Consider a $1\mathrm{.}2-$m$-$high and $2-$m$-$wide glass window with a thickness of $6$ mm$,$ thermal conductivity k $=0\mathrm{.}78$ W$/$m$$K$,$ and emissivity$$ $=0\mathrm{.}9.$ The room and the walls that face the window are maintained at $25$C$,$ and the average temperature of the inner surface of the window is measured to be $5$C and the temperature of the outdoors is $5$C$.$ Given: The properties of air at Tf$,$c $=15$C$.$

k $=0\mathrm{.}02476$ W$/$m$$C$,$

$=1\mathrm{.}470$ x $105$ m$2/$s$,$

Pr $=0\mathrm{.}7323$

Determine the rate of total heat transfer through the window.