Answer
$P_{cond} = 18~W/m^2$
Work Step by Step
We can find the rate of energy loss:
$P_{cond} = \frac{A~(T_H-T_C)}{\sum L/k}$
$P_{cond} = \frac{(1.0~m^2)(72^{\circ} F-(-20^{\circ} F))}{(0.0030~m/1.0~W/m~K)+(0.075~m/0.026~W/m~K)+(0.0030~m/1.0~W/m~K)}$
$P_{cond} = \frac{(1.0~m^2)(92~F^{\circ})}{2.89~m^2~K/W}$
$P_{cond} = \frac{(1.0~m^2)(51.1~K)}{2.89~m^2~K/W}$
$P_{cond} = 18~W/m^2$
