Thermal mass can warm your home, if you let it

Apparently “heat pumps don’t work in older buildings”, yet heating engineers keep reporting that, not only do they work well, but that they often perform better than expected, with lower consumption, and lower peak loads. 

I’m convinced that something crucial at play here is the thermal mass in the building. 

Thermal mass refers to materials in buildings absorbing, storing, and then releasing heat. These older buildings tend to have thick stone walls and often have stone floors too - which means they have a lot of thermal mass, by weight, and also by surface area. 

I explored the effect of thermal mass on heating by very simply modelling heat transfer in buildings during a period of cold weather. This is a very complex area, and my approach is overly simplistic and inaccurate, yet I’m happy enough with it as a first try. It points to areas for further investigation and wider concepts to consider. 

I discovered that it's very easy to create self-referential loops which then make the whole spreadsheets error! 

As the temperature of the house drops the heat starts to move from the brick into the house, but the bricks are also dropping in temperature which slows the rate of transfer, and the house is also changing temperature which in turn affects the rate of transfer, and so on and so forth.

The transitions in temperature that I have used are inaccurate - I am assuming stepped transitions between temperatures. But of course they change continuously and smoothly. This is exactly what Newton co-invented/discovered Calculus for - to model changing variables and their accumulative effects - the areas under a curve on a graph. But I've forgotten my calculus and only wanted to take a very rough look at this, without having to take the time to relearn calculus. So we can learn some general things from this, but it's not super accurate.

The external walls are tricky - they lose heat to the outside world, and to the inside of the building at the same time, with the temperatures on each side, and of the wall itself, all changing all the time. So I ignored those for the moment, and “cheated” by only considering a block of mass inside a building. 

I assumed that everything in the building, including the mass, was all at the room temperature of 21ºC.

The temperature of the building needs to drop to below 21ºC before heat can flow from the thermal mass into the building. So the outside temperature needs to have dropped to the point where the heating system can't keep up.

My imaginary house has a peak heat load of 8kW when it’s -4.3 outside, and has a heating appliance which delivers up to 8KW regardless of how much colder it is outside. -4.3 is the “outdoor design temperature” - this is the calculated coldest temperature which we then use to size a heating system with. The outdoor temperature will drop below this at times, but these are very rare events and tend to happen for a few hours at a time and at night/early morning. 

I also assumed that the “base temperature” of the house was 15.5ºC. When the outside temperature drops below the base temperature then the heating will need to be on. Above it and no heating is needed. 

I used outdoor hourly temperatures from the Birmingham airport