Stack effect in airtight house
I built a 2 story 2000 sqft house in southern Vermont with zip sheathing and double stud walls with 12 inches of dense pack cellulose and 22 inches of cellulose in the attic. This will be our first winter living in the house. So far it is performing well. Temps haven’t been very cold. 20’s at night, 30-40’s during the day. The 12000 btu cold climate heat pump has been keeping the house warm while using about 12-17 kwh per day (we have a woodstove for when the real cold hits.) The down stairs stays at 72 while the upstairs is 68. Am I right to assume that the airtight envelope is preventing a stack effect and the “heat rises” principle? Even if that is the case does a 4 degree temp difference seem high? With a thermal imaging camera I did find several stud bays upstairs that seem to be light on insulation at the top. Based on my rough calculations these cold spots are equivalent to having an extra 4×5 triple pane window on the second floor. Would this be a significant reason for the 4 degree temp difference? I did all of the prep work and rolling for the cellulose so these light spots are almost certainly my fault and not the installer. Would topping off the cellulose significantly reduce the temperature difference or is it not worth the effort?
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Stack effect is still in effect. Hotter air is less dense and being pushed upwards by the cooler mor dense air.
Air tight homes have less stack driven in/ex filtration. Measured stack pressures are correspondingly higher (Bernoullis law)
Stack effect is much less in a well-sealed house because the temperature differentials are smaller. In a leaky house you have air at outside temperature coming in that is a lot colder and a lot denser than the interior air.
In any case, it's a lot to ask to expect stack effect alone to heat the upstairs. The amount of heat moved is equal to 1.03 times the flow in CFM times the temperature difference in degrees F; that's BTU/hr. With a relatively small delta between first and second floor -- 4F -- you're going to need substantial air flow to move meaningful amounts of heat.
Just spitballing, let's say at night your heat pump is drawing 1kW and has a COP of 2, that's 6800 BTU/hr. Let's say half of that goes upstairs. With a 4F delta you'd need 850 CFM to move that much heat, that would blow your hair back.
There is also heat transfer due to conduction. I'd estimate the floor and ceiling between first and second is about R2. If it's 1000 square feet, with a 4F delta you'd get conductive flow of 2000 BTU/hr.
Note that both of these flows are driven by temperature differences. The colder it is outside the more heat you need upstairs, and the bigger the delta needs to be to get that flow.
Thank you for those calculations. I'll have to run some numbers and see what I come up with. After hearing your explanation I guess my question is If stack effect can't be relied upon to heat the second floor of a home what is the explanation for the common scenario around here where people heat with wood stoves on the first floor as there only source of heat and the second floor is warmer than the first floor?
Problems with overheated upper floors usually involve an open loft overlooking a two-storey living space. That allows for strong convective currents to form, driven by the much hotter air rising from the stove. Those houses probably have much less insulation and are much leakier than yours, so the occupants have to keep the stove burning hot to maintain comfortable temps on the ground floor. If there is no two-storey living space, then the hot air has to make its way across the ceiling until it gets to the stair. Unless there is some other return path, cooler air has to come down the same stair, resulting in much weaker convective currents, but possibly still enough to overheat the upper floor. The hot air at the ceiling will also be warming the floors above.
850 CFM will blow your hair back?
I'll argue the point on units.
If it's 850CFM over 1000 sq.ft., that's... 0.85 feet per minute? Not blowing my hair back.
What is the relevant area for this convection?
I will take the opportunity to correct myself-- I confused stack effect with stack pressure. DC's take is correct and mine isn't. Stack effect will be decreased.
How big is the opening between floors? It's not the whole thousand square feet, it might be a stairwell that's 40 square feet or so.
Yes, about a 35 sqft opening for the stairs.
“The down stairs stays at 72 while the upstairs is 68."
DC why do you think it is cooler on the upper floor? Seems like the OP has a reverse stack affect.
Unless the upper floor has very different walls and windows the numbers do not compute for me.
Walta
I have a similar situation in my home when I heat the whole house only with my downstairs mini split. About a 4 degree differential. The stack effect is why the second floor is comfortable at all without heating it directly.
In a conventional home you are heating both floors. It is hotter on the second floor because you are delivering heat plus the stack effect.
Kyle's comment demonstrates the driving principle: When heating at one end of an assembly (in this case the bottom floor of the house) and cooling at the other end (2nd floor walls, windows, ceiling), there will and has to be a temperature differential for heat to move by whichever of the a.m. mechanisms. Similar to fluid pressure differential driving flow in a piping system. To eliminate the differential, heat loss from the 2nd floor has to be compensated by intentional supply. To reduce it, more insulation to reduce the amount of heat loss (already done in this case) or improve the transport of the heat (transfer vents / ducts, maybe with inline fans, ....) But, most sleep better at night when it's a bit cooler. The OP's house sounds perfect to me!
