Problem $1(30$ points$)$

$($a$)$ Calculate the convective, radiative and total heat transfer inside the window cavity and the center$-$ofglass R $-$value for a double$-$glazed window, if the surface temperature of the interior glass is equal to $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the surface temperature of the exterior glass is equal to $\backslash (10^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$($b$)$ Repeat the calculation for the case of low$-$emissivity coating on the outside surface of the interior glass $(\backslash (\backslash$varepsilon$=0\mathrm{.}1\backslash )).$

$($c$)$ What is the overall window thermal resistance and conductance if there is an aluminum frame with thermal break occupying $\backslash (10\backslash \%\backslash )$ of the total area of the window $($for both cases$)?$

Assume a total window area $($including frame$)$ equal to $\backslash (10\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ for this question. Exclude exterior convective$/$radiative film coefficients.