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The outlet header of a steam super heater consists a pipe (ε = 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε = 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8 W/m2K4)
- a)7.4 kW/m2
- b)4.4 kW/m2
- c)5.4 kW/m2
- d)8.5 kW/m2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The outlet header of a steam super heater consists a pipe (ε= ...
Given, ε1 = 0.9, ε
The heat transfer per unit area by thermal radiation without screen provision,
Q1 = ε1σ (T14−T24) = 0.9×5.67×10-8 × (7004−3004) = 11.838 kW/m2
The heat transfer per unit area by thermal radiation with screen provision,
After provision of screen the new system reduces to a problem of heat exchange between two concentric cylinders and equivalent emissivity
is given as
Q2 = 0.735×5.67×10-8 × (7004−5004) = 7.4 kW/m2
The reduction in heat transfer due to screen provision = 11.838−7.4 = 4.438 kW/m2
2
= 0.75, T1 = 4270C = 700 K, T2 = 270C =300 K, Ts = 2270C = 500 K, σ =5.67×10-8 W/m2K4The heat transfer per unit area by thermal radiation without screen provision,
Q1 = ε1σ (T14−T24) = 0.9×5.67×10-8 × (7004−3004) = 11.838 kW/m2
The heat transfer per unit area by thermal radiation with screen provision,
After provision of screen the new system reduces to a problem of heat exchange between two concentric cylinders and equivalent emissivity
is given asQ2 = 0.735×5.67×10-8 × (7004−5004) = 7.4 kW/m2
The reduction in heat transfer due to screen provision = 11.838−7.4 = 4.438 kW/m2
Most Upvoted Answer
The outlet header of a steam super heater consists a pipe (ε= ...
Calculation of Reduction in Heat due to Screen Provision:
- Given data:
- Diameter of pipe (D) = 30 cm = 0.3 m
- Surface temperature of header (T1) = 427°C = 700K
- Enclosure temperature (T2) = 270°C = 543K
- Diameter of screen (D') = 40 cm = 0.4 m
- Temperature of screen (T') = 227°C = 500K
- Stefan-Boltzmann constant (σ) = 5.67×10-8 W/m2K4
Step 1: Calculation of Heat Loss without Screen
- Q = εσA(T1^4 - T2^4)
- Area of pipe without screen (A) = πDL = π*0.3*4 = 0.942 m2
- Heat loss without screen (Q1) = 0.9*5.67×10-8*0.942*(700^4 - 543^4) = 746.5 kW
Step 2: Calculation of Heat Loss with Screen
- Area of pipe with screen (A') = πD'L = π*0.4*4 = 1.2566 m2
- Heat loss with screen (Q2) = 0.75*5.67×10-8*1.2566*(700^4 - 500^4) = 742.1 kW
Step 3: Calculation of Reduction in Heat due to Screen Provision
- Reduction in heat = Q1 - Q2 = 746.5 - 742.1 = 4.4 kW/m2
Therefore, the reduction in heat due to screen provision is 4.4 kW/m2, which corresponds to option 'B'.
- Given data:
- Diameter of pipe (D) = 30 cm = 0.3 m
- Surface temperature of header (T1) = 427°C = 700K
- Enclosure temperature (T2) = 270°C = 543K
- Diameter of screen (D') = 40 cm = 0.4 m
- Temperature of screen (T') = 227°C = 500K
- Stefan-Boltzmann constant (σ) = 5.67×10-8 W/m2K4
Step 1: Calculation of Heat Loss without Screen
- Q = εσA(T1^4 - T2^4)
- Area of pipe without screen (A) = πDL = π*0.3*4 = 0.942 m2
- Heat loss without screen (Q1) = 0.9*5.67×10-8*0.942*(700^4 - 543^4) = 746.5 kW
Step 2: Calculation of Heat Loss with Screen
- Area of pipe with screen (A') = πD'L = π*0.4*4 = 1.2566 m2
- Heat loss with screen (Q2) = 0.75*5.67×10-8*1.2566*(700^4 - 500^4) = 742.1 kW
Step 3: Calculation of Reduction in Heat due to Screen Provision
- Reduction in heat = Q1 - Q2 = 746.5 - 742.1 = 4.4 kW/m2
Therefore, the reduction in heat due to screen provision is 4.4 kW/m2, which corresponds to option 'B'.
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The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. Can you explain this answer?
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The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. 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 The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. Can you explain this answer?.
The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. 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 The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. Can you explain this answer?.
Solutions for The outlet header of a steam super heater consists a pipe (ε= 0.9) of diameter 30 cm and it is placed in an enclosure at 270C. The surface temperature of header is 4270C. If the header is enveloped in a 40 cm diameter cylindrical screen (ε= 0.75) then the reduction in heat due to screen provision is (take temperature of screen = 2270C, Stefan- Boltzmann constant = 5.67×10-8W/m2K4)a)7.4 kW/m2b)4.4 kW/m2c)5.4 kW/m2d)8.5 kW/m2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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