But even recovering 95% of heat isn't exactly great. If you live in Canada and have a 2600 sq ft house with 8 ft ceilings and 10 changes of air per hour, and the indoors is 70F and outdoors is 0F, thats 2600810 cubic feet of air/ per hour, or 12000 BTU/hr. That means you are more than doubling your heating costs compared to sealing the building and just having conductive losses through the walls.
This is true for most climates - even the best energy recovery systems still double heating/cooling costs compared to having barely any fresh air.
Or maybe I had less than ten air changes?
And we're looking at the margins; 1 air change per hour can do wonders for preventing the spread of disease and improving air quality, compared to 0 air changes per hour.
Nevertheless, I redid your math, and found that your hypothetical home has 26,728 more BTUs of energy in its air, compared to the outside air[-1][0][1], and that the recommended furnace for such a climate should be 160,000 BTU/hr [2].
Using those numbers as a base, I find that, with an efficiency of 95%, it would require 120 (that's one hundred and twenty) air changes per hour to double heating costs.
With 60% efficiency, it would require 15 air changes per hour to double heating costs.
And it only takes a few air changes per hour to increase comfort and prevent illness.
[-1] I suddenly realized that the google search links that I used for these calculations are messy and unwieldy, so I'll summarize my calculations: (2600 ft^2) * (8 ft) represent the volume of the house; (1.225 kg / m^3) represents the density of air, (1.005 kJ/(kg * Kelvin)) represents the specific heat of air, (70 * (5/9)) represents the temperature difference you gave me, in Kelvin. Multiplying everything together, and letting Google automatically take care of unit conversions, gives me 28.2 MegaJoules of energy in the house.
[0] https://www.google.com/search?q=%282600+ft%5E2%29*%288+ft%29...
[1] https://www.google.com/search?q=convert+28199142.9+joules+to...
Very interesting! The concept makes a lot of sense, and I was able to find some companies online that produce such a thing, often under the phrase "counterflow heat exchanger".
Frustratingly there's little details online for actual pricing, but you can find the bare exchange units on ebay for $200-300.
Shouldn't the air ideally move in the same direction?
In a countercurrent heat exchanger, the hot air will get colder and colder until it is at the same temperature as the cold air, and the cold air will get hotter and hotter until it is the same temperature as the hot air.
This is because the hot air is not warming up the same air molecules that it relies on to cool down, and the cold air is not cooling down the same air molecules that it relies on to warm up. Each current of air gives up a part of their heat/coldness, becomes colder/hotter, and then moves towards a section of pipe that's even colder/hotter than the previous section of pipe.
A picture is worth a thousand words, although it takes some staring and studying before the concept finally clicks: https://en.wikipedia.org/wiki/Countercurrent_exchange#/media...
If anyone has a half-hour of time to waste, you can look into the science of "countercurrent heat exchangers".
It's fascinating to see how 2 pipes of air current switch temperatures when they're in contact and moving in opposite directions.
So if you want to be green AND have fresh air constantly circulating through a building, then forcing the warm inside air to pass by the cold outside air as they leave/enter the building can lead to somewhere around 95% energy recovery.
Add in a humidifier to the incoming air, and you'll have a comfortable room with humidity that will attach to airborne droplets, prevent evaporative release of a raw airborne virus, and help pull the droplet down to the ground via gravity.