A new bathroom (7 feet x 11 feet x 8 feet high) with two (2) adjacent exterior walls, that are insulated with 3.5 inches of thermal insulation with a thermal conductivity of 0.026 W/mK, has "radiant" electrical floor heat. The ceiling, floor and the other two (2) adjacent walls are interior surfaces.

1) Sketch, physical phenomena and assumptions:

a) Sketch the physical situation with all symbols used clearly defined

b) Identify (using words) the physical phenomena (specific heat transfer modes) that characterize the problem and are critical to its situation

c) Make a list of all assumptions and the reasonableness thereof

2) Prepare a mathematical model of the phenomena suitable for analysis of the problem with all symbols used clearly defined:

a) Draw the DC electric circuit analogy diagram with all symbols used clearly defined

b) Write the equations that characterize the problem and are critical to its solution with all symbols used clearly defined

3) Solve the mathematical equations to calculate the floor temperature, inside and outside wall temperatures and the electrical power required to maintain the interior air temperature at 68 F when the exterior temperature is -40 F and the wind speed is 40 mph

4) Plot the quantities calculated in part 3 as a function of wind speed from 10 to 40 mph and for exterior air temperatures of: 0, -20, -40 F.