A hot dog at \(5^{\circ} \mathrm{C}\) is to be cooked by dipping it in boiling water at \(100^{\circ} \mathrm{C}\). Model the hot dog as a long cylinder with a diameter of \(20 \mathrm{~mm}\). Find the cooking time, which is defined as the time, for the center temperature to reach \(80^{\circ} \mathrm{C}\). The heat transfer coefficient from the water to the surface is \(90 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\).

The following data can be used: \(k=0.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, ho=880 \mathrm{~kg} / \mathrm{m}^{3}\), and \(c_{p}=\) \(3350 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\).