A composite plane wall consists of a 3-in.-thick layer of insulation (κs = 0.029 Btu/h · ft · °R) and a 0.75-in.-thick layer of siding (κs = 0.058 Btu/h · ft · °R). The inner temperature of the insulation is 67°F. The outer temperature of the siding is −8°F. Determine at steady state (a) the temperature at the interface of the two layers, in °F, and (b) the rate of heat transfer through the wall in Btu per ft2 of surface area.

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.