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It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:
- a)0.25 mm
- b)0.5 mm
- c)1 mm
- d)2 mm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1...
Ans. (b) Critical radius of insulation (rc) =
= 1mm∴ Critical thickness of enamel point = 
= 0.5 mm
= 0.5 mmMost Upvoted Answer
It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1...
No, not A. Here critical radius = k/h = 1 mm. Thickness will be 1- wire radius. i.e. 1- .5= .5 mm
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It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1...
Problem Statement
We need to determine the optimum thickness of enamel paint required to increase heat transfer with air for a 1 mm diameter wire. Given data:
- Diameter of wire: 1 mm
- Thermal conductivity of enamel paint: k = 0.1 W/mK
- Air side heat transfer coefficient: h = 100 W/m2K
Solution
To find the optimum thickness of enamel paint, we need to consider the resistance to heat transfer on both sides of the wire: the resistance of the enamel paint and the resistance of the air.
Resistance of the enamel paint (R1)
The resistance of the enamel paint can be calculated using the formula:
R1 = (ln(r2/r1))/(2πkL)
Where:
- r1 = radius of the wire (1 mm/2 = 0.5 mm = 0.0005 m)
- r2 = radius of the wire with enamel paint (r1 + thickness of enamel paint)
- k = thermal conductivity of enamel paint (0.1 W/mK)
- L = length of the wire (assumed to be 1 m)
Using the given data, we can calculate the resistance of the enamel paint.
Resistance of the air (R2)
The resistance of the air can be calculated using the formula:
R2 = 1/(hA)
Where:
- h = heat transfer coefficient of air (100 W/m2K)
- A = surface area of the wire (2πr2L)
Using the given data, we can calculate the resistance of the air.
Total resistance (Rtotal)
The total resistance to heat transfer is given by:
Rtotal = R1 + R2
Optimum thickness of enamel paint
To find the optimum thickness of enamel paint, we need to minimize the total resistance. Therefore, we can differentiate the total resistance with respect to the thickness of the enamel paint and set it equal to zero.
dRtotal/d(thickness of enamel paint) = 0
Solving this equation will give us the optimum thickness of enamel paint.
Calculations and Results
Performing the calculations using the given data, we find that the optimum thickness of enamel paint is 0.5 mm.
Therefore, the correct answer is option B (0.5 mm).
We need to determine the optimum thickness of enamel paint required to increase heat transfer with air for a 1 mm diameter wire. Given data:
- Diameter of wire: 1 mm
- Thermal conductivity of enamel paint: k = 0.1 W/mK
- Air side heat transfer coefficient: h = 100 W/m2K
Solution
To find the optimum thickness of enamel paint, we need to consider the resistance to heat transfer on both sides of the wire: the resistance of the enamel paint and the resistance of the air.
Resistance of the enamel paint (R1)
The resistance of the enamel paint can be calculated using the formula:
R1 = (ln(r2/r1))/(2πkL)
Where:
- r1 = radius of the wire (1 mm/2 = 0.5 mm = 0.0005 m)
- r2 = radius of the wire with enamel paint (r1 + thickness of enamel paint)
- k = thermal conductivity of enamel paint (0.1 W/mK)
- L = length of the wire (assumed to be 1 m)
Using the given data, we can calculate the resistance of the enamel paint.
Resistance of the air (R2)
The resistance of the air can be calculated using the formula:
R2 = 1/(hA)
Where:
- h = heat transfer coefficient of air (100 W/m2K)
- A = surface area of the wire (2πr2L)
Using the given data, we can calculate the resistance of the air.
Total resistance (Rtotal)
The total resistance to heat transfer is given by:
Rtotal = R1 + R2
Optimum thickness of enamel paint
To find the optimum thickness of enamel paint, we need to minimize the total resistance. Therefore, we can differentiate the total resistance with respect to the thickness of the enamel paint and set it equal to zero.
dRtotal/d(thickness of enamel paint) = 0
Solving this equation will give us the optimum thickness of enamel paint.
Calculations and Results
Performing the calculations using the given data, we find that the optimum thickness of enamel paint is 0.5 mm.
Therefore, the correct answer is option B (0.5 mm).
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It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer?.
It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer?.
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It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer with air. If the air side heat transfer coefficient is 100 W/m2K, then optimum thickness of enamel paint should be:a)0.25 mmb)0.5 mmc)1 mmd)2 mmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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