Chapter 4, Problem 112P

A 2-cm-high cylindrical ice block $(k=22\text{W/m}\text{.K},\alpha =0.124\times {\text{ 10}}^{\text{-7}}{\text{m}}^{\text{2}}\text{/s)}$ and is placed on a table on its base of diameter 2 cm in a room at 24°C. The heat transfer coefficient on the exposed surfaces of the ice block is 13 W/m² K, 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. Solve this problem using the analytical onet erm approximation method.