Chapter 4, Problem 67P

A 30-cm-diameter, 4-m-high cylindrical column of a house made of concrete $(k=0.79\text{ W/m}\text{.K, and }\alpha \text{ = 5}\text{.94 }\times {\text{ 10}}^{\text{-7}}{\text{ m}}^{\text{2}}{\text{/s, p = 1600 kg/m}}^{\text{3}}{\text{, and c}}_{\text{p}}\text{ = 0}\text{.84 kJ/kg}\text{.K)}$ and cooled to 14°C during a cold night is heated again during the day by being exposed to ambient air at an average temperature of 28°C with an average heat transfer coefficient of 14 W/m² K. Using the analytical one-term approximation method, determine (a) how long it will take for the column surface temperature to rise to 27°C, (b) the amount of heat transfer until the center temperature reaches to 28°C, and (c) the amount of heat transfer until the surface temperature reaches 27°C.