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.

Find the steady-state temperature at the center of the plate = /2, = /2) for sums of w from n=1 to n=19 (only odd values). find the value of n for which the change in /2, /2) is less than 1% from the value at the previous n. at this point, we consider the solution converged. does the value of the temperature at the center seem reasonable? in this part, the values of x and y are constant scalar values. you should produce a plot of the value of n on the horizontal and the estimate of the temperature at the center of the plate on the vertical. b. using the value of n (or larger) that resulted in convergence in part (a), create a contourf plot of the temperature distribution across the entire plate. use enough spatial subdivisions to create a useful plot. comment on the results. hint: you need to determine what “x” and “y” values to use to make your t matrix. i recommend using a different number of x and y values. use enough x and y values so that the plot is “smooth”.