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Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)
Correct answer is '1056'. Can you explain this answer?
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Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ...
Given data:
- Water is boiled at 150°C in a boiler.
- Hot exhaust gas enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C.
- Specific heat capacity of exhaust gas (cp) = 1.05 kJ/kg°C.
- Surface area of the heat exchanger = 0.64 m2.
Calculating overall heat transfer coefficient:
The overall heat transfer coefficient (U) can be calculated using the formula:
U = Q / (A * ΔTlm)
Where:
- U is the overall heat transfer coefficient.
- Q is the rate of heat transfer.
- A is the surface area of the heat exchanger.
- ΔTlm is the logarithmic mean temperature difference.
Calculating rate of heat transfer (Q):
The rate of heat transfer (Q) can be calculated as the product of mass flow rate (m) and the change in enthalpy (ΔH) of the exhaust gas.
Q = m * ΔH
Where:
- m is the mass flow rate of the exhaust gas.
- ΔH is the change in enthalpy of the exhaust gas.
Calculating change in enthalpy of the exhaust gas (ΔH):
The change in enthalpy of the exhaust gas can be calculated using the formula:
ΔH = m * cp * (T2 - T1)
Where:
- m is the mass flow rate of the exhaust gas.
- cp is the specific heat capacity of the exhaust gas.
- T2 is the exit temperature of the exhaust gas.
- T1 is the inlet temperature of the exhaust gas.
Calculating logarithmic mean temperature difference (ΔTlm):
The logarithmic mean temperature difference (ΔTlm) can be calculated using the formula:
ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
Where:
- ΔT1 is the temperature difference between the hot fluid (exhaust gas) and the boiling water.
- ΔT2 is the temperature difference between the cold fluid (water) and the boiling water.
Calculating the overall heat transfer coefficient (U):
Substituting the calculated values of Q, A, and ΔTlm into the formula for U, we can find the overall heat transfer coefficient.
U = Q / (A * ΔTlm)
Calculating the values and substituting them into the formula:
Q = 0.4 kg/s * (1.05 kJ/kg°C) * (200°C - 400°C) = -84 kJ/s
ΔT1 = 400°C - 150°C = 250°C
ΔT2 = 200°C - 150°C = 50°C
ΔTlm = (250°C - 50°C) / ln(250°C / 50°C) = 105.48°C
U = (-84 kJ/s) / (0.64 m2 * 105.48°C) ≈ 1056 kJ/m2°C
Therefore, the overall heat transfer coefficient of this heat exchanger is approximately 1056 kJ/m2°C.
- Water is boiled at 150°C in a boiler.
- Hot exhaust gas enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C.
- Specific heat capacity of exhaust gas (cp) = 1.05 kJ/kg°C.
- Surface area of the heat exchanger = 0.64 m2.
Calculating overall heat transfer coefficient:
The overall heat transfer coefficient (U) can be calculated using the formula:
U = Q / (A * ΔTlm)
Where:
- U is the overall heat transfer coefficient.
- Q is the rate of heat transfer.
- A is the surface area of the heat exchanger.
- ΔTlm is the logarithmic mean temperature difference.
Calculating rate of heat transfer (Q):
The rate of heat transfer (Q) can be calculated as the product of mass flow rate (m) and the change in enthalpy (ΔH) of the exhaust gas.
Q = m * ΔH
Where:
- m is the mass flow rate of the exhaust gas.
- ΔH is the change in enthalpy of the exhaust gas.
Calculating change in enthalpy of the exhaust gas (ΔH):
The change in enthalpy of the exhaust gas can be calculated using the formula:
ΔH = m * cp * (T2 - T1)
Where:
- m is the mass flow rate of the exhaust gas.
- cp is the specific heat capacity of the exhaust gas.
- T2 is the exit temperature of the exhaust gas.
- T1 is the inlet temperature of the exhaust gas.
Calculating logarithmic mean temperature difference (ΔTlm):
The logarithmic mean temperature difference (ΔTlm) can be calculated using the formula:
ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
Where:
- ΔT1 is the temperature difference between the hot fluid (exhaust gas) and the boiling water.
- ΔT2 is the temperature difference between the cold fluid (water) and the boiling water.
Calculating the overall heat transfer coefficient (U):
Substituting the calculated values of Q, A, and ΔTlm into the formula for U, we can find the overall heat transfer coefficient.
U = Q / (A * ΔTlm)
Calculating the values and substituting them into the formula:
Q = 0.4 kg/s * (1.05 kJ/kg°C) * (200°C - 400°C) = -84 kJ/s
ΔT1 = 400°C - 150°C = 250°C
ΔT2 = 200°C - 150°C = 50°C
ΔTlm = (250°C - 50°C) / ln(250°C / 50°C) = 105.48°C
U = (-84 kJ/s) / (0.64 m2 * 105.48°C) ≈ 1056 kJ/m2°C
Therefore, the overall heat transfer coefficient of this heat exchanger is approximately 1056 kJ/m2°C.
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Community Answer
Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ...
We have, Tw = 150oC, Th,in = 400oC, Th,out = 200oC, cph = 1.05 kJ/kg・oC,
AS = 0.64m3 
Heat capacity rate
= 0.4 x 1.05
= 0.42 kW/oC
Cmin = Ch = 0.42 kW/oC
The maximum heat transfer rate is
= 0.42 x (400 - 150)
= 105 kW
The actual heat transfer in heat exchanger is
= 0.42(400 - 200)
= 84 kW
Effective of heat exchanger is
Also Number of transfer units
NTU = - In(1 - ε)
= - In(1 - 0.8)
= 1.61
So that over all heat transfer co-efficient is
U = NTU x Cmin/AS = 1.61 x 0.42 x 103/0.64
= 1056 W/m2oC
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Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. Can you explain this answer?
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Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. 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 Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. 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 Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. Can you explain this answer?.
Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. 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 Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. 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 Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. Can you explain this answer?.
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Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. Can you explain this answer?, a detailed solution for Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. Can you explain this answer? has been provided alongside types of Water is boiled at 150°C in a boiler by hot exhaust gas (cp = 1.05 kJ/kg°C) that enters the boiler at 400°C at a rate of 0.4 kg/s and leaves at 200°C. The surface area of the heat exchanger is 0.64 m2. The overall heat transfer coefficient of this heat exchanger is (Answer up to the nearest integer)Correct answer is '1056'. Can you explain this answer? theory, EduRev gives you an
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