Problem $3(30$ Points$)$

A window in a tall building experiences a horizontal wind flow parallel to the surface at a velocity of $8\frac{m}{s}.$ The window measures $2$ m high, $1\mathrm{.}5$ m wide and $6\mathrm{.}5$ mm thick. The transition from the building wall to the window glass surface is not smooth. The window casement that surrounds the edge of glass pane is raised $10$ mm above the surface of the glass and adjacent wall structure. Inside the building, the air temperature and heat transfer coefficient for the interior surface are $21C$ and $9\frac{W}{m^2}K$ respectively. The window has a uniform thermal conductivity of $1\mathrm{.}4\frac{W}{m}K.$ If the outdoor air temperature is $5C,$ determine the rate of convective heat loss from the window. Develop a thermal resistance network for the window system. Please state and justify all assumptions. Neglect any conduction through the casement.

Assume the following air properties: $k_{\text{a}\text{i}\text{r}}=0\mathrm{.}0248\frac{W}{m}K,v=14\mathrm{.}20{10}^{-6}\frac{m^2}{s},Pr=0\mathrm{.}712.$

Outside Air

$u=8\frac{m}{s}$

$T=5C$