Question

A plastic sleeve of outer radius $r_o=1mm$ covers a wire (radius r = 0.5 mm) carrying electric current, thermal conductivity of the plastic is 0.15 W/mK. The heat transfer coefficient on the outer surface of the sleeve exposed to air is $25W/m^{2}K$. Due to the addition of the plastic cover, the heat transfer from the wire to the ambient will

• A. Increase
• B. Remain the same
• C. Decrease
• D. be zero

Answer 1

The correct option is A Increase

Given data:
$r_o=1mm$
inner radius: $r_i=0.5mm$
$k=0.15W/mK$
$h_o=25W/m^{2}K$
Critical radius,
$r_c=\frac{k}{h_o}=\frac{0.15}{25}$
$=6\times {10}^{-3}m=6mm$
As $r_o<r_c$, due to addition of plastic cover heat transfer will increase till $r_o=r_c$ beyond that heat transfer will decrease.