White potatoes $\left(k=0.50 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right.$ and $\alpha=0.13 \times$ $10^{-6} \mathrm{~m}^2 / \mathrm{s}$ ) that are initially at a uniform temperature of $25^{\circ} \mathrm{C}$ and have an average diameter of 6 cm are to be cooled by refrigerated air at $2^{\circ} \mathrm{C}$ flowing at a velocity of $4 \mathrm{~m} / \mathrm{s}$. The average heat transfer coefficient between the potatoes and the air is experimentally determined to be $19 \mathrm{~W} / \mathrm{m}^2$. ${ }^{\circ} \mathrm{C}$. Determine how long it will take for the center temperature of the potatoes to drop to $6^{\circ} \mathrm{C}$. Also, determine if any part of the potatoes will experience chilling injury during this process.