Question No. 11: a) Derive the general heat conduction equation in Cartesian coordinates. o) Electric heater wires are installed in a solid wall having a thickness of \( 8 \mathrm{~cm} \) and \( k=2.5 \mathrm{~W} / \mathrm{m}{ }^{\circ} \mathrm{C} \). The right face is exposed to an environment with \( \mathrm{h}=50 \mathrm{~W} / \mathrm{m}^{2}{ }^{\circ} \mathrm{C} \) and \( \mathrm{T} \infty=30^{\circ} \mathrm{C} \), while the left face is exposed to \( \mathrm{h}=75 \mathrm{~W} / \mathrm{m}^{2 \circ} \mathrm{C} \) and \( \mathrm{T} \infty \) \( =50 \circ \). What is the maximum allowable heat-generation rate such that the maximum temperature in the solid does not exceed \( 300^{\circ} \mathrm{C} \) ?