A fin of length \(1 \mathrm{~cm}\) is initially at the ambient temperature of \(30^{\circ} \mathrm{C}\). If the base temperature is suddenly raised to a temperature of \(150{ }^{\circ} \mathrm{C}\) and maintained at that value, determine the temperature distribution in the fin after 30 seconds if the thermal diffusivity of the material of the fin is \(1 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\). The heat transfer coefficient between fin surface and ambient is \(100 \mathrm{~W} / \mathrm{m}^{2}{ }^{\circ} \mathrm{C}\). The cross-section of the fin is \(6 \mathrm{~mm} \times 5 \mathrm{~mm}\).