Question$4(10$ Marks$)$

Consider a $0\mathrm{.}8-$m$-$high and $1\mathrm{.}5-$m$-$wide double$-$pane window consisting of two $4-$mm thick layers of glass $(k=0\mathrm{.}78W*m^{-1}*K^{-}{?}^1)$ separated by a $10-mm-$wide stagnant air space $(k=0\mathrm{.}026W*m^{-1}*K^{-1})$

a$)$ Draw a thermal circuit for the heat transfer process across the wall, clearly identifying each thermal resistance.

b$)$ Determine the total thermal resistance to the heat transfer process.

c$)$ Determine the steady$-$state heat transfer rate through the window.

d$)$ Find the temperature of its inner surface for a day during which the room was maintained at $20C$ while the outdoors temperature is $-10C.$

Note: Take the convection heat transfer coefficients of the inner and outer surfaces of the window as $h_1=10W{m}^{-2}{C}^{-1},$ and $h_2=40W{m}^{-2}{C}^{-1},$ which also includes the effect of radiation.