A composite one-dimensional plane wall is of overall thickness \(2 L\). Material A spans the domain \(-L \leq x<0\) and experiences an exothermic chemical reaction leading to a uniform volumetric generation rate of \(\dot{q}_{\mathrm{A}}\). Material B spans the domain \(0 \leq x \leq L\) and undergoes an endothermic chemical reaction corresponding to a uniform volumetric generation rate of \(\dot{q}_{\mathrm{B}}=-\dot{q}_{\mathrm{A}}\). The surfaces at \(x= \pm L\) are insulated. Sketch the steady-state temperature and heat flux distributions \(T(x)\) and \(q_{x}^{\prime \prime}(x)\), respectively, over the domain \(-L \leq x \leq L\) for \(k_{\mathrm{A}}=k_{\mathrm{B}}, k_{\mathrm{A}}=0.5 k_{\mathrm{B}}\), and \(k_{\mathrm{A}}=2 k_{\mathrm{B}}\). Point out the important features of the distributions you have drawn. If \(\dot{q}_{\mathrm{B}}=-2 \dot{q}_{\mathrm{A}}\), can you sketch the steady-state temperature distribution?