Physics - Heat & Thermo Question with Solution | TestHub

When heat flows perpendicular to the wall surface, the layers are in series. The total thermal resistance is the sum of individual resistances.$R_{total}=R_1+R_2=\frac{d_1}{K_{1}A}+\frac{d_2}{K_{2}A}$. The effective thermal resistance for the composite wall is $R_{total}=\frac{d_1+d_2}{K_{eff}A}$. Equating the two expressions for $R_{total}$: $\frac{d_1+d_2}{K_{eff}A}=\frac{d_1}{K_{1}A}+\frac{d_2}{K_{2}A}$. This simplifies to $K_{eff}=\frac{d_1+d_2}{\frac{d_1}{K_1}+\frac{d_2}{K_2}}=\frac{K_1{K}_2(d_1+d_2)}{K_1{d}_2+K_2{d}_1}$.