Consider a $0\mathrm{.}6-m0\mathrm{.}6-m$ thin square plate in a room at $30C.$ One side of the plate is maintained at a temperature of $90C,$ while the other side is insulated, as shown in Figure. Determine the rate of heat iransfer from the plate by natural convection if the plate is $($ n $)$ therizontal with hot surface facing up$,(=0\mathrm{.}54R{a}^{\frac{1}{4}})$ and $($b$)$ horizontal with hot surface facing down.