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Heat is conducted through a uniformly tapered rod of square cross-section and length 50 cm. At the left end, the side of face is 3 cm and the temperature is 600°C. At the right end, the corresponding values are 8 cm and 150°C. Determine the rate of heat conduction. It may be presumed that thermal conductivity of the material of rod is 60 W/mK and heat is conducted only along the length of rod.
- a)129
- b)130
Correct answer is between '129,130'. Can you explain this answer?
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Heat is conducted through a uniformly tapered rod of square cross-sec...
For one-dimensional heat conduction in the x-direction, we have
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Where Ax is the cross-sectional area at a distance x from the smaller end of the rod.
Side of face at distance x meter from the small end
From the fourier heat conduction equation
Separating the variables and upon integration
The boundary conditions are:
At x = 0, T = T1 = 600°C
At x = ? = 0.5 m, T = T2 = 150°C
∴ Heat flow,
Most Upvoted Answer
Heat is conducted through a uniformly tapered rod of square cross-sec...
To determine the rate of heat conduction, we can use Fourier's law of heat conduction, which states that the rate of heat conduction is directly proportional to the thermal conductivity, the cross-sectional area, and the temperature gradient across the rod.
The formula for heat conduction can be written as:
Q = k * A * ΔT / L
Where:
Q = rate of heat conduction
k = thermal conductivity of the material (given as 60 W/mK)
A = cross-sectional area of the rod
ΔT = temperature difference across the rod
L = length of the rod
Let's calculate the cross-sectional area at both ends of the rod:
- At the left end: side of the face = 3 cm
Area = side^2 = (3 cm)^2 = 9 cm^2 = 0.0009 m^2
- At the right end: side of the face = 8 cm
Area = side^2 = (8 cm)^2 = 64 cm^2 = 0.0064 m^2
Next, let's calculate the temperature difference across the rod:
ΔT = T2 - T1
ΔT = 150°C - 600°C = -450°C
Now, we can substitute the values into the formula to calculate the rate of heat conduction:
Q = 60 W/mK * (0.0009 m^2 - 0.0064 m^2) * (-450°C) / 0.5 m
Simplifying the equation:
Q = -60 W/mK * 0.0055 m^2 * 450°C / 0.5 m
Q = -60 W/mK * 0.0055 m^2 * 450°C / 0.5 m
Q = -60 W/mK * 0.0055 m * 450°C / 0.5
Q = -60 W/mK * 0.002475 W/K
Q ≈ -0.1485 W
Since the rate of heat conduction cannot be negative, we take the absolute value of the result:
Q ≈ 0.1485 W
Therefore, the rate of heat conduction is approximately 0.1485 W, which is between 129 and 130 as given in the options.
The formula for heat conduction can be written as:
Q = k * A * ΔT / L
Where:
Q = rate of heat conduction
k = thermal conductivity of the material (given as 60 W/mK)
A = cross-sectional area of the rod
ΔT = temperature difference across the rod
L = length of the rod
Let's calculate the cross-sectional area at both ends of the rod:
- At the left end: side of the face = 3 cm
Area = side^2 = (3 cm)^2 = 9 cm^2 = 0.0009 m^2
- At the right end: side of the face = 8 cm
Area = side^2 = (8 cm)^2 = 64 cm^2 = 0.0064 m^2
Next, let's calculate the temperature difference across the rod:
ΔT = T2 - T1
ΔT = 150°C - 600°C = -450°C
Now, we can substitute the values into the formula to calculate the rate of heat conduction:
Q = 60 W/mK * (0.0009 m^2 - 0.0064 m^2) * (-450°C) / 0.5 m
Simplifying the equation:
Q = -60 W/mK * 0.0055 m^2 * 450°C / 0.5 m
Q = -60 W/mK * 0.0055 m^2 * 450°C / 0.5 m
Q = -60 W/mK * 0.0055 m * 450°C / 0.5
Q = -60 W/mK * 0.002475 W/K
Q ≈ -0.1485 W
Since the rate of heat conduction cannot be negative, we take the absolute value of the result:
Q ≈ 0.1485 W
Therefore, the rate of heat conduction is approximately 0.1485 W, which is between 129 and 130 as given in the options.
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Heat is conducted through a uniformly tapered rod of square cross-section and length 50 cm. At the left end, the side of face is 3 cm and the temperature is 600°C. At the right end, the corresponding values are 8 cm and 150°C. Determine the rate of heat conduction. It may be presumed that thermal conductivity of the material of rod is 60 W/mK and heat is conducted only along the length of rod.a)129b)130Correct answer is between '129,130'. Can you explain this answer?
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Heat is conducted through a uniformly tapered rod of square cross-section and length 50 cm. At the left end, the side of face is 3 cm and the temperature is 600°C. At the right end, the corresponding values are 8 cm and 150°C. Determine the rate of heat conduction. It may be presumed that thermal conductivity of the material of rod is 60 W/mK and heat is conducted only along the length of rod.a)129b)130Correct answer is between '129,130'. 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 Heat is conducted through a uniformly tapered rod of square cross-section and length 50 cm. At the left end, the side of face is 3 cm and the temperature is 600°C. At the right end, the corresponding values are 8 cm and 150°C. Determine the rate of heat conduction. It may be presumed that thermal conductivity of the material of rod is 60 W/mK and heat is conducted only along the length of rod.a)129b)130Correct answer is between '129,130'. 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 Heat is conducted through a uniformly tapered rod of square cross-section and length 50 cm. At the left end, the side of face is 3 cm and the temperature is 600°C. At the right end, the corresponding values are 8 cm and 150°C. Determine the rate of heat conduction. It may be presumed that thermal conductivity of the material of rod is 60 W/mK and heat is conducted only along the length of rod.a)129b)130Correct answer is between '129,130'. Can you explain this answer?.
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