Consider the water of Example 1.5 to be initially liquid at its fusion temperature. The outer wall surface is suddenly reduced to \(T_{1}=-30^{\circ} \mathrm{C}\), resulting in solidification of the water. In reality, thermal contact resistances develop at the interface between the solid wall and the ice as the solidification progresses. Determine the interfacial thermal resistance, \(R_{t, c}^{\prime \prime}\), shortly after the onset of freezing, given the dimensions in Comment 2. The initial solidification rate is \(0.05 \mathrm{gram} / \mathrm{s}\).

Data From Example 1.5:-

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Consider a mass m of ice at the fusion temperature (T;= 0C) that is enclosed in a cubical container of width W on a side. The container wall is of thickness L and thermal conductiv- ity k. If the outer surface of the wall is heated to a temperature T>T,to melt the ice, obtain an expression for the time needed to melt the entire mass of ice.