$3\mathrm{.}68$ Consider one$-$dimensional conduction in a plane com$-$

posite wall. The outer surfaces are exposed to a fluid at

$25C$ and a convection heat transfer coefficient of $1000$

$\frac{W}{m^2}*K.$ The middle wall B experiences uniform heat

generation $q_B^{},$ while there is no generation in walls

A and C $.$ The temperatures at the interfaces are $T_1=$

$261C$ and $T_2=211C.$

$k_A=25\frac{W}{m}*K,L_A=30mm$

$k_C=50\frac{W}{m}*K,L_B=30mm$

$,L_C=20mm$

$($a$)$ Assuming negligible contact resistance at the inter$-$

faces, determine the volumetric heat generation $q_B^{}$

and the thermal conductivity $k_B.$

$($b$)$ Plot the temperature distribution, showing its impor$-$

tant features.

$($c$)$ Consider conditions corresponding to a loss of

coolant at the exposed surface of material

$0.$ Determine $T_1$ and $T_2$ and plot the temperature

distribution throughout the system.