Energy Vanguard Blog

U R A ΔT, and Other Building Science Blandishments

Posted by Allison Bailes on Mon, Nov 14, 2011

heat flow by conduction spray foam insulation in wallRemember that science class where you learned about the three forms of heat flow: conduction, convection, and radiation? Well, class, let's make it real today. You insulate your walls, floors, and ceilings to limit the amount of heat your home loses on cold days and gains on hot days. That tells us that the amount of heat flow depends on the stuff in the surfaces that make up the building envelope, but what else affects it?

This is where we have to do a little thinking. Without too much difficulty, you might figure out that size matters, right? A bigger house will lose more heat on a cold day than a smaller house, all else being equal. The third factor is the difference in temperature between inside and out. These three factors are tied together nicely in a simple, little equation:

heat flow by conduction equation

U is the quantity that accounts for the insulation and how well the materials conduct or resist heat. A is the area of the surface that heat is flowing through. ΔT is the temperature difference. Multiply them all together and you know how much heat flows through a wall, floor, or ceiling. Pretty simple, right?

To find the total amount of heat flow through your home, you just do this calculation for all the surfaces of the building envelope, the boundary between conditioned and unconditioned space. The answer will be in BTU per hour, where BTU stands for British Thermal Unit (an antiquated unit that the British no longer use). When we do a Manual J load calculation, our software does this calculation for all the surfaces in the house we model. The same thing happens in a home energy rating.

If U seems unfamiliar to you, maybe you've heard the term R-value. Those two are intimately related, and if you know one, you know the other. R tells you how much something resists heat flow, and U tells you how much it helps it. When you're trying to reduce heat flow, you want high R-values and low U-values. They're inversely related to each other:

heat flow by conduction r to u equation

heat flow by conduction u to r equation

The other really important bit of building science here is that heat flows from higher to lower temperatures. If it's warm inside and cold outside, your house loses heat to the outside.

heat flow by conduction wall diagram

It seems obvious to us, but that's only because our experience has conditioned us to take it as a fundamental truth. The universe didn't have to be this way, though. There's nothing but our observation that heat actually does behave this way that tells us that it must be so. In other words, heat from the cooler air outside won't start piling up on its own inside your house. That's a good thing because if it did, your house might just burst into flames for no reason. This observation that heat flows from warmer to cooler is one part of the second law of thermodynamics.

If you want to think about how weird this really is, meditate on the fact that only the second law of thermodynamics stands between you and suffocation. That's right. For the same reason that heat won't pile up in your house, all the air molecules in the room you're sitting in now won't pile up in one corner, leaving you gasping for air. According to statistical mechanics, though, it's possible.


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Tags: building envelope, building science, heating & cooling