problem 01 Calculate the heat losses through the walls of an industrial furnace The wall of an industrial furnace can be considered to be composed of the following four layers: - a first layer of thickness e, is composed of refractory bricks with thermal conductivity ₁; - a second (thickness, e₂) is made up of clay bricks with thermal conductivity, ₂ - a third: glass wool (thickness, e₃ conductivity thermal, ₃); - a thick mechanical protection sheath e₄ Composed of thermal conductivity steel, ₄ The temperature inside the oven is assumed to be constant. and equal to T_i

Questions The plant manager wants to get an idea of the magnitude of the energy flow from the furnace to the outside. You know the average temperature of the surrounding environment, ^oT_a. Therefore, his supervisor asks him to calculate: 1) the flux density of heat losses to the outside, if the furnace jacket were made up only of thicknesses e₁ and e₄ 2) the flux density of heat losses to the outside, if the jacket were made up of all the internal walls, e₁, e₂, e₃, and e₄; 3) the monetary value of these losses, in US$ per year, in both cases. The technician in charge of operating the oven provides you with the following information:

Annual operating time: T = 8,700 hrs/year Energy cost: C_E = 3.2 US$/kWh Transfer area between the oven and the outside: A = 60 m²

Ti=650C;hi=90W/m2C;e1=30cm;e2=35cme3=15cme4=0,3cmTa=32Cho=48W/m2C1=27W/mC2=5,2W/mC3=0,04W/mC4=45W/mC Protective