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One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.
- a)115
- b)116
Correct answer is between '115,116'. Can you explain this answer?
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One end of a long rod is inserted into a furnace while the other proj...
The temperature distribution is given by
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At x = 0, ? = ?0, and at x → ∞,? = 0
∴ C2 = 0
? = C1e-mx
Let ? be the distance between the two points where the temperatures are measured. Then,
?1 = ?0e-mx1
ml = 0.427
Most Upvoted Answer
One end of a long rod is inserted into a furnace while the other proj...
Given:
- Temperature at point A: 125°C
- Temperature at point B: 88.5°C
- Ambient temperature: 20°C
- Distance between points A and B: 75 mm
- Diameter of the rod: 25 mm
- Heat transfer coefficient (h): 23.36 W/m^2-K
To Find:
Thermal conductivity of the rod material
Assumptions:
- Steady-state conditions
- One-dimensional heat transfer
- Negligible heat generation within the rod
Solution:
Step 1: Calculate the temperature difference
The temperature difference across the rod can be calculated using the equation:
ΔT = T_A - T_B
ΔT = 125°C - 88.5°C = 36.5°C
Step 2: Calculate the heat transfer rate
The heat transfer rate through the rod can be calculated using the equation:
Q = h * A * ΔT
Where:
- Q is the heat transfer rate
- h is the heat transfer coefficient
- A is the surface area of the rod
- ΔT is the temperature difference
The surface area of the rod can be calculated using the equation:
A = π * d * L
Where:
- A is the surface area
- d is the diameter of the rod
- L is the distance between the two temperature points
Substituting the given values:
A = π * (25 mm)^2 * (75 mm)
A = 58823.53 mm^2
Converting the surface area to m^2:
A = 0.05882353 m^2
Now, substituting the values into the heat transfer rate equation:
Q = 23.36 W/m^2-K * 0.05882353 m^2 * 36.5°C
Q = 48.024 W
Step 3: Calculate the thermal conductivity
The heat transfer rate can also be expressed as:
Q = k * A * ΔT / L
Where:
- k is the thermal conductivity
Rearranging the equation to solve for k:
k = Q * L / (A * ΔT)
Substituting the given values:
k = 48.024 W * 0.075 m / (0.05882353 m^2 * 36.5°C)
k = 115.976 W/m-K
Therefore, the thermal conductivity of the rod material is approximately 116 W/m-K.
- Temperature at point A: 125°C
- Temperature at point B: 88.5°C
- Ambient temperature: 20°C
- Distance between points A and B: 75 mm
- Diameter of the rod: 25 mm
- Heat transfer coefficient (h): 23.36 W/m^2-K
To Find:
Thermal conductivity of the rod material
Assumptions:
- Steady-state conditions
- One-dimensional heat transfer
- Negligible heat generation within the rod
Solution:
Step 1: Calculate the temperature difference
The temperature difference across the rod can be calculated using the equation:
ΔT = T_A - T_B
ΔT = 125°C - 88.5°C = 36.5°C
Step 2: Calculate the heat transfer rate
The heat transfer rate through the rod can be calculated using the equation:
Q = h * A * ΔT
Where:
- Q is the heat transfer rate
- h is the heat transfer coefficient
- A is the surface area of the rod
- ΔT is the temperature difference
The surface area of the rod can be calculated using the equation:
A = π * d * L
Where:
- A is the surface area
- d is the diameter of the rod
- L is the distance between the two temperature points
Substituting the given values:
A = π * (25 mm)^2 * (75 mm)
A = 58823.53 mm^2
Converting the surface area to m^2:
A = 0.05882353 m^2
Now, substituting the values into the heat transfer rate equation:
Q = 23.36 W/m^2-K * 0.05882353 m^2 * 36.5°C
Q = 48.024 W
Step 3: Calculate the thermal conductivity
The heat transfer rate can also be expressed as:
Q = k * A * ΔT / L
Where:
- k is the thermal conductivity
Rearranging the equation to solve for k:
k = Q * L / (A * ΔT)
Substituting the given values:
k = 48.024 W * 0.075 m / (0.05882353 m^2 * 36.5°C)
k = 115.976 W/m-K
Therefore, the thermal conductivity of the rod material is approximately 116 W/m-K.
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One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. Can you explain this answer?
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One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. 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 One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. 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 One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. Can you explain this answer?.
One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. 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 One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. 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 One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. Can you explain this answer?.
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One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. Can you explain this answer?, a detailed solution for One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. Can you explain this answer? has been provided alongside types of One end of a long rod is inserted into a furnace while the other projects into ambient air. Under steady state the temperature of the rod is measured at two points 75 mm apart and found to be 125°C and 88.5°C.respectively, while the ambient temperature is 20°C. If the rod is 25 mm in diameter and h is 23.36 W/m2-K, find the thermal conductivity of the rod material.a)115b)116Correct answer is between '115,116'. Can you explain this answer? theory, EduRev gives you an
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