Energy for Heating

We can use the heat conduction formula due to Fourier,

$$ P = \frac{dQ}{dT} = \frac{k A (T_2 - T_1)}{d} $$

Formula will calculate the power of the heat transfer between two temperatures, for our needs from an ideal inside to a known outside. Therefore to keep the inside at that temp level, we'll know how much power we have to add in the inside (with a heating unit).

Formula needs surface size $A$, the surface through which heat flows (or leaks), which will be all four walls roof and floors. Material heat conductivity $k$, wall thickness $d$, a target temperature $T_2$, and outside temperature $T_1$.

Target temperature is room temperature 22 degrees C.

Outside temperature can be annual world average temperature (the one that keeps rising, and everyone is freaked out about), 13.7 deg C. We can assume it's always at that level outside for everyone all the time, and people want room temperature on the inside. What was that movie line? "It's chilly outside, and it's Chilly inside". We just want chilly outside.

Home sizes differ from country to country, as average we'll take Denmark, 150 m2. Multiply by 4 meter height, get home volume. Assume a cube for volume, so we w/ cube root calc one side, then using sides side^2 x 6 gives a complete outside surface area.

Material heat conductivity? Units $W/m \cdot C$, or $J/s \cdot m \cdot C$. We have concrete brick 0.84, plasterboard 0.16, wood 0.10. I dont know.. what would average material be? Better than mere bricks, but little worse than wood? Let's take 0.15.

We'll further assume 4.2 people per home (I looked this up), a 2013 world population of 7.17 billion (I am trying to reach an annual energy needed for heating, worldwide), so

ppl_per_home = 4.2
pop = 7.17*1e9 # world 2013
world_t =  13.7 # C
room_temp = 22
home_vol = 150*4 # m3
d = 11 # cm, wall width
k = 0.15 # W/m*C = J/s*m*C

side = np.power(home_vol,1/3.)
A = (side**2)*6

P = k*(room_temp-world_t)*A / (d*0.01)

total = (pop/ppl_per_home)*P*24*365
print ('home heating %d twh' % (total / 1e12))

home heating 72244 twh

The entire world energy consumption for that year was 157,481 Terrawatt Hours. The number above is a good chunk of that.