GATE 2021 ME (ME1) – Question 53
An uninsulated cylindrical wire of radius 1.0 mm produces electric heating at the rate of 5.0 W/m. The temperature of the surface of the wire is 75°C when placed in air at 25°C. When the wire is coated with PVC of thickness 1.0 mm, the temperature of the surface of the wire reduces to 55°C. Assume that the heat generation rate from the wire and the convective heat transfer coefficient are same for both uninsulated wire and the coated wire. The thermal conductivity of PVC is _____ W/m.K (round off to two decimal places).
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Correct answer: 0.10 to 0.12
Explanation
Bare-wire convection gives resistance per metre $R_{bare}=(75-25)/5=10$ K m/W. Doubling outer radius halves this convection resistance to 5 K m/W.
Coated total resistance is (55−25)/5=6, leaving PVC conduction resistance 1. For a cylinder, $R=\ln(r_2/r_1)/(2\pi k)$, so $k=\ln2/(2\pi)=\mathbf{0.11}$ W/(m K).