Chapter 3, Problem 3.18P

The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, $k_A=20\text{W/m}\cdot \text{K}$ and $k_C=50\text{W/m}\cdot \text{K,}$ and known thickness, $L_A=0.30\text{m}$ and $L_C=0.15\text{m}\text{.}$ The third material, B, which is sandwiched between materials A and C, is of known thickness, $L_B=0.15\text{m,}$ but unknown thermal conductivity $k_B.$

Under steady-state operating conditions, measurements reveal an outer surface temperature of $T_{S,O}=20°\text{C,}$ an inner surface temperature of $T_{s,i}=600°\text{C,}$ and an oven air temperature of $T_{\infty }=800°\text{C}\text{.}$ The inside convection coefficient h is known to be $25{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ What is the value of $k_B?$