Consider a furnace that is situated in a room with a surrounding air temperature of 30°C and an average convection coefficient of 10 W/m²°C. Convection and radiation heat transfer occur between the outer surface of the furnace and the surroundings. The front of the furnace is made up of two parallel plates, where the inner plate has a temperature of 600°C. To ensure safety and prevent thermal burns on the people working around the furnace, the outer surface temperature of the furnace should be kept below 458°C. Based on the above information, determine the number of radiation shields that should be placed in parallel on the front surface.
Furnace front:
T_inner = 600°C
Air: 30°C, h = 10 W/m²K
Radiation shields:
T_max = 458°C
Assume all the surfaces have the same emissivity of 0.1 and show the different steps of calculations with necessary diagrams.