A finite cylinder is \(2 \mathrm{~cm}\) in diameter and \(3 \mathrm{~cm}\) long and at a temperature of \(200^{\circ} \mathrm{C}\), and is cooled in air at \(30^{\circ} \mathrm{C}\). The convective heat transfer coefficient is estimated as \(10 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Calculate and plot the center temperature.

Use the following physical property values: \(k=50 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, ho=2000 \mathrm{~kg} / \mathrm{m}^{3}\), and \(c_{p}=\) \(1000 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\).