Consider a setup where a gray, diffuse Plate 1 with an absorptivity of 1 = 0.3 is installed on the ground, with its bottom side insulated (adiabatic). Directly above this plate, another gray, diffuse Plate 2 with an emissivity of 2 = 0.8 is suspended, separated by a narrow air gap (g). A fully-developed air at a temperature of = 27 flows through this gap, characterized by an average Nusselt number of =300. Both plates have a length of = 30 cm, where , and the thermal conductivity of the air is = 0.03 W/mK. Determine the necessary top plate temperature 2 to maintain the surface temperature of the bottom plate at 1 = 320 K