Consider heat transfer along a conducting block as shown in figure 4.25. The conductor, modeled here as a rectangular region, is insulated at the top and bottom, and there is no heat flow in the direction normal to the plane (zdirection). The thickness in the zdirection is \(t=5 \mathrm{~mm}\). The conductivity of the material is \(k=0.2 \mathrm{~W} / \mathrm{mm}^{\circ} \mathrm{C}\). Heat is generated in the block due to electrical current flow, and the corresponding distributed heat source is \(Q_{g}=\) \(0.06 \mathrm{~W} / \mathrm{mm}^{3}\). On the left side, heat enters the block with a known heat flux of \(q_{0}=0.04\) \(\mathrm{W} / \mathrm{mm}^{2}\). Heat is lost on the other side to the surrounding air, which has an ambient temperature of \(25^{\circ} \mathrm{C}\). The convection coefficient for this heat transfer is \(h=1.2 \times 10^{-2} \mathrm{~W} / \mathrm{mm}^{20} \mathrm{C}\). Determine the temperature distribution in the domain using a 3node triangular element.

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90 0.04 W/mm 5 mm Figure 4.25 Heat conduction example 10 mm h 1.2x 102 W/mm C 7 = 25 C