Answer to Question #54186 in Mechanics | Relativity for Kate

Question

The air temperature inside a room is maintained constant at 25o C. The room consists of 6 walls as shown below. The outside temperature is -15oC. The length, width and height of the room walls are 4m, 2.5m and 2m respectively. The six room walls consist each of three different layers of plastic, cement and brick respectively. The thickness of the plastic layer is 5 mm and the thickness of the brick layer is 100 mm. The thermal conductivity of the plastic, cement and plastic layers are: Kplastic=0.5, Kcement=2 and Kbrick=1 W/(m·K). The heat transfer coefficients for the air inside the room and the air outside are: 20 and 25 W/(m2K) respectively. Ignore the radiation and heat losses from the corners.
(a) Using the Fourier’s law and the Newton’s law of cooling express the rate of heat loss from the room, in parametric form.
(b) Find the thickness of the cement layer which results in constant total heat loss rate of 7kW through all six oven walls.