Answer
$P_{cond} = 1.7\times 10^4~W/m^2$
Work Step by Step
We can find the rate of energy loss:
$P_{cond} = k~A~\frac{T_H-T_C}{L}$
$P_{cond} = (1.0~W/m~K)(1.0~m^2)~\frac{72^{\circ} F-(-20^{\circ} F)}{0.0030~m}$
$P_{cond} = (1.0~W/m~K)(1.0~m^2)~\frac{92~F^{\circ}}{0.0030~m}$
$P_{cond} = (1.0~W/m~K)(1.0~m^2)~\frac{51.1~K}{0.0030~m}$
$P_{cond} = 1.7\times 10^4~W/m^2$
