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Consider a bare long copper wire of $1$ $\text{mm}$ diameter. Its surface temperature is $T_{s}$ and the ambient temperature is $T_{a}\:(T_{s} > T_{a})$. The wire is to be coated with a $2$ $\text{mm}$ thick insulation. The convective heat transfer coefficient is $20\: W\: m^{-2}\: K^{-1}$. Assume that $T_{s}$ and $T_{a}$ remain unchanged. To reduce heat loss from the wire, the maximum allowed thermal conductivity of the insulating material, in $W\:m^{-1}\:K^{-1}$, rounded off to two decimal places, is

  1. $0.02$
  2. $0.04$
  3. $0.10$
  4. $0.01$
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