Chapter 4, Problem 82P

A 9-cm-diameter potato $(p=1100{\text{ kg/m}}^{\text{3}}\text{, cp = 3900 J/kg}\text{.K, k = 0}\text{.6 W/m}\text{.K, }\alpha \text{ = 1}\text{.4 }\times {\text{ 10}}^{\text{-7}}{\text{ m}}^{\text{2}}\text{/s)}$ and that is initially at a uniform temperature of 25°C is baked in an oven at 170°C until a temperature sensor inserted into the center of the potato indicates a reading of 70°C. The potato is then taken out of the oven and wrapped in thick towels so that almost no heat is lost from the baked potato. Assuming the heat transfer coefficient in the oven to be 40 W/m² K, determine (a) how long the potato is baked in the oven and (b) the final equilibrium temperature of the potato after it is wrapped. Solve this problem using the analytical one-term approximation method.