Warm air is flowing through an exposed, rectangular PVC duct $($k$=0\mathrm{.}25$ W$/$m K$)$ that is $0\mathrm{.}5$ m wide x $0\mathrm{.}2$ m tall. The PVC walls are $4$ mm thick. The duct is well insulated on three sides, but the insulation has been removed on the top. The duct passes through a $12-$m$-$long section of basement, which is at a temperature of $15$oC and which exhibits h$=8$ W$/$m$2$K$.$ The convection coefficient in the interior of the duct is $30$ W$/$m$2$K$.$ Take the specific heat of air as $1\mathrm{.}0$ kJ$/$kg K$.$