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An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate $\dot{Q}_{1}$ to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes $\dot{Q}_{2}$. The ratio $\dot{Q}_{2}/\dot{Q_{1}}$ is

  1. $\sqrt{2}$
  2. $2$
  3. $\frac{1}{\sqrt{2}}$
  4. $\frac{1}{2}$
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