A composite plane wall consists of a 12-in.-thick layer of

Chapter 2, Problem 2.49

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A composite plane wall consists of a 12-in.-thick layer of insulating concrete block \(\left(\kappa_{\mathrm{c}}=0.27 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{R}\right)\) and a 0.625-in.-thick layer of gypsum board \(\left(\kappa_{\mathrm{b}}=1.11 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{R}\right)\). The outer surface temperature of the concrete block and gypsum board are \(460^{\circ} \mathrm{R} \text { and } 560^{\circ} \mathrm{R}\), respectively, and there is perfect contact at the interface between the two layers. Determine at steady state the instantaneous rate of heat transfer, in Btu/h per \(\mathrm{ft}^{2}\) of surface area, and the temperature, in \({ }^{\circ} \mathrm{R}\), at the interface between the concrete block and gypsum board.