One end of a steel rod (K=46 J/m-s-°C.) of length of 1.0m

One end of a steel rod $\left(\mathrm{K}=46 \mathrm{~J} / \mathrm{m}-\mathrm{s}-{ }^{\circ} \mathrm{C}\right.$. $)$ of length of $1.0 \mathrm{~m}$ is kept in ice at $0^{\circ} \mathrm{C}$ and the other end is kept in boiling water at $100^{\circ} \mathrm{C}$ The area of cross - section of the rod is $0.04 \mathrm{~cm}^{2}$. Assuming no heat loss to the atmosphere, find the mass of the ice melting per second. Latent heat of fusion of ice $=3.36 \times 10^{6} \mathrm{~J} / \mathrm{kg}$.