QUESTION $1$

A $0\mathrm{.}7$ m high and width of $1\mathrm{.}3$ m double pane window has two $6$ mm thick layers of glass with thermal conductivity of $0\mathrm{.}78\frac{W}{m}.$ K which are separated by a $12$ mm wide stagnant air space with a thermal conductivity of $0\mathrm{.}026\frac{W}{m}.$K$.$ If the temperature of the surfaces inside the room is kept at $22C$ and the outside temperature is $-8C,$ calculate the steady rate of heat transfer through the double pane window. Consider the convection heat transfer coefficients of the inner and outer surface of the window as $10\frac{W}{m^2}.K$ and $40\frac{W}{m^2}.K,$ respectively, which includes the effects of radiation. Figure $1$ below illustrates the problem described.

Figure $1$: Schematic illustration of Question $1$

$[15$ Marks$]$