EXAMPLE

A plane wall is a composite of two materials, A and B $.$ The wall of muterial A has uniform heat generation $q^{}=1\mathrm{.}5{10}^6\frac{W}{m^3},k_A=75\frac{W}{m}K,$ and thickness $L_A=50mm.$ The wall material $B$ has no generation with $k_B=150\frac{W}{m}K,$ and thickness $L_B=20mm.$ The inner surface of material $A$ is well insulated, while the outer surface of material $B$ is cooled by a water stream with $T_{}=30C$ and $h=1000\frac{W}{m^2}C.$ Determine the temperature of

a$)$ insulated surface $(T_0)$

b$)$ inner surface $(T_1)$

c$)$ cooled surface $(T_2)$