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A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.
Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.
Neglect all other modes of heat transfer except radiation.
Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).
Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.
Neglect all other modes of heat transfer except radiation.
Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).
Correct answer is '218.33'. Can you explain this answer?
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Most Upvoted Answer
A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 ...
Solar flux (Qenter) 600 W/m2
Absorptivity (α)= 0.21
Ambient temperature (T∞) 250C = 298 K
Stefan Boltzmann constant (σ) = 5.669 x10-8 W/m2 -K4
Because all flux is absorbed by the plate, so, we can say that the value of absorptivity is equal to 1.
From Kirchoff’s law,
Emissivity = absorptivity, ε = α = 0.21
At equilibrium, Qenter =Qleave
Hence, the correct answer is 218.33.
Absorptivity (α)= 0.21
Ambient temperature (T∞) 250C = 298 K
Stefan Boltzmann constant (σ) = 5.669 x10-8 W/m2 -K4
Because all flux is absorbed by the plate, so, we can say that the value of absorptivity is equal to 1.
From Kirchoff’s law,
Emissivity = absorptivity, ε = α = 0.21
At equilibrium, Qenter =Qleave
Hence, the correct answer is 218.33.
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A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 ...
Given data:
- Solar flux (radiation intensity) = 600 W/m2
- Ambient temperature = 25°C
- Absorptivity of cast iron = 0.21
- Stefan-Boltzmann constant = 5.669 x 10-8 W/m2-K4
Calculating the radiation equilibrium temperature:
1. The solar flux is absorbed by the plate, so the absorbed power per unit area can be calculated using the equation:
Absorbed power density = Solar flux x Absorptivity
Absorbed power density = 600 x 0.21 = 126 W/m2
2. The rate of radiation heat transfer from the plate can be calculated using the Stefan-Boltzmann law:
Radiation heat transfer rate = Stefan-Boltzmann constant x Surface area x (Temperature of the plate)^4
Radiation heat transfer rate = 5.669 x 10-8 x Surface area x (Temperature of the plate)^4
3. At radiation equilibrium, the rate of radiation heat transfer from the plate is equal to the absorbed power density:
5.669 x 10-8 x Surface area x (Temperature of the plate)^4 = 126
4. The surface area of the plate can be calculated using the equation:
Surface area = Absorbed power / (Stefan-Boltzmann constant x (Temperature of the plate)^4)
Surface area = 126 / (5.669 x 10-8 x (Temperature of the plate)^4)
5. Substituting the value of surface area in equation 3:
5.669 x 10-8 x (Temperature of the plate)^4 = 126 / (5.669 x 10-8 x (Temperature of the plate)^4)
6. Simplifying the equation:
(Temperature of the plate)^4 = 126 / (5.669 x 10-8)
(Temperature of the plate)^4 = 2.215 x 109
7. Taking the fourth root of both sides:
Temperature of the plate = (2.215 x 109)1/4
8. Evaluating the result:
Temperature of the plate ≈ 218.33°C
Conclusion:
The radiation equilibrium temperature of the cast iron plate, when exposed to a solar flux of 600 W/m2 at an ambient temperature of 25°C, is approximately 218.33°C.
- Solar flux (radiation intensity) = 600 W/m2
- Ambient temperature = 25°C
- Absorptivity of cast iron = 0.21
- Stefan-Boltzmann constant = 5.669 x 10-8 W/m2-K4
Calculating the radiation equilibrium temperature:
1. The solar flux is absorbed by the plate, so the absorbed power per unit area can be calculated using the equation:
Absorbed power density = Solar flux x Absorptivity
Absorbed power density = 600 x 0.21 = 126 W/m2
2. The rate of radiation heat transfer from the plate can be calculated using the Stefan-Boltzmann law:
Radiation heat transfer rate = Stefan-Boltzmann constant x Surface area x (Temperature of the plate)^4
Radiation heat transfer rate = 5.669 x 10-8 x Surface area x (Temperature of the plate)^4
3. At radiation equilibrium, the rate of radiation heat transfer from the plate is equal to the absorbed power density:
5.669 x 10-8 x Surface area x (Temperature of the plate)^4 = 126
4. The surface area of the plate can be calculated using the equation:
Surface area = Absorbed power / (Stefan-Boltzmann constant x (Temperature of the plate)^4)
Surface area = 126 / (5.669 x 10-8 x (Temperature of the plate)^4)
5. Substituting the value of surface area in equation 3:
5.669 x 10-8 x (Temperature of the plate)^4 = 126 / (5.669 x 10-8 x (Temperature of the plate)^4)
6. Simplifying the equation:
(Temperature of the plate)^4 = 126 / (5.669 x 10-8)
(Temperature of the plate)^4 = 2.215 x 109
7. Taking the fourth root of both sides:
Temperature of the plate = (2.215 x 109)1/4
8. Evaluating the result:
Temperature of the plate ≈ 218.33°C
Conclusion:
The radiation equilibrium temperature of the cast iron plate, when exposed to a solar flux of 600 W/m2 at an ambient temperature of 25°C, is approximately 218.33°C.
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A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.Neglect all other modes of heat transfer except radiation.Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).Correct answer is '218.33'. Can you explain this answer?
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A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.Neglect all other modes of heat transfer except radiation.Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).Correct answer is '218.33'. 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 flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.Neglect all other modes of heat transfer except radiation.Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).Correct answer is '218.33'. 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 flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.Neglect all other modes of heat transfer except radiation.Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).Correct answer is '218.33'. Can you explain this answer?.
A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.Neglect all other modes of heat transfer except radiation.Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).Correct answer is '218.33'. 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 flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.Neglect all other modes of heat transfer except radiation.Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).Correct answer is '218.33'. 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 flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 250C. Assume that the entire solar flux is absorbed by the plate.Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 x10-8 W/m2 -K4.Neglect all other modes of heat transfer except radiation.Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ 0C (round off to the nearest integer).Correct answer is '218.33'. Can you explain this answer?.
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