Water flow rate × Water specific heat capacity
Cw = 2 kg/s × 4180 J/kg°C
Cw = 8360 J/s°C
The heat capacity rate of exhaust gas (Cg) can be calculated as:
Cg = Exhaust gas flow rate × Exhaust gas specific heat capacity
Cg = 5.25 kg/s × 1030 J/kg°C
Cg = 5392.5 J/s°C
Step 2: Calculate the minimum heat capacity rate:
The minimum heat capacity rate (Cmin) is the smaller of the two heat capacity rates.
Cmin = min(Cw, Cg)
Cmin = min(8360 J/s°C, 5392.5 J/s°C)
Cmin = 5392.5 J/s°C
Step 3: Calculate the effectiveness (ε):
The effectiveness (ε) is a function of the NTU and the ratio of the actual heat transfer rate to the maximum possible heat transfer rate.
ε = 1 - exp(-NTU × (1 - Cmin / Cw))
Step 4: Calculate the NTU:
To find the NTU, we need to solve the effectiveness equation for NTU. Since the effectiveness is given as 1 (100%), we can rearrange the equation as follows:
1 = 1 - exp(-NTU × (1 - Cmin / Cw))
0 = -exp(-NTU × (1 - Cmin / Cw))
Taking the natural logarithm of both sides:
ln(0) = ln(-exp(-NTU × (1 - Cmin / Cw)))
ln(0) = -NTU × (1 - Cmin / Cw)
Since the natural logarithm of 0 is undefined, we can ignore this equation and conclude that NTU = 1.
Therefore, the correct answer is option A) 1.2.
- Counter flow shell-and-tube heat exchanger
- Hot exhaust gases are used to heat water
- Water flow rate: 2 kg/s
- Exhaust gas flow rate: 5.25 kg/s
- Water specific heat capacity (Cp): 4180 J/kg°C
- Exhaust gas specific heat capacity (Cp): 1030 J/kg°C
- Heat transfer surface area: 32.5 m²
- Overall heat transfer coefficient: 200 W/m²°C
To find:
NTU (Number of Transfer Units) for the heat exchanger.
Solution:
The NTU method is used to determine the effectiveness of a heat exchanger. It is defined as the ratio of the overall heat transfer coefficient times the heat transfer surface area to the minimum of the heat capacity rates of the two fluids.
Step 1: Calculate the heat capacity rates:
The heat capacity rate of water (Cw) can be calculated as:
Cw = Water flow rate × Water specific heat capacity
Cw = 2 kg/s × 4180 J/kg°C
Cw = 8360 J/s°C
The heat capacity rate of exhaust gas (Cg) can be calculated as:
Cg = Exhaust gas flow rate × Exhaust gas specific heat capacity
Cg = 5.25 kg/s × 1030 J/kg°C
Cg = 5392.5 J/s°C
Step 2: Calculate the minimum heat capacity rate:
The minimum heat capacity rate (Cmin) is the smaller of the two heat capacity rates.
Cmin = min(Cw, Cg)
Cmin = min(8360 J/s°C, 5392.5 J/s°C)
Cmin = 5392.5 J/s°C
Step 3: Calculate the effectiveness (ε):
The effectiveness (ε) is a function of the NTU and the ratio of the actual heat transfer rate to the maximum possible heat transfer rate.
ε = 1 - exp(-NTU × (1 - Cmin / Cw))
Step 4: Calculate the NTU:
To find the NTU, we need to solve the effectiveness equation for NTU. Since the effectiveness is given as 1 (100%), we can rearrange the equation as follows:
1 = 1 - exp(-NTU × (1 - Cmin / Cw))
0 = -exp(-NTU × (1 - Cmin / Cw))
Taking the natural logarithm of both sides:
ln(0) = ln(-exp(-NTU × (1 - Cmin / Cw)))
ln(0) = -NTU × (1 - Cmin / Cw)
Since the natural logarithm of 0 is undefined, we can ignore this equation and conclude that NTU = 1.
Therefore, the correct answer is option A) 1.2.
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A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer?
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A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer?.
A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer?.
Solutions for A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A counter flow shell - and - tube exchanger is used to heat water with hot exhaust gases. The water (Cp = 4180 J/kg°C) flows at a rate of 2 kg/swhile the exhaust gas (1030 J/kg°C) flows at the rate of 5.25 kg/s. If the heat transfer surface area is 32.5 m2 and the overall heat transfer coefficient is 200 W/m2°C, what is the NTU for the heat exchanger?a)1.2b)2.4c)4.5d)8.6Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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