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Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.
The location of maximum temperature within the plate from its left face is
The location of maximum temperature within the plate from its left face is
[2013]
- a)15 mm
- b)10 mm
- c)5 mm
- d)0 mm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider steady one-dimensional heat flow in a plate of 20 mm thicknes...
At x = 0, T = 433 K
∴ C2 = 433
At x = 20 × 10–3 m, T = 393 K.
∴ C1 = 200
For maximum temperature,
x = 5 × 10–3 = 5 mm
Most Upvoted Answer
Consider steady one-dimensional heat flow in a plate of 20 mm thicknes...
°C and 40°C, respectively. The thermal conductivity of the plate is 15 W/mK. Find the temperature distribution in the plate.
Solution:
We can use the steady-state heat conduction equation in one dimension:
q = -kA(dT/dx)
where q is the heat flux (W/m2), k is the thermal conductivity (W/mK), A is the cross-sectional area (m2), and dT/dx is the temperature gradient (°C/m).
Assuming the plate has a width of 1 m, the heat generation rate per unit area can be calculated as:
Q'' = q''/A = 80 MW/m3 = 80,000 W/m3
The heat flux through the plate is constant and can be calculated as:
q = (160 - 40) / 0.02 = 6,000 W/m2
Using the above values and the given thermal conductivity, the temperature gradient can be calculated as:
dT/dx = -q / (kA) = -6000 / (15 x 1) = -400 °C/m
Integrating this temperature gradient equation with respect to x, we get:
T(x) = -400x + C1
where C1 is the constant of integration. To determine this constant, we use the boundary conditions:
At x=0, T=160°C
At x=0.02 m (thickness of the plate), T=40°C
Solving for C1, we get:
C1 = 160°C + 400 x 0 = 160°C
Therefore, the temperature distribution in the plate is given by:
T(x) = -400x + 160°C
This equation shows that the temperature decreases linearly from 160°C at the left face to 40°C at the right face, as expected.
Solution:
We can use the steady-state heat conduction equation in one dimension:
q = -kA(dT/dx)
where q is the heat flux (W/m2), k is the thermal conductivity (W/mK), A is the cross-sectional area (m2), and dT/dx is the temperature gradient (°C/m).
Assuming the plate has a width of 1 m, the heat generation rate per unit area can be calculated as:
Q'' = q''/A = 80 MW/m3 = 80,000 W/m3
The heat flux through the plate is constant and can be calculated as:
q = (160 - 40) / 0.02 = 6,000 W/m2
Using the above values and the given thermal conductivity, the temperature gradient can be calculated as:
dT/dx = -q / (kA) = -6000 / (15 x 1) = -400 °C/m
Integrating this temperature gradient equation with respect to x, we get:
T(x) = -400x + C1
where C1 is the constant of integration. To determine this constant, we use the boundary conditions:
At x=0, T=160°C
At x=0.02 m (thickness of the plate), T=40°C
Solving for C1, we get:
C1 = 160°C + 400 x 0 = 160°C
Therefore, the temperature distribution in the plate is given by:
T(x) = -400x + 160°C
This equation shows that the temperature decreases linearly from 160°C at the left face to 40°C at the right face, as expected.
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Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.The location of maximum temperature within the plate from its left face is[2013]a)15 mmb)10 mmc)5 mmd)0 mmCorrect answer is option 'C'. Can you explain this answer?
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Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.The location of maximum temperature within the plate from its left face is[2013]a)15 mmb)10 mmc)5 mmd)0 mmCorrect answer is option 'C'. 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 Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.The location of maximum temperature within the plate from its left face is[2013]a)15 mmb)10 mmc)5 mmd)0 mmCorrect answer is option 'C'. 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 Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.The location of maximum temperature within the plate from its left face is[2013]a)15 mmb)10 mmc)5 mmd)0 mmCorrect answer is option 'C'. Can you explain this answer?.
Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.The location of maximum temperature within the plate from its left face is[2013]a)15 mmb)10 mmc)5 mmd)0 mmCorrect answer is option 'C'. 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 Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.The location of maximum temperature within the plate from its left face is[2013]a)15 mmb)10 mmc)5 mmd)0 mmCorrect answer is option 'C'. 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 Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. The left and right faces are kept at constant temperatures of 160°C and 120°C respectively. The plate has a constant thermal conductivity of 200 W/mK.The location of maximum temperature within the plate from its left face is[2013]a)15 mmb)10 mmc)5 mmd)0 mmCorrect answer is option 'C'. Can you explain this answer?.
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