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Question

In order to reduce heat loss, a steam line with a tube diameter of 1.0 cm is insulated with a material having thermal conductivity of 0.108 W/mK. Heat is dissipated from the outer surface of the insulating material by natural convection with a heat transfer coefficient of 12 W/m2K into the ambient at a constant temperature. The heat loss becomes maximum when the critical diameter is

A
18 mm
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B
4 mm
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C
2 mm
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D
9 mm
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Solution

The correct option is A 18 mm

d1=1cm

r1=0.5cm=5mm

ho = 12 W/m2K

(k)insu = 0.108 W/mK

For maximum heat transfer,

Critical radius =rc=r2=kinsuh0=0.10812=9×103m

r2=9mm

Critical diameter = 2 × 9 = 18 mm


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