Chapter 3, Problem 3.18P

The composite wall of an oven consists of three materials,two of which are of known thermal conductivity, $k_{\text{A}}=20\text{W/m}\cdot \text{K}$ and $k_{\text{C}}=50\text{W/m}\cdot \text{K,}$ and knownthickness, $L_{\text{A}}=0.30\text{m}$ and $L_{\text{C}}=0.15\text{m}\text{.}$ The thirdmaterial, B, which is sandwiched between materialsA and C, is of known thickness, $L_{\text{B}}=0.15\text{m,}$ butunknown thermal conductivity $k_{\text{B}}.$

Under steady-state operating conditions, measurementsreveal an outer surface temperature of $T_{s,o}=20°\text{C,}$ aninner surface temperature of $T_{s,i}=600°\text{C,}$ and an ovenair temperature of $T_{\infty }=800°\text{C}\text{.}$ The inside convectioncoefficient h is known to be $25{\text{W/m}}^2\cdot \text{K}\text{.}$ What is thevalue of $k_{\text{B}}?$