I don't disagree, 72 downstairs and 68 upstairs is pretty nice and I'd be happy if it stayed right there but my suspicion is that as the temps outside drop the difference between floors will increase. But maybe fixing my insulation weak spots can counteract that.
The standard model for heat flow through conduction is that it's directly proportional to the temperature difference. So the heat loss from a house at 70F is going to be half as much when it's 35F outside as when it's 0F outside.
If conduction is doing the work in your house, that's driven by the temperature difference between first floor and second floor. So when the heat loss from the second floor doubles, the heat flow from the first floor has to double, which means the temperature difference has to double.
In short, if you're seeing that when it's 35F the second floor is 4F below the first floor, I'd expect it to be 8F below when it's 0F outside.
So this thread has me thinking.
The standard answer is that heat needs a differential to travel, if you have a point source of heat you would expect the further away from the source you are the cooler it would be. But we've all been in houses in the winter where it's warmer upstairs than downstairs, even if the only source of heat is downstairs.
So is the explanation incomplete? Or are our senses deceiving us?
I have one answer, which is that stack effect is driven not by temperature gradients, but by the difference in buoyancy. If you have a point source of heat and the air around it is warmer than the room, that air is going to tend to flow up rather than diffuse through the room. And when it flows up it brings the heat it contains with it.
This is going to work counter to regular heat flows, in that the greater the heat stratification, the greater the buoyant forces and the more the heat flows up. Which is why heat stratification is much more pronounced in poorly-insulated houses.
I have no idea how you would quantify this though.
Just as a follow up with some anecdotal evidence I think you are on to something with buoyancy. In my previous example the indoor temp was 70 outdoor temp 35 temp difference between first and second floor was 4 degrees, source of heat was a minisplit pumping out heat around 120 degrees at the head.
My current situation with a wood stove with a flue temp of 350 degrees is 75 degrees indoors temp 25 degrees outdoor temp and 3 degree temp difference between upstairs and down. So with a 10 degree great temp difference between indoor and outdoor am getting a superior temp difference between floors of 3 degrees. So it would seem the increased buoyancy of the higher temps Woodstove heat is causing a more even distribution through the two floors.
I might hypothesize that this could be a difference between a furnace and a heat pump. The buoyancy of 140 degree air relative to 70 is different from 90 degree air. And that impact on convection (and corresponding mixing) may be significant. One of my HVAC teachers is always emphasizing mixing-- it's probably not happening nearly as much as we think it is.
That is an interesting thought. So with this hypothesis I should notice more warming upstairs when I run my Woodstove which will be putting out hotter air?
That depends on how mixed the air is when it gets to the aperture of your stairwell, assuming that's the main conduit for airflow to the upstairs. You could study this in a crude way with an IR camera. At least see the temperature gradients on the surfaces of your home.
is it safe to assume from your original post that you don't have any wall mounted units on the second floor?
have you given any thought to what your summers might be like?
I did consider putting a minisplit upstairs for cooling but we made it through the summer ok With opening windows at night and closing shades during the day. Not a huge demand for AC being in southern VT and 1400 ft in elevation.
Not yet (I'm from No Berkshire county)!
But you had then "planned on" this type of "stack effect" to keep the second floor "warmer"?
Yeah, based on prior personal experiences of being in homes with single heat sources on the first floor and it being warmer up stairs, I knew the stratification would be less because of the airtightness of the envelope but I still figured the temps would even out. Live and learn.
I didn't see it mentioned but by the context I assume that you're using a single mini-split indoor unit located on the first floor?
The saying "Heat rises" is a pet peeve of mine. All else equal, warm air tends to rise due to buoyancy, but heat (energy) goes to where there is less of it. There's a limit of how perfectly a system will balance those temperatures; you're still losing heat through your second floor building envelope.
What is the airtightness of the house? A really airtight house with the upper and main level open will have very little temperature difference between levels. I have observed this over the years with very energy efficient homes, ACH50 of 1 or less.
I can offer some insight on this. I'm in central/northern NH with a similar house setup as yours, but smaller (1500 sg ft) and no woodstove. A few degrees of temperature difference between the 1st and 2nd floor is what we've experienced and what I would expect (your measured 4 degree difference doesn't seem high).
When cooling in the summer, we put a Vornado DC fan (633DC) on a stool at the bottom of our stairway and it helps move the cooler/dryer air upstairs.
This isn't a perfect situation in winter or summer, but it works fine and is cheaper than installing another mini-split upstairs, although we might do that someday.
Thanks brp, it's nice to have another real world example.