A composite plane wall consists of a 3-in.-thick layer of

Chapter 2, Problem 2.50

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A composite plane wall consists of a 3-in.-thick layer of insulation \(\left(\kappa_{\mathrm{s}}=0.029 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{R}\right)\) and a 0.75-in.-thick layer of siding \(\left(\kappa_{\mathrm{s}}=0.058 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{R}\right)\). The inner temperature of the insulation is \(67^{\circ} \mathrm{F}\). The outer temperature of the siding is \(-8^{\circ} \mathrm{F}\). Determine at steady state (a) the temperature at the interface of the two layers, in \({ }^{\circ} \mathrm{F},\) and (b) the rate of heat transfer through the wall in Btu per \(\mathrm{ft}^{2}\) of surface area.