Consider a large plane wall of thickness L = 0.4 m and thermal conductivity k = 8.4 W/m ·...

Consider a large plane wall of thickness L = 0.4 m and thermal conductivity k = 8.4 W/m · K. There is no access to the inner side of the wall at x = 0 and thus the thermal conditions on that surface are not known. However, the outer surface of the wall at x = L, whose emissivity is ε = 0.7, is known to exchange heat by convection with ambient air at T∞ = 25°C with an average heat transfer coefficient of h = 14 W/m2 · K as well as by

radiation with the surrounding surfaces at an average temperature of Tsurr = 290 K. Further, the temperature of the outer surface is measured to be T2 = 45°C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the plate, (b) obtain a relation for the temperature of the outer surface of the plate by solving the differential equation, and (c) evaluate the inner surface temperature of the wall at x = 0. Answer:(c) 64.3°C.