Wednesday 11 November 2015

Lesson 4. How to slow down heat

Some questions for starters:
How do you stop heat flow?
What is a "thermal envelope"?
What is "heat loss form factor"?
What can nature tell us about building a low-energy house?
Are there are situations when you don't want high insulation and low form-factor?

The first four were revising what happened the previous week. This was especially helpful for two of the students who had missed the last lesson. After reminding them of fourier's law, I started making things a bit more complicated. What if there are two different insulators? You know, like in the real world. Because you can't just make a building out of glass wool. I guess you could try to make one out of polystyrene, but it would probably break. Or blow away. 

First of all, and with the lobster fresh in our minds, I put a layer of glass wool on top of a layer of wood. I should have brought some actual insulation materials to the class to show the students what I was talking about, but I don't have any handy. I saw some bits of foam insulation on a building site yesterday, ready to go under the floor I think. If I go today, there may be some offcuts in their skip. I can probably work out better ways than prowling around builders' rubbish, but maybe not much better! And I wouldn't really want to bring glass wool to the class.

Anyway, absent of real materials, I used a powerpoint slide.
I told them about the R value, which is the inverse of the U value. This is resistance, and works just like resistance in an electrical circuit. This seemed to be familiar to most of them, not just the electrical engineer and the IT engineer in the class. In the same way as adding the resistors together, you can add up the resistances.

In terms of U value, it looks a bit more complicated: 1/U = 1/U1 + 1/U2 + ...

We have to remember it's upside down. This made one of the students laugh, as he remembered a scene in Pirates of the Caribbean. This equation is a bit like that. First you have to turn each of the maps (U values) upside down, then you have to turn the whole boat, I mean ship, upside down. 

Next I showed them some insulation in parallel. We used the same amount of insulation, but instead of a 100mm layer of wood on top of a 100mm layer of insulation, we had 200 mm of wood next to 200 mm of insulation.

Before starting the calculation, I got them to guess whether this would be better or worse than the last case, and they guessed it would be worse, so the U value should be higher. Sure enough, when they did the calculation it came out worse. 


Next, we delved further into the real world with a mixture of serial and parallel elements. 

There are two ways you can work this out. The serial method is to break it up into layers, calculate the R value for each layer, then add the R values. The middle element has 90% insulation and 10% wood, so you need to work out the U value of that by adding 9/10 of the insulation U value and 1/10 of the wood U value. 
The parallel method is to break it up into different bits of wall, work out their U values, then average those. 

I got half the class to work this out with the serial method, and the other half to work it out with the parallel method. I had hoped they would come up with their answers at more or less the same time, so I could then compare them. The two methods produce two different answers, and I was hoping for an argument to ensue, in which both sides would recheck their numbers, and insist they were correct.

In practice what happened was that the highly numerate students finished working out the first calculation, I suggested they try using the other method, which they also worked out, realised the two answers were different, and the less numerate students were still struggling with the first calculation. By this stage of the course, I should really have worked out which students were which, and paired the mathematical with the non-mathematical, so they would help each other, then go and help other pairs when both of them had finished. I did regroup them to some extent at the beginning of the lesson, but need to work a bit harder next time.  

So we established that the two methods produced different results. Here was another of those important lesson that has relevance way beyond low energy building. If you do two calculations and get two different answers, there are three possible reasons: one of the answers is correct and you made a mistake in the other one; you made a mistake both times; or you are using two different methods that produce different answers. Getting calculations right is a good idea, since you could be paying for the wrong answer in heating or cooling bills for the rest of your life. A few minutes checking the calculations is worth it!

So, the two methods gave different answers, and I wondered, in a rhetorical sort way, whether the formula for serial or the formula for parallel insulation was incorrect. One student suggested the parallel calculation was wrong because this wouldn't happen in the real world. Why on earth would anyone put insulation between bits of wooden structure? 

I had to tell him that alas, this was often the way insulation was used. Building structures are frequently made up of pillars, and builders see insulation as a magical ingredient that can be added at random to reduce the heat loss. Although this was the wrong answer, I was quite pleased that this student had learnt more about insulation in a couple of lessons than some architects seem to have in their whole careers.  

The parallel calculation is incorrect, not because it doesn't happen, but because there will be some lateral heat flow between the two kinds of insulation, so the heat is moving in two dimensions. For the serial insulation, heat is basically flowing in one direction, so fourier's law holds true. 

To work out what is really going on within complex structures, you need to use finite element analysis, and software like Therm. The computer makes a grid of squares and triangles, it calculates heat flow between each element, and repeats the process for every element several times until the numbers stop changing. Then it can tell you what the temperature and heat flux will be throughout the wall. You can see more details in my previous blog post slits in the envelope.

Then I got to the last question from the beginning of the lesson. In preparation for the lesson I'd been looking for a climate where you don't need any insulation. This would have to be between 20 and 30 degrees pretty much every day. The climate in the Caribbean is fairly constant and not too hot, but the best I found was in Ecuador and Columbia.

Everywhere else either gets hot or cold, or both.

40% of power in Mumbai is used for air conditioning, and it has been estimated that by 2060 the energy used worldwide for cooling will exceed the energy used for heating. The US, original home of the air conditioner, and country of vast wealth uses more electricity for cooling than Africa uses for everything. If I had invented an air conditioner and was wondering which continent needed it, I would have made a different choice!

Air conditioning may seem like a great idea for individuals with a bit more cash in their pocket who want a bit more cool in their lives, but it's a bit of a disaster for global warming. As well as the energy used by the air conditioners, often from coal-fired power stations, the refrigerants used in the air conditioners are often 4,000 times worse than CO2 as a greenhouse gas. 

And of course more energy use and more refrigerants leaking into the air will lead to hotter temperatures and more need for air conditioners. 

People often think that insulation will make buildings hotter in the summer, but insulation does not make anything hotter. It just slows down heat flow. So if it's cooler inside and hotter outside, then less of the heat will get in. Of course there are differences. Many things in a house create heat, such as electrical appliances, hot water and people. If you are in a heating situation, these are all on your side and will reduce the amount of heating you need. In a cooling situation these are all enemies for which you need extra cooling. 

Also, colder places are a lot colder than hotter places are hot. The average winter temperature in Yakutsk, probably the coldest city in the world, is -34°C. The average summer temperature in Kuwait is 38°C. There seems to be some symmetry to these numbers, but remember the temperature we want to live in is around 25°C, so Yakutsk is four or five times further away. Also cold weather seems to be more deadly than hot weather. 

We tend to think of Australia as a hot country, but cold weather kills more people in Australia than hot weather does. However, we should also note that more people die of cold in Australia than in Sweden. Almost twice as many. Sweden is not a hot country, but Swedish houses are insulated. If Australia insulated its houses less people would die. People who aren't paying with their lives would pay less on their heating bills. If Mumbai used more insulation they would use less energy for their cooling. 

I didn't have time but was hoping to talk a bit about thermal mass, and whether that can be used instead of insulation. The short answer is that it can't. 

So far we've got to the following implications for the basic design decisions: keep form factor low, put insulation on the outside, and beware of thermal bridges.

References and further reading:

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