Q$1.$ Consider a $2-ft2-ft$ thin square plate in a room at $75F.$ One side of the plate is maintained at a temperature of $130F,$ while the other side is insulated. Determine the rate of heat transfer from the plate by natural convection if the plate is $($a$)$ vertical, and $($b$)$ horizontal with hot surface facing up$.$ Given that The properties of air at $1$ atm and the film temperature of $102\mathrm{.}5F(562\mathrm{.}5R)$ :

$k=0\mathrm{.}01535Bt\frac{u}{f}t.*F$

$v=0\mathrm{.}1823{10}^{-3}f\frac{t^2}{s}$

$Pr=0\mathrm{.}7256$