A 30-cm-diameter, 4-m-high cylindrical column of a house made of concrete ( $k=0.79 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}, \alpha=5.94 \times$ $10^{-7} \mathrm{~m}^2 / \mathrm{s}, \rho=1600 \mathrm{~kg} / \mathrm{m}^3$, and $c_p=0.84 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ ) cooled to $14^{\circ} \mathrm{C}$ during a cold night is heated again during the day by being exposed to ambient air at an average temperature of $28^{\circ} \mathrm{C}$ with an average heat transfer coefficient of $14 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$. Determine (a) how long it will take for the column surface temperature to rise to $27^{\circ} \mathrm{C}$, (b) the amount of heat transfer until the center temperature reaches to $28^{\circ} \mathrm{C}$, and (c) the amount of heat transfer until the surface temperature reaches to $27^{\circ} \mathrm{C}$.