Question $2-(30$ Points$)$: A three$-$part composite plane wall has uniform volumetric heat

generation $q_g^{}$ in its middle layer as depicted on the diagram. The left side of the composite wall

is insulated, and the right side is exposed to convective flow at $T_{}$ and with convective heat

transfer coefficient between $h.$ The thermal conductivities of the layers are $k_1,k_2$ and

$k_3=2k_2),$ and their respective thicknesses $L_1,L_2$ and $L_3.$

a$.(10$ points$)$ Sketch the temperature profile in the composite wall, clearly annotating it and

explaining your reasoning for it$.$

b$.(6$ points$)$ Derive an expression for the temperature $T_3$ in terms of the parameters provided in

the problem statement $($note that the temperatures at the different interfaces of the wall are only

provided as reference in the schematic and are not provided in the problem statement or

known$).$

c$.(6$ points$)$ Derive an expression for the temperature $T_2$ in terms of the parameters provided in

the problem statement $($note that the temperatures at the different interfaces of the wall are only

provided as reference in the schematic and are not provided in the problem statement or

known$).$

d$.(8$ points$)$ Find the location and an expression for the maximum temperature in the composite

wall in terms of the parameters provided in the problem statement $($note that the temperatures

at the different interfaces of the wall are only provided as reference in the schematic and are

not provided in the problem statement or known$).$