An uncoated, solid cable of length \(L=1 \mathrm{~m}\) and diameter \(D=40 \mathrm{~mm}\) is exposed to convection conditions characterized by \(h=55 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(T_{\infty}=20^{\circ} \mathrm{C}\). Determine the maximum electric current that can be carried by the cable if it is pure copper, pure aluminum, or pure tin. Calculate the corresponding minimum wire temperatures. The electrical resistivity is \(ho_{e}=10 \times 10^{-8}\) \(\Omega \cdot \mathrm{m}\) for copper and aluminum at their melting points, while the electrical resistivity of tin is \(ho_{e}=20 \times 10^{-8}\) \(\Omega \cdot \mathrm{m}\) at its melting point.