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A copper pipe carrying refrigerant at – 200 C is covered by cylindrical insulation of thermal conductivity 0.5 W/m K. The surface heat transfer coefficient over the insulation is 50 W/m2 K. The critical thickness ofthe insulation would be: 
  • a)
    0.01 m
  • b)
    0.02 m
  • c)
    0.1 m
  • d)
    0.15 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A copper pipe carrying refrigerant at – 200 C is covered by cyli...
Ans. (a) Critical radius of insulation ( rc) =
= 0.5m = 0.01m
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Most Upvoted Answer
A copper pipe carrying refrigerant at – 200 C is covered by cyli...
Given data:
Temperature of refrigerant, T1 = 200°C
Thermal conductivity of insulation, k = 0.5 W/m K
Surface heat transfer coefficient, h = 50 W/m² K

Critical thickness of insulation:

The critical thickness of insulation is the thickness at which the rate of heat transfer through the insulation is minimum. Beyond this thickness, the rate of heat transfer increases.

Heat transfer through insulation:

The rate of heat transfer through the insulation can be calculated using the formula:

Q/A = (T1 - T2)/ (1/h + t/k)

Where,
Q/A = Heat transfer rate per unit area
T1 = Temperature of refrigerant
T2 = Temperature of outer surface of insulation
h = Surface heat transfer coefficient
t = Thickness of insulation
k = Thermal conductivity of insulation

To find the critical thickness, we need to minimize the heat transfer rate per unit area with respect to thickness (t). This can be done by differentiating the above equation with respect to t and equating it to zero.

d(Q/A)/dt = 0

Solving the above equation, we get:

t = (2k/h) = 0.01 m

Therefore, the critical thickness of insulation is 0.01 m (Option A).
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A copper pipe carrying refrigerant at – 200 C is covered by cylindrical insulation of thermal conductivity 0.5 W/m K. The surface heat transfer coefficient over the insulation is 50 W/m2 K. The critical thickness ofthe insulation would be:a)0.01 mb)0.02 mc)0.1 md)0.15 mCorrect answer is option 'A'. Can you explain this answer?
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