The steady$-$state temperature distribution in a composite plane wall of the three different materials, each of constant thermal conductivity, is shown.

a$)$ Compare heat flux, $q_2^{\text{'}\text{'}}$ and $q_3^{\text{'}\text{'}}?$

b$)$ Compare conduction coefficients, $K_A$ and $K_B?$

The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, $k_{A}25\frac{W}{m}.K$ and $k_C=60\frac{W}{m}.K,$ and known thickness $L_A=0\mathrm{.}40m$ and $L_c=0\mathrm{.}20$ m $.$ The third material, B $,$ which is sandwiched between materials A and C $,$ is of known thickness, $L_B=0\mathrm{.}20m,$ but unknown thermal conductivity $k_B.$ Under steady$-$state operating conditions, measurements reveal an outer surface temperature of $T_{s,o}=20C,$ an inner surface temperature $T_{s,i}=600C,$ and an overn air temperature of $T_{}=800C.$ The inside convection coefficient h is known to be $25\frac{W}{m^{2}K}.$ What is the value of $k_B?$

Problem $14.$