$(10$ Points$)$ A thin square plate $(0\mathrm{.}5m0\mathrm{.}5m)$ whose base is perfectly insulated and the top surface is maintained at a uniform temperature of $T_s=120C$ is suspended in stagnant air at $T_{}=20C$ in a horizontal position $($such that the hot surface is pointing up$).$ Neglecting radiation, what is the rate of heat transfer from the plate's top surface? $=1\mathrm{.}068k\frac{g}{m^3},=2\mathrm{.}049{10}^{-5}k\frac{g}{m}s,Pr=0\mathrm{.}7,=\frac{0\mathrm{.}00291}{K},=2\mathrm{.}886{10}^{-5}\frac{m^2}{s},v=2\mathrm{.}022{10}^{-5}\frac{m^2}{s},$ and $k=0\mathrm{.}0295\frac{W}{m}K.$