Small holes and framing members make a difference when calculating the heat flow through building assemblies like walls, floors, and roofs.
Dr. Allison Bailes, aka The Energy vanguard, explains the difference between series and parallel heat flow: heat that flows through layers of an assembly, and heat that flows through different paths of the assembly. Does thermal bridging really add up to heat loss? Or is a small gap in the insulation more important?
The answer to both questions: Yes.
This is video number 10 in the building science module and I am Allison Bailes of Energy Vanguard, here to guide you through this lesson on series and parallel heat flow.
Let's start with the easy case of series heat flow
This is where you have an assembly made up of different layers. The layers separate the hot side from the cool side, so the heat has to travel through every single layer from the hot side to the cool side.
That means that the amount of heat flow is going to be the same no matter which path it takes and the R-values in this case will add. So the total R value is going to be the R-value of layer A plus the R-value of layer B. That's our total R-value. It doesn't matter how many layers we have, we could have a hundred layers here, we just add up all the R-values.
Let's look at a quick example. Let's say we have foam board that has an R-value of 10 and we put that on a concrete foundation wall that has an R-value oif 1. Its very simple, the total R-value is ten plus one, or eleven.
We've got an R-11 foundation wall by putting that foam board on it. Series heat flow.
Parallel heat flow: rather than layers, we have pathways
The pathways are choices that the heat has—the heat can go either through one path, or another. The amount of heat that travels through the assembly depends on which path it takes. The way we handle this is to average the U-values, and we do that with this formula:
In this case, we have only two pathways, so we're going to multiple the U-value for 1 and multiply it by its area, and then add it to the multiplication of U2 and A2. we do all that math on the top and then divide by the total amount of area and that will give us the average U-value.
This works for any number of pathways, I've shown it here with two pathways (studs and cavity insulation) but it would work for fifty pathways.
Let's look at an example of parallel heat flow.
We have an attic floor that's 1000 square feet total; 990 sq ft of it has R-38 insulation, and we have 10 sq ft of attic stairs that's uninsulated, and we're going to call that R-1.
We apply the formula, remembering that we are given R-values here, but we need U-values, which is 1/R.
So doing the math, we end up with an R-value of 27.7.
The takeaway here is that 1% uninsulated area can have a huge effect on your heat flow (more than 25% loss of R-value).
Now, let's look at series and parallel heat flow
This is more complex and more realistic because most of the time we do have series and parallel heat flow.
Let's consider a ceiling assembly:
- 1,000 SF area
- 2x10 joists@16 in. o.c. (R 11.5)
- R-30 insulation blown between joists
- Drywall (R-0.5)
- Relative areas:
- 9.4% of the ceiling area is taken up by joists
- 90.6% of the area is taken up by insulation
- Areas: 9.4% of 1000 = 94 sq ft, 90.6% of 1,000 = 906 sq ft
The first thing we do is look at the pathways and add the R-values in each pathway.
If path 1 is through the ceiling joist and the drywall, we add R-11.5 + R 0.5 = R-12, the area is 94
In path 2 (insulation and drywall) we add those R-values too (R-30.5), and the area is 906.
Then we convert the R-values to U-values.
[(94/12) + (906/30.5)]/1000 = 0.038 U-value, or R-26.6
So you can see the framing does have an effect, it lowers the R-value from 30 to 26.6 — a little more than a 10% penalty, but overall it is not nearly as bad as having the 1% uninsulated area that we had in the previous problem.
So that is a quick introduction to series and parallel heat flow. In energy modeling, we use this stuff all of the time.