Consider a heat chamber in which the temperature inside is maintained at a constant value of \(200^{\circ} \mathrm{C}\) (see figure 4.8). The chamber is covered by a 1.0 meterthick metal wall, and outside is insulated so that no heat flows to the outer surface of the wall. There is a uniform heat source inside the wall generating \(Q_{g}=400 \mathrm{~W} / \mathrm{m}^{3}\). The thermal conductivity of the wall is \(k=25 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\). Assuming that the temperature only varies in the \(x\)-direction, find the temperature distribution in the wall.

200 C Wall X 1 m Figure 4.8 Heat transfer problem for insulated wall Insulated No heat flow