Project ForgeHeat is generated at a steady rate of 100 W due to resistance heating in a long wire (length=5 m, diameter=2 mm). This wire is wrapped with an insulation of thickness 1 mm that has a thermal conductivity of 0.1 W/m.K. The insulated wire is exposed to air at 30°C. The convective heat transfer between the wire and surrounding air is characterized by a heat transfer coefficient of 10 W/m².K. The temperature (in °C) at the interface between the wire and the insulation is
- 211.2
- B242.1
- C311.2
- D484.2
Explanation
Per unit length, q'=100/5=20 W/m. R'cond=ln(r2/r1)/(2πk)=ln(2/1)/(2π×0.1)=1.103 m·K/W. R'conv=1/(h·2πr2)=1/(10×2π×0.002)=7.958 m·K/W. Total ΔT=q'(R'cond+R'conv)=20×9.061=181.2°C. Interface temperature=Tair+ΔT=30+181.2=211.2°C.
Source: GATE CH 2012 (2012)
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