$3\mathrm{.}5$ A dormitory at a large university, built $50$ years ago, has

exterior walls constructed of $L_s=25-mm-$thick sheath$-$

ing with a thermal conductivity of $k_s=0\mathrm{.}1\frac{W}{m}*K.$ To

reduce heat losses in the winter, the university decides

to encapsulate the entire dormitory by applying an

$L_i=25-mm-$thick layer of extruded insulation charac$-$

terized by $k_i=0\mathrm{.}029\frac{W}{m}*K$ to the exterior of the

original sheathing. The extruded insulation is$,$ in turn,

covered with an $L_g=5-mm-$thick architectural glass

with $k_g=1\mathrm{.}4\frac{W}{m}*K.$ Determine the heat flux through

the original and retrofitted walls when the interior and

exterior air temperatures are $T_{,i}=22C$ and $T_{,0}=$

$-20C,$ respectively. The inner and outer convection heat

transfer coefficients are $h_i=5\frac{W}{m^2}*K$ and $h_o=$

$25\frac{W}{m^2}*K,$ respectively.$$