10
Design Maximum Load
A design maximum heating condition might be -25C outdoors with a 20C indoor temperature. Losses from our condo from conduction through the walls (subscript w) and windows (subscript f for fenestration) would be
\begin{align}
q_c = \sum{\frac{A}{R}(T_i-T_o)} &= \left(\frac{A_w}{R_w} +\frac{A_f}{R_f}\right)(T_i-T_o)\\
&= \left(\frac{36.5}{2.5} + \frac{11.5}{0.6}\right)\left(20-(-25)\right)\\
&= 1520\;\rm W
\end{align}
and we would also need to supply enough energy to warm up the air that leaks in to replace the air that leaks out. We will be close using constant values for specific heat $C_p = 1004\;\rm J/kgK$, density $\rho = 1.2\;\rm kg/m^3$ and dimensions from our condo model above that results in $0.032\;\rm m^3/s$ air flow for 0.5 air changes per hour.
\begin{align}
q_i = \dot m C_p (T_i-T_o) &= \rho \dot V C_p(T_i-T_o)\\
&= 1.2\times 0.032\times 1004\times (20-(-25)) \\
&= 1735\;\rm W
\end{align}
for a total of 3255 W or 3.3 kW (or 11000 Btu/hr for comparison to product literature) heating power required on a cold dark night in mid-winter and we would need heating equipment that could deliver that output.
If we needed this level of heating 24/7 for the entire month of January it would amount to about 2400 kWh of heating power. Fortunately this is a worst case and our overall electric consumption in January is about half that amount, which makes sense given average temperatures just below freezing. For performance prediction we will need to look at more than just the most demanding case when the temperatures are coldest. We have ignored humidity in our estimates and could need more energy to humidify for comfort. Humidity will be much more important for air conditioning situations.
Heating Equipment
Electric resistance heaters like baseboards or electric fan heaters are simple, cheap, and transfer 100% of the electrical energy into the room air.
Mini-Split Heat Pumps like the Fujitsu Halcyon line are a common energy efficient solution for heating small and medium sized living spaces. There are DC versions like this one from HotSpot Energy, however they don’t have a DC unit that can handle a Canadian winter. The advantage of heat pumps over traditional electric resistance heating is higher output. Heat pumps provide more heat than the electrical energy that goes into them. They transfer heat from a cold location to a warmer location through a refrigeration cycle and have an apparent efficiency of more than 100%, which just sounds wrong, so we call it a Coefficient of Performance (COP).
A heat pump system will be more effective if it can draw heat from a reservoir that is warmer than the outside air, like ground water or lake water.
Fired Heaters like furnaces or stoves can burn fossil fuels like propane or bio-fuels like wood. They are simple, moderately priced, and transfer up to about 85% of the heating energy value of the fuel to the room air.
Heat Pump Figures of Merit
The dimensionless coefficient of performance is t