Is heat loss a linear or parabolic function?

[btuser]

I'm trying to predict the future. I'm keeping a daily log of fuel usage this year. No, I'm not employed, just not drinking right now.

If my indoor design temp is 70f, and my outdoor temp is 40 degrees, do I burn twice as much wood when its 10 degrees (double the differential), or is it more? We've all been in the house during a nasty cold snap (-20 degrees or so) and felt the cold air clawing it way in through cracks and holes we wouldn't have thought were there.

My guess is it takes more than twice as much to heat a house when its twice as cold. Does anyone know?

 

[sgschwend]

As you have pointed out your heat loss is a combination of losses, therefore it is neither. Your losses are unique to your system which includes the exterior conditions, the building, air movement, solar, air leaks an on and on.

I would guess that most folks use a linear model and assume the best.

 

[btuser]

As you have pointed out your heat loss is a combination of losses, therefore it is neither. Your losses are unique to your system which includes the exterior conditions, the building, air movement, solar, air leaks an on and on.

I would guess that most folks use a linear model and assume the best.

My only variable under consideration is outdoor temperature. I'm assuming the solar gain/wind/ect are the same from one day to the next. I just tried an online heat loss calc and just adjusted the design temp and came up with a linear relation. Now, I will admit there is less and less Solar gain until the Winter equinox, which goes along with the drop in temp over the months in the NorthEast.

 

[PJF1313]

I'm trying to predict the future. I'm keeping a daily log of fuel usage this year. No, I'm not employed, just not drinking right now.

If my indoor design temp is 70f, and my outdoor temp is 40 degrees, do I burn twice as much wood when its 10 degrees (double the differential), or is it more? We've all been in the house during a nasty cold snap (-20 degrees or so) and felt the cold air clawing it way in through cracks and holes we wouldn't have thought were there.

My guess is it takes more than twice as much to heat a house when its twice as cold. Does anyone know?

...but I am

I am new to the forum - Hello ya'll boys and girls!

But you may also have to take the relative humidity also into effect. I don't know how damp it is where you are, but living on an
island, it does play a factor on how cold it IS and how cold it SEEMS.

Just my .002 (inflation adjusted) worth....

 

[btuser]

I am new to the forum - Hello ya'll boys and girls!

But you may also have to take the relative humidity also into effect. I don't know how damp it is where you are, but living on an
island, it does play a factor on how cold it IS and how cold it SEEMS.

Just my .002 (inflation adjusted) worth....

My thermostat doesn't care what the humidity is. I agree its much more comfortable at the right level.

 

[tom in maine]

It is linear, except if your house is real drafty and it is real windy.

 

[stee6043]

As you have pointed out your heat loss is a combination of losses, therefore it is neither. Your losses are unique to your system which includes the exterior conditions, the building, air movement, solar, air leaks an on and on.

I would guess that most folks use a linear model and assume the best.

My only variable under consideration is outdoor temperature. I'm assuming the solar gain/wind/ect are the same from one day to the next. I just tried an online heat loss calc and just adjusted the design temp and came up with a linear relation. Now, I will admit there is less and less Solar gain until the Winter equinox, which goes along with the drop in temp over the months in the NorthEast.

Much of engineering and physics involves "getting close". That's what most online calculators attempt to do as well. The physics involved in heat transfer through your house is far from linear and outside air temperature is far from your only variable. Different materials display different heat transfer rates and different temperatures and pressures. Some may be measurable, some may not be. Arguably the most critical "variable" in your equation is the difference between the inside temperature and the outside temperature. The equation to solve for rate of loss in this situation is likely so complex no sane person would do it without a computer.

And for what it's worth - even if we were to simplify the heat transfer it would never be "parabolic". For a function to be parabolic you would have to have 2 solutions for every value of your independent variable (you state this should be outside temperature). It's more appropriate to say it is simply non-linear. The equation to solve for "heat loss" I suspect would be considered a differential equation.

 

[tom in maine]

For the sake of discussion and not to split hairs, if you are trying to estimate wood consumption,
I think it is safe to consider it linear and leave it at that.

Yes, it is not linear in the realm of physics, but
anyone who is doing heat load analysis' is going to mostly look at a linear model (except for infiltration).
IMHO, the rest is academic and the realm of academicians and physicists.

 

[btuser]

Ok Ok, 1/2 parabolic. I'm thinking of the "parabolic curve". To me it seems once it gets really cold (-5 or below) there's an acceleration in fuel use that is definitively non-linear. I'm curious about the behavior of insulating materials in relation to temperature. What works best when it gets worst?

 

[tom in maine]

Fiberglass and to a slightly lesser degree, cellulose and other fluffy insulations tend to have some convection within their structure that is enhanced
as the temperature drops. Foam insulation or foam over fluffy insulation tends to mitigate the problem.

Most energy codes are minimums, which builders accept as the standard. A super-insulated building makes everything much simpler. Heat loss drops way down and the amount of wood you have to handle goes down accordingly. And the parabolic or exponential effect diminishes.

Unfortunately, a R-19 fiberglass insulated wall is not as effective as a R-19 foam insulated wall.

 

[EL DRIFTO]

btus r btus & it's linear.
the slope you're imagining is probably the fact that most homes lived in have significant electric resistant heat coming off every circut, all stays in the house.
then there' the heat coming out of a basement, that's higher than 0 if you leave the heat off entirely.
underground stays same temp year round, but you'd be capturing heat from the earth @ 45, not putting it back in.
i completely shut my heat off one winter & the coldest the house ever got was 45, upstairs, even when it was 0 outside.
two of us were living in the basement.
a shower would steam the entire house & you could barely get the tooth paste out of the tube.

when the inside of the house is 45 & the average temp is 20 throughout the day, the differential is so low that any heat will stay in.
when it's 75 inside & 20 out, the difference is 55 degrees & the differential is looking @ frozen water on the inside of a window.