#### 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.

##### OFFICIAL TRANSCRIPT:

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 U_{2} and A_{2. 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 [email protected] 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.

*—Allison Bailes is a physicist, HVAC expert, blogger, and owner of Energy Vanguard in Decatur, GA*

## Comments

## How much heat leaks through an attic hatch in a ceiling

Hi, Thanks for the video. It is good to continuously force these formulas in! After all- we'd be R&R mechanics without them!! I'll get to my question...

You didn't factor in the air leakage in an unsealed attic hatch. This could actually be a trick question because focusing on heat only kind of suggests using thermal calculations leading to R and U values as you suggest.

Lets say there is a 1/8" gap on 2 sides of a 24" x 24" attic hatch. So essentially we'd have a gap equivalent to 1/8" x 48 1/8" long or a hole approximately 6 square inches with surface area of 96.5 lineal inches and if the door is 3/4" thick then our surface area multiplies by 6.

Now we know that typically convective heat loss occurs much more aggressively than conductive heat loss, so the formular doesn't get the opportunity to work reliably until all the air sealing has been done. If you stated that somewhere in the video then I apologize for stating the obvious. I am not trying to be funny. I am trying to further my calculative abilities. I have a legitimate question. Thanks for your patience...

What is the formula to measure the potential air flow through that 6 inch hole? I can't fathom it as I would think pressure on the conditioned side vs. pressure on the vented attic side would come into play, as so many other things. I detailed the surface area thinking that friction may play a part. Actually you could forego all the technical ingredients to this formula. What is the simplest formula to calculate potential air flow through that 1/8" gap?

Thanks for hearing my question - I sincerely hope to get an answer. If that isn't possible for some reason then perhaps a lead on where to take that question for answering.

Regards,

Ron Wright

## You are correct,

Heat loss calculations like those do not take into account air leakage. And you are also correct that it will complexify the calculations because it will vary with pressure differentials. It would also depend on the volume of the house. But you'd probablty be more interested in all of the air leakage, rather than just the one hole, so ...

A blower door will tell you how leaky the house is (in air changes per hour) at 50 pascals pressure, which is an arbitrary number.

For more information on blower doors:## Adding air

Ron,

No, the calculations I showed do not include air leakage. In energy modeling tools, that's added separately. Also, air leakage is measured for the whole building enclosure with a blower door, not assembly by assembly. Then you have to do some extrapolation and use an infiltration model (typically the Sherman-Grimsrud model) to add in the heat loss/gain by infiltration. It's not an easy task.

The Thermal Metric Project at the University of Waterloo was an attempt to combine the effects of moisture and air with conduction. Unfortunately, they don't have money to continue the project at this time.

Also, you wrote, "convective heat loss occurs much more aggressively than conductive heat loss..." I'm not sure what you mean by this. In most houses, the conductive heat loss dominates.

## Parallel heat loss through steel studs

Your formula for parallel heat loss is straightforward and analagous to electrical resistors in parallel versus series, same idea, and it seems quite easy to see the issue with bridging members having uniform cross section. However, with steel studs there are larger conducation areas on the inner and outer surfaces joined by a relatively thin bridging member. MY guess is that the thinner bridging member offers greater resistance. Is this greater resistance only the result of the longer path through the conducting material, or is there some sort of "density" limit to the heat flux? In any case, could you advise the means to handle steel studs in your model?

Thanks very much.

## Steel studs are much worse than wood for thermal resistance

Gary,

Steel studs are excellent conductors of heat and energy. Thicker steel is better, but all of the steel studs I've worked with, they are the same thickness, just bent into a C-shape. Here's an image from BuildingScience.com

Oak Ridge National Lab has a paper on making steel stud construction more thermally resistant. It is a little old, but the physics have not changed. Here's a quote from the paper:

That's a pretty serious penalty. They also list some possible solutions (other than using wood):

You read the Building Science Corporation paper here:

I hope that helps,

Dan

## COMPARE 24 IN ATTIC FLOOR TO 7 1/2 IN SPRAY FOAM ROOF DECK

In the south, TX, it is common to have the air handler and duct work for an AC/Heat pump in a ventilated attic with typically 24 in of blown in insulation on the attic floor. This leaves the air handler and duct work exposed to very high delta T. In the summer on a 100 degree day the attic is often + 30 -40 degrees hotter or about 135 degrees or more if the attic is not power ventilated. With the air inside the air handler and duct work at about 55 degrees the delta T across the typical R6 ductwork and 1/4 in fiberglass matt on sheet metal air handler is a whopping 80 degrees. In winter with a 30 degree outside temperature, the attic is about 40 or maybe 50 degrees and the heat pump air is about 85 degrees so the delta T is about 40 degrees.

Now with 7 1/2 in spray foam on the underside of the roof deck and all ventilation sealed and no insulation on the attic floor the temperature in the attic is about 1-2 degrees cooler in the summer than the set point for the conditioned space, say set at 75 degrees the attic is 73 -74 and the delta T to the air handler and duct work is 18-19 degrees. I the winter with a set point at 72 heated the attic will be about 73-74 and the delta T will be about 11-12 degrees across the ductwork and air handler.

The concept of sealing the underside if the roof deck with spray foam insulation, especially if duct work, air handlers, water heaters or plumbing are in the attic, and leave the attic floor not insulated, seems far superior to me.

Do you have some formulas or comments for this situation?

My friend did this and cut his heating and AC costs in half! I did this and got about a 40% reduction because about 70% of my house has vaulted ceilings with only a 2X6 between the inside and outside and about 3 in of blown in insulation in the air space.

In the south, TX, it is common to have the air handler and duct work for an AC/Heat pump in a ventilated attic with typically 24 in of blown in insulation on the attic floor. This leaves the air handler and duct work exposed to very high delta T. In the summer on a 100 degree day the attic is often + 30 -40 degrees hotter or about 135 degrees or more if the attic is not power ventilated. With the air inside the air handler and duct work at about 55 degrees the delta T across the typical R6 ductwork and 1/4 in fiberglass matt on sheet metal air handler is a whopping 80 degrees. In winter with a 30 degree outside temperature, the attic is about 40 or maybe 50 degrees and the heat pump air is about 85 degrees so the delta T is about 40 degrees.

Now with 7 1/2 in spray foam on the underside of the roof deck and all ventilation sealed and no insulation on the attic floor the temperature in the attic is about 1-2 degrees cooler in the summer than the set point for the conditioned space, say set at 75 degrees the attic is 73 -74 and the delta T to the air handler and duct work is 18-19 degrees. In the winter with a set point at 72 heated the attic will be about 73-74 and the delta T will be about 11-12 degrees across the ductwork and air handler.

The concept of sealing the underside if the roof deck with spray foam insulation, especially if duct work, air handlers, water heaters or plumbing are in the attic, and leave the attic floor not insulated, seems far superior to me.

Do you have some formulas or comments for this situation?

My friend did this and cut his heating and AC costs in half! I did this and got about a 40% reduction because about 70% of my house has vaulted ceilings with only a 2X6 between the inside and outside and about 3 in of blown in insulation in the air space.

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