Determine the steadystate temperature distribution in a thin rectangular fin shown in figure 4.18. The fin is \(120 \mathrm{~mm}\) long, \(160 \mathrm{~mm}\) wide, and \(1.25 \mathrm{~mm}\) thick. The inside wall is at a temperature of \(330^{\circ} \mathrm{C}\). Two side surfaces are insulated, while the top and bottom surfaces as well as the tip surface are exposed to the air. The ambient air temperature is \(30{ }^{\circ} \mathrm{C}\). Assume \(k=0.2 \mathrm{~W} / \mathrm{mm} /{ }^{\circ} \mathrm{C}\) and \(h=2 \times 10^{-4} \mathrm{~W} / \mathrm{mm}^{2} /{ }^{\circ} \mathrm{C}\).

330 C Convection T = 30 C Insulated 120 mm 160 mm 1.25 mm T1 T T3 T4 1 2 3 Figure 4.18 Heat flow through a thin fin and finite element model