2. Assume that an igloo is a hemispherical shell of ice ($k = 0.15 \frac{W}{m \cdot ^\circ C}$) with an outer diameter of 2.2 m and an inner
diameter of 1.8m.
Assume the igloo sits on an ice cap ($T_{cap} = -20^\circ C$), that the air temperature outside is $T_{\infty} = -40^\circ C$, and that
the convection heat-transfer due to wind is $h_o = 40 \frac{W}{m^2 \cdot ^\circ C}$.
Assume also that convection heat transfer within the igloo due to drafts is $h_i = 5 \frac{W}{m^2 \cdot ^\circ C}$.
If the folks in the igloo are generating heat at the rate of 400 W, what is the air temperature in the igloo?