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A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.
- a)0.9
- b)0.09
Correct answer is between '0.9,0.09'. Can you explain this answer?
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Understanding the Biot Number
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. It compares the thermal resistance within a body to the thermal resistance at its surface.
Formula for Biot Number
The Biot number is calculated using the formula:
Bi = hL/k
Where:
- h = heat transfer coefficient (W/m²-K)
- L = characteristic length (m)
- k = thermal conductivity (W/m-K)
Given Data
- Diameter of the cylindrical body = 30 cm = 0.3 m
- Length of the cylindrical body = 170 cm = 1.7 m
- Heat transfer coefficient (h) = 8 W/m²-K
- Thermal conductivity (k) = 6.08 W/m-K
Characteristic Length Calculation
For a cylinder, the characteristic length (L) is typically taken as the radius (r).
- Radius (r) = Diameter/2 = 0.3 m / 2 = 0.15 m
Calculating the Biot Number
Now substituting the values into the Biot number formula:
Bi = hL/k
Bi = (8 W/m²-K)(0.15 m) / (6.08 W/m-K)
Bi = 1.2 / 6.08
Bi ≈ 0.197
Conclusion
This calculated Biot number indicates that the heat conduction within the cylinder is much more significant than the heat transfer at the surface, which is consistent with typical expectations for a solid body in a fluid environment.
The correct answer falls between the options a) 0.9 and b) 0.09. However, based on our calculations, the Biot number is approximately 0.197, suggesting it is closer to 0.09.
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. It compares the thermal resistance within a body to the thermal resistance at its surface.
Formula for Biot Number
The Biot number is calculated using the formula:
Bi = hL/k
Where:
- h = heat transfer coefficient (W/m²-K)
- L = characteristic length (m)
- k = thermal conductivity (W/m-K)
Given Data
- Diameter of the cylindrical body = 30 cm = 0.3 m
- Length of the cylindrical body = 170 cm = 1.7 m
- Heat transfer coefficient (h) = 8 W/m²-K
- Thermal conductivity (k) = 6.08 W/m-K
Characteristic Length Calculation
For a cylinder, the characteristic length (L) is typically taken as the radius (r).
- Radius (r) = Diameter/2 = 0.3 m / 2 = 0.15 m
Calculating the Biot Number
Now substituting the values into the Biot number formula:
Bi = hL/k
Bi = (8 W/m²-K)(0.15 m) / (6.08 W/m-K)
Bi = 1.2 / 6.08
Bi ≈ 0.197
Conclusion
This calculated Biot number indicates that the heat conduction within the cylinder is much more significant than the heat transfer at the surface, which is consistent with typical expectations for a solid body in a fluid environment.
The correct answer falls between the options a) 0.9 and b) 0.09. However, based on our calculations, the Biot number is approximately 0.197, suggesting it is closer to 0.09.
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A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.a)0.9b)0.09Correct answer is between '0.9,0.09'. Can you explain this answer?
Question Description
A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.a)0.9b)0.09Correct answer is between '0.9,0.09'. 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 A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.a)0.9b)0.09Correct answer is between '0.9,0.09'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.a)0.9b)0.09Correct answer is between '0.9,0.09'. Can you explain this answer?.
A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.a)0.9b)0.09Correct answer is between '0.9,0.09'. 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 A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.a)0.9b)0.09Correct answer is between '0.9,0.09'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical body of 30 cm diameter, 170 cm long having a uniform temperature of 75 °C and thermal conductivity k is 6.08 W/m-K is placed in a surrounding of 20 °C with a heat transfer coefficient to of 8 W/m2-K. The Biot number is ____________.a)0.9b)0.09Correct answer is between '0.9,0.09'. Can you explain this answer?.
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