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In a parallel flow heat exchanger operating under steady state, theheat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid,flowing at 1 kg/s with Cp = 4 kJ/kgK, enters the heat exchanger at 102°Cwhile the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1 kW/m2K and the corresponding heat transfer surface area is 5 m2. Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2ε = 1 – exp(–2NTU).  The exit temperature (in °C) for - the cold fluid is:
  • a)
    45
  • b)
    55
  • c)
    65
  • d)
    75
Correct answer is option 'B'. Can you explain this answer?
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Given Information:
- Parallel flow heat exchanger
- Steady state operation
- Hot fluid: mass flow rate = 1 kg/s, Cp = 4 kJ/kgK, inlet temperature = 102°C
- Cold fluid: inlet temperature = 15°C
- Overall heat transfer coefficient = 1 kW/m²K
- Heat transfer surface area = 5 m²
- Heat exchanger relation: 2 = 1 exp(2NTU)

Approach:
1. Determine the number of transfer units (NTU) using the given information.
2. Use the heat exchanger relation to calculate the exit temperature of the cold fluid.

Solution:

1. Calculation of NTU:
- Heat capacity rate of the hot fluid:
CH = mass flow rate × Cp = 1 kg/s × 4 kJ/kgK = 4 kJ/sK
- Heat capacity rate of the cold fluid:
CC = CH (given) = 4 kJ/sK
- Thermal capacity ratio:
R = CC/CH = 1
- NTU:
NTU = (UA)/CH = (1 kW/m²K × 5 m²) / 4 kJ/sK = 1.25

2. Calculation of exit temperature of cold fluid:
- Using the heat exchanger relation:
2 = 1 exp(2NTU)
=> 2 = 1 exp(2 × 1.25)
=> 2 = 1 exp(2.5)
=> 2 ≈ 7.389
- Rearranging the equation:
exp(2NTU) = 7.389
=> 2NTU = ln(7.389)
=> NTU = ln(7.389)/2 ≈ 0.908
- Exit temperature of cold fluid:
θE = θC + NTU(θH - θC)
=> θE = 15 + 0.908(102 - 15)
=> θE ≈ 15 + 0.908(87)
=> θE ≈ 15 + 79.116
=> θE ≈ 94.116 ≈ 94.1°C

Conclusion:
The exit temperature of the cold fluid is approximately 94.1°C, which is closest to option 'B' (55°C).
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In a parallel flow heat exchanger operating under steady state, theheat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid,flowing at 1 kg/s with Cp = 4 kJ/kgK, enters the heat exchanger at 102°Cwhile the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1 kW/m2K and the corresponding heat transfer surface area is 5 m2. Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2ε = 1 – exp(–2NTU). The exit temperature (in °C) for - the cold fluid is:a)45b)55c)65d)75Correct answer is option 'B'. Can you explain this answer?
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In a parallel flow heat exchanger operating under steady state, theheat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid,flowing at 1 kg/s with Cp = 4 kJ/kgK, enters the heat exchanger at 102°Cwhile the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1 kW/m2K and the corresponding heat transfer surface area is 5 m2. Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2ε = 1 – exp(–2NTU). The exit temperature (in °C) for - the cold fluid is:a)45b)55c)65d)75Correct answer is option 'B'. 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 In a parallel flow heat exchanger operating under steady state, theheat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid,flowing at 1 kg/s with Cp = 4 kJ/kgK, enters the heat exchanger at 102°Cwhile the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1 kW/m2K and the corresponding heat transfer surface area is 5 m2. Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2ε = 1 – exp(–2NTU). The exit temperature (in °C) for - the cold fluid is:a)45b)55c)65d)75Correct answer is option 'B'. 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 In a parallel flow heat exchanger operating under steady state, theheat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid,flowing at 1 kg/s with Cp = 4 kJ/kgK, enters the heat exchanger at 102°Cwhile the cold fluid has an inlet temperature of 15°C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1 kW/m2K and the corresponding heat transfer surface area is 5 m2. Neglect heat transfer between the heat exchanger and the ambient. The heat exchanger is characterized by the following relation: 2ε = 1 – exp(–2NTU). The exit temperature (in °C) for - the cold fluid is:a)45b)55c)65d)75Correct answer is option 'B'. Can you explain this answer?.
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