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