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An electric cable of aluminium conductor (k = 240 W/mK) is to be insulated with rubber (k = 0.15 W/mK). The cable is to be located in air (h = 6W/m2). The critical thickness of insulation will be:
- a)25mm
- b)40 mm
- c)160 mm
- d)800 mm
Correct answer is option 'A'. Can you explain this answer?
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Solution:
Given data:
Conductivity of aluminium, k1 = 240 W/mK
Conductivity of rubber, k2 = 0.15 W/mK
Heat transfer coefficient of air, h = 6W/m2K
Critical thickness of insulation, x = ?
Formula used:
Heat transfer rate through the insulation,
q = (T1 - T2) / [(1/h) + (x/k2) + (x/k1)]
where,
T1 = temperature of cable
T2 = temperature of air
By assuming T1 = 80°C and T2 = 20°C, the above equation can be written as,
q = (80 - 20) / [(1/6) + (x/0.15) + (x/240)]
q = 60 / [(1/6) + (x/0.15) + (x/240)]
For critical thickness of insulation, q = 0
0 = 60 / [(1/6) + (x/0.15) + (x/240)]
0 = [(1/6) + (x/0.15) + (x/240)]
0 = (1/6) + (x/0.15) + (x/240)
Solving the above equation, we get,
x = 0.025 m or 25 mm
Therefore, the critical thickness of insulation will be 25 mm.
Given data:
Conductivity of aluminium, k1 = 240 W/mK
Conductivity of rubber, k2 = 0.15 W/mK
Heat transfer coefficient of air, h = 6W/m2K
Critical thickness of insulation, x = ?
Formula used:
Heat transfer rate through the insulation,
q = (T1 - T2) / [(1/h) + (x/k2) + (x/k1)]
where,
T1 = temperature of cable
T2 = temperature of air
By assuming T1 = 80°C and T2 = 20°C, the above equation can be written as,
q = (80 - 20) / [(1/6) + (x/0.15) + (x/240)]
q = 60 / [(1/6) + (x/0.15) + (x/240)]
For critical thickness of insulation, q = 0
0 = 60 / [(1/6) + (x/0.15) + (x/240)]
0 = [(1/6) + (x/0.15) + (x/240)]
0 = (1/6) + (x/0.15) + (x/240)
Solving the above equation, we get,
x = 0.025 m or 25 mm
Therefore, the critical thickness of insulation will be 25 mm.
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An electric cable of aluminium conductor (k = 240 W/mK) is to be insulated with rubber (k = 0.15 W/mK). The cable is to be located in air (h = 6W/m2). The critical thickness of insulation will be:a)25mmb)40 mmc)160 mmd)800 mmCorrect answer is option 'A'. Can you explain this answer?
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