A 30-cm-diameter, 4-m-high cylindrical column of a house made of concrete (k = 0.79 W/m·K, α = 5.94 × 107 m2/s, ρ = 1600 kg/m3, and cp = 0.84 kJ/kg·K) 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 analytical one-term approximation method (not the Heisler charts), 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 to 27°C.
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