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A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient is
Nu = 0.13 (Gr Pr) 1/3
Nu = 0.13 (Gr Pr) 1/3
- a)143 MW
- b)153 MW
- c)163 MW
- d)173 MV
Correct answer is option 'B'. Can you explain this answer?
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A nuclear reactor with its core constructed of parallel vertical plate...
Q = 2 h A d t = 153 MW.
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A nuclear reactor with its core constructed of parallel vertical plate...
Calculating Maximum Heat Dissipation from a Nuclear Reactor
Given parameters:
- Height of the vertical plates = 2.25 m
- Width of the vertical plates = 1.5 m
- Maximum surface temperature of the plate = 975°C
- Lowest allowable temperature of bismuth = 325°C
- Correlation for convection coefficient = Nu = 0.13 (Gr Pr)1/3
To estimate the maximum possible heat dissipation from both sides of each plate, we need to follow the below steps:
1. Calculate the average temperature of the plate:
The average temperature of the plate can be calculated using the formula:
Avg. Temperature = (Max. Temperature + Min. Temperature) / 2
= (975°C + 325°C) / 2
= 650°C
2. Calculate the Grashof number:
The Grashof number can be calculated using the formula:
Gr = gβΔT L3 / ν2
where g = acceleration due to gravity = 9.81 m/s2
β = coefficient of thermal expansion of bismuth = 1.24 x 10-4 K-1
ΔT = temperature difference = 650°C - 325°C = 325°C
L = height of the vertical plate = 2.25 m
ν = kinematic viscosity of bismuth = 2.9 x 10-7 m2/s
Substituting the values in the formula, we get:
Gr = 9.81 x 1.24 x 10-4 x 325 x (2.25)3 / (2.9 x 10-7)2
= 1.53 x 1013
3. Calculate the Prandtl number:
The Prandtl number can be calculated using the formula:
Pr = ν / α
where α = thermal diffusivity of bismuth = 1.22 x 10-5 m2/s
Substituting the values in the formula, we get:
Pr = 2.9 x 10-7 / 1.22 x 10-5
= 0.0238
4. Calculate the Nusselt number:
The Nusselt number can be calculated using the correlation given:
Nu = 0.13 (Gr Pr)1/3
Substituting the values in the correlation, we get:
Nu = 0.13 (1.53 x 1013 x 0.0238)1/3
= 1,082.8
5. Calculate the heat transfer coefficient:
The heat transfer coefficient can be calculated using the formula:
h = k Nu / L
where k = thermal conductivity of bismuth = 15.8 W/mK
Substituting the values in the formula, we get:
h = 15.8 x 1,082.8 / 2.25
= 7,593.2 W/m2K
6. Calculate the maximum heat dissipation:
The maximum heat dissipation can be calculated using the formula:
Qmax = h A (Max. Temperature - Avg. Temperature)
where A = surface area of the plate = height x width = 2.25 x 1.5 = 3.375 m2
Substituting the values in the formula, we get:
Qmax
Given parameters:
- Height of the vertical plates = 2.25 m
- Width of the vertical plates = 1.5 m
- Maximum surface temperature of the plate = 975°C
- Lowest allowable temperature of bismuth = 325°C
- Correlation for convection coefficient = Nu = 0.13 (Gr Pr)1/3
To estimate the maximum possible heat dissipation from both sides of each plate, we need to follow the below steps:
1. Calculate the average temperature of the plate:
The average temperature of the plate can be calculated using the formula:
Avg. Temperature = (Max. Temperature + Min. Temperature) / 2
= (975°C + 325°C) / 2
= 650°C
2. Calculate the Grashof number:
The Grashof number can be calculated using the formula:
Gr = gβΔT L3 / ν2
where g = acceleration due to gravity = 9.81 m/s2
β = coefficient of thermal expansion of bismuth = 1.24 x 10-4 K-1
ΔT = temperature difference = 650°C - 325°C = 325°C
L = height of the vertical plate = 2.25 m
ν = kinematic viscosity of bismuth = 2.9 x 10-7 m2/s
Substituting the values in the formula, we get:
Gr = 9.81 x 1.24 x 10-4 x 325 x (2.25)3 / (2.9 x 10-7)2
= 1.53 x 1013
3. Calculate the Prandtl number:
The Prandtl number can be calculated using the formula:
Pr = ν / α
where α = thermal diffusivity of bismuth = 1.22 x 10-5 m2/s
Substituting the values in the formula, we get:
Pr = 2.9 x 10-7 / 1.22 x 10-5
= 0.0238
4. Calculate the Nusselt number:
The Nusselt number can be calculated using the correlation given:
Nu = 0.13 (Gr Pr)1/3
Substituting the values in the correlation, we get:
Nu = 0.13 (1.53 x 1013 x 0.0238)1/3
= 1,082.8
5. Calculate the heat transfer coefficient:
The heat transfer coefficient can be calculated using the formula:
h = k Nu / L
where k = thermal conductivity of bismuth = 15.8 W/mK
Substituting the values in the formula, we get:
h = 15.8 x 1,082.8 / 2.25
= 7,593.2 W/m2K
6. Calculate the maximum heat dissipation:
The maximum heat dissipation can be calculated using the formula:
Qmax = h A (Max. Temperature - Avg. Temperature)
where A = surface area of the plate = height x width = 2.25 x 1.5 = 3.375 m2
Substituting the values in the formula, we get:
Qmax
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A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer?
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A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer?.
A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Chemical Engineering.
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ample number of questions to practice A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 m wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 degree Celsius and the lowest allowable temperature of bismuth is 325 degree Celsius. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient isNu = 0.13 (Gr Pr)1/3a)143 MWb)153 MWc)163 MWd)173 MVCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Chemical Engineering tests.
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