A radiant$-$heating system is installed in the plaster ceiling of a room $18$ ft long by $18$ ft wide by $8$ ft high. The temperature of the concrete floor is maintained at $65$ F$.$ Assume no heat flows through the walls, which are coated with a re$-$radiating material. The temperature of air passing through the room is held at $65$ F$.$ If the required heat supply to the floor is $3500$ BTU$/$hr$,$ calculate the necessary temperature at the ceiling surface. How much heat is transferred to the air in BTU $/$ hr $?$ Emissivity of plaster is $0\mathrm{.}93,$ absorptivity of concrete is $0\mathrm{.}63,$ the convective heat transfer coefficient between the ceiling and the air is given by h $=0\mathrm{.}20$T$0\mathrm{.}25$ in BTU $/$ hr ft$2$ F