To warm up some milk for a baby, a mother pours milk into a thin-walled glass whose diameter is 6 cm . The height of the milk in the glass is 7 cm . She then places the glass into a large pan filled with hot water at $60^{\circ} \mathrm{C}$. The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer coefficient between the water and the glass is $120 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$, determine how long it will take for the milk to warm up from $3^{\circ} \mathrm{C}$ to $38^{\circ} \mathrm{C}$. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system? Why?