A one-dimensional plane wall of thickness \(2 L=\) \(80 \mathrm{~mm}\) experiences uniform thermal energy generation of \(\dot{q}=1000 \mathrm{~W} / \mathrm{m}^{3}\) and is convectively cooled at

\(x= \pm 40 \mathrm{~mm}\) by an ambient fluid characterized by \(T_{\infty}=\) \(30^{\circ} \mathrm{C}\). If the steady-state temperature distribution within the wall is \(T(x)=a\left(L^{2}-x^{2}\right)+b\) where \(a=15^{\circ} \mathrm{C} / \mathrm{m}^{2}\) and \(b=40^{\circ} \mathrm{C}\), what is the thermal conductivity of the wall? What is the value of the convection heat transfer coefficient, \(h\) ?