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An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C is
- a)40
- b)60
- c)75.7
- d)85.7
Correct answer is option 'D'. Can you explain this answer?
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°C and the outer surface of iron is kept at 50°C. The thermal conductivity of aluminium is 237 W/m°C and the thermal conductivity of iron is 80 W/m°C. Calculate the heat transfer per unit area and the temperature at the interface between the two sheets.
To calculate the heat transfer per unit area, we can use the formula:
Q/A = (T2 - T1) / (R1 + R2)
Where:
Q/A is the heat transfer per unit area
T2 is the temperature of the outer surface of the aluminium sheet (100°C)
T1 is the temperature of the outer surface of the iron sheet (50°C)
R1 is the thermal resistance of the aluminium sheet
R2 is the thermal resistance of the iron sheet
To calculate the thermal resistance of each sheet, we can use the formula:
R = L / (k * A)
Where:
R is the thermal resistance
L is the thickness of the sheet
k is the thermal conductivity of the sheet
A is the cross-sectional area of the sheet
For the aluminium sheet:
L = 10 mm = 0.01 m
k = 237 W/m°C
A = 1 m² (assuming the sheets are 1 m² in area)
R1 = 0.01 / (237 * 1) = 0.000042194 m²°C/W
For the iron sheet:
L = 20 mm = 0.02 m
k = 80 W/m°C
A = 1 m²
R2 = 0.02 / (80 * 1) = 0.00025 m²°C/W
Now we can calculate the heat transfer per unit area:
Q/A = (100 - 50) / (0.000042194 + 0.00025) = 240,000 W/m²
Therefore, the heat transfer per unit area is 240,000 W/m².
To calculate the temperature at the interface between the two sheets, we can use the formula:
T_interface = T2 - ((Q/A) * R2)
T_interface = 100 - (240,000 * 0.00025) = 100 - 60 = 40°C
Therefore, the temperature at the interface between the two sheets is 40°C.
To calculate the heat transfer per unit area, we can use the formula:
Q/A = (T2 - T1) / (R1 + R2)
Where:
Q/A is the heat transfer per unit area
T2 is the temperature of the outer surface of the aluminium sheet (100°C)
T1 is the temperature of the outer surface of the iron sheet (50°C)
R1 is the thermal resistance of the aluminium sheet
R2 is the thermal resistance of the iron sheet
To calculate the thermal resistance of each sheet, we can use the formula:
R = L / (k * A)
Where:
R is the thermal resistance
L is the thickness of the sheet
k is the thermal conductivity of the sheet
A is the cross-sectional area of the sheet
For the aluminium sheet:
L = 10 mm = 0.01 m
k = 237 W/m°C
A = 1 m² (assuming the sheets are 1 m² in area)
R1 = 0.01 / (237 * 1) = 0.000042194 m²°C/W
For the iron sheet:
L = 20 mm = 0.02 m
k = 80 W/m°C
A = 1 m²
R2 = 0.02 / (80 * 1) = 0.00025 m²°C/W
Now we can calculate the heat transfer per unit area:
Q/A = (100 - 50) / (0.000042194 + 0.00025) = 240,000 W/m²
Therefore, the heat transfer per unit area is 240,000 W/m².
To calculate the temperature at the interface between the two sheets, we can use the formula:
T_interface = T2 - ((Q/A) * R2)
T_interface = 100 - (240,000 * 0.00025) = 100 - 60 = 40°C
Therefore, the temperature at the interface between the two sheets is 40°C.
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An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C isa)40b)60c)75.7d)85.7Correct answer is option 'D'. Can you explain this answer?
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An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C isa)40b)60c)75.7d)85.7Correct answer is option 'D'. 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 An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C isa)40b)60c)75.7d)85.7Correct answer is option 'D'. 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 An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C isa)40b)60c)75.7d)85.7Correct answer is option 'D'. Can you explain this answer?.
An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C isa)40b)60c)75.7d)85.7Correct answer is option 'D'. 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 An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C isa)40b)60c)75.7d)85.7Correct answer is option 'D'. 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 An aluminium sheet of 10 mm thickness is brought into contact with an iron sheet of 20 mm thickness. The outer surface of aluminium is kept at 100°C. Where as the outer surface of iron is maintained at 0°C. if the ratio of thermal conductivity of aluminium and iron is 3 : 1, then the interface temperature in °C isa)40b)60c)75.7d)85.7Correct answer is option 'D'. Can you explain this answer?.
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