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Building Science

The Fundamentals of Series and Parallel Heat Flow

The R-value of a building assembly depends on how heat can flow through it

This insulated wall is an assembly of cavities filled with insulation and wood framing members and covered with various layers of other materials. Heat flowing through different parts of the wall encounters different amounts of resistance, but we can describe the overall quality of the wall by an average U-factor calculated from an understanding of series and parallel heat flow.
Image Credit: Energy Vanguard

We used to build houses without giving much thought to heat flow through the walls, ceilings, and floors. The main thing was to provide some resistance against wind and rain, and then we’d get a fire going to try to make the indoor temperatures bearable.

If you’ve ever lived in an old, uninsulated house, you know that method didn’t work that well so later we started putting insulation into the cavities in building assemblies. Homes with insulated cavities are much more comfortable, but how exactly does heat flow through building assemblies? Turns out there are two ways.

Layers in series

One way heat flows is layer by layer through a building assembly made of multiple materials stacked together. The diagram below shows two layers separating the hot side from the cool side1.

This method of heat flow is pretty simple. All the heat has to flow through each layer. Starting from the hot side (because of the Second Law of Thermodynamics), the heat flows through the pink layer2, then the grey layer. With the caveat about one-dimensional heat flow below, the same amount of heat flows through any section of the assembly.

OK, here’s the caveat. It’s not really as simple as I’m making it out to be. It never is really, but we always have to start with the simplified cases and add complexity. In reality, heat flows in three dimensions, and we have to consider what happens at the boundaries. For this analysis, though, we’re considering heat flow in only one dimension. That means a red arrow represents the same amount of heat flow no matter where it enters the assembly.

If all our assemblies were like this, we’d have an easy time with the math for R-values: you just add…

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