A hot dog can be considered to be a 12 -cm-long cylinder whose diameter is 2 cm and whose properties are $\rho=980 \mathrm{~kg} / \mathrm{m}^3, c_p=3.9 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}, k=0.76 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$, and $\alpha=2 \times 10^{-7} \mathrm{~m}^2 / \mathrm{s}$. A hot dog initially at $5^{\circ} \mathrm{C}$ is dropped into boiling water at $100^{\circ} \mathrm{C}$. The heat transfer coefficient at the surface of the hot dog is estimated to be $600 \mathrm{~W} / \mathrm{m}^2$. ${ }^{\circ} \mathrm{C}$. If the hot dog is considered cooked when its center temperature reaches $80^{\circ} \mathrm{C}$, determine how long it will take to cook it in the boiling water.