Consider a tapered fin of length \(5 \mathrm{~cm}\) dissipating heat to an ambient at \(30^{\circ} \mathrm{C}\). The heat transfer coefficient on the surface at the tip is \(100 \mathrm{~W} / \mathrm{m}^{2}{ }^{\circ} \mathrm{C}\). The fin tapers from a thickness of \(5 \mathrm{~mm}\) to a thickness of \(2 \mathrm{~mm}\) at the tip. The thermal conductivity of the material of the fin is \(100 \mathrm{~W} / \mathrm{m}^{\circ} \mathrm{C}\). The width of the fin is constant along the length and equal to \(2 \mathrm{~mm}\). Determine the heat dissipation from the fin for a base temperature of \(100^{\circ} \mathrm{C}\). Use

(a) Two linear elements;

(b) One quadratic element. Also calculate the fin efficiency.