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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod?
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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wal...
To calculate the heat lost by the aluminum rod due to convection, we can utilize Newton's Law of Cooling. Here’s a detailed breakdown of the process:
Step 1: Determine the Surface Area of the Rod
- The formula for the surface area \( A \) of a cylindrical rod is given by:
\[
A = \pi d L
\]
- Where:
\( d \) = diameter of the rod = 2.0 cm = 0.02 m
\( L \) = length of the rod = 12 cm = 0.12 m
- Substituting the values:
\[
A = \pi \times 0.02 \, \text{m} \times 0.12 \, \text{m} \approx 0.00754 \, \text{m}^2
\]
Step 2: Calculate the Temperature Difference
- The temperature difference \( \Delta T \) between the rod and the environment is:
\[
\Delta T = T_{\text{rod}} - T_{\text{ambient}} = 250°C - 15°C = 235°C
\]
Step 3: Calculate the Heat Transfer Rate
- The heat transfer rate \( Q \) can be calculated using the formula:
\[
Q = hA\Delta T
\]
- Where:
\( h \) = convection heat-transfer coefficient = 12 W/m²·°C
- Substituting the values:
\[
Q = 12 \, \text{W/m}^2\cdot°C \times 0.00754 \, \text{m}^2 \times 235°C \approx 21.16 \, \text{W}
\]
Conclusion
- The heat lost by the aluminum rod is approximately 21.16 Watts. This calculation illustrates how convection affects heat loss in materials with significant temperature differences.
Step 1: Determine the Surface Area of the Rod
- The formula for the surface area \( A \) of a cylindrical rod is given by:
\[
A = \pi d L
\]
- Where:
\( d \) = diameter of the rod = 2.0 cm = 0.02 m
\( L \) = length of the rod = 12 cm = 0.12 m
- Substituting the values:
\[
A = \pi \times 0.02 \, \text{m} \times 0.12 \, \text{m} \approx 0.00754 \, \text{m}^2
\]
Step 2: Calculate the Temperature Difference
- The temperature difference \( \Delta T \) between the rod and the environment is:
\[
\Delta T = T_{\text{rod}} - T_{\text{ambient}} = 250°C - 15°C = 235°C
\]
Step 3: Calculate the Heat Transfer Rate
- The heat transfer rate \( Q \) can be calculated using the formula:
\[
Q = hA\Delta T
\]
- Where:
\( h \) = convection heat-transfer coefficient = 12 W/m²·°C
- Substituting the values:
\[
Q = 12 \, \text{W/m}^2\cdot°C \times 0.00754 \, \text{m}^2 \times 235°C \approx 21.16 \, \text{W}
\]
Conclusion
- The heat lost by the aluminum rod is approximately 21.16 Watts. This calculation illustrates how convection affects heat loss in materials with significant temperature differences.
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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod?
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An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod?.
An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An aluminum rod 2.0 cm in diameter and 12 cm long protrudes from a wall that is maintained at 250°C. The rod is exposed to an environment at 15°C. The convection heat-transfer coefficient is the rod 12~W/m^{2}\cdot\cdot\cdot C Calculate the heat lost by rod?.
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