A 2-cm-high cylindrical ice block ( $k=2.22 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ and $\alpha=0.124 \times 10^{-7} \mathrm{~m}^2 / \mathrm{s}$ ) is placed on a table on its base of diameter 2 cm in a room at $24^{\circ} \mathrm{C}$. The heat transfer coefficient on the exposed surfaces of the ice block is $13 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$, and heat transfer from the base of the ice block to the table is negligible. If the ice block is not to start melting at any point for at least 3 h , determine what the initial temperature of the ice block should be