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Heat generated at a steady rate of $100\: W$ due to resistance heating in a long wire (length = $5\:\text{m}$, diameter = $2\:\text{mm}$). This wire is wrapped with an insulation of thickness $1\: \text{mm}$ that has a thermal conductivity of $0.1 \text{ W/mK}$. The insulated wire is exposed to air at $30^\circ\: C$. The convective heat transfer between the wire and surrounding air is characterized by a heat transfer coefficient of $10\text{ W/m$^2$.K}$. The temperature (in $^{\circ}C$) at the interface between the wire and the insulation is

  1. $211.2$
  2. $242.1$
  3. $311.2$
  4. $484.2$
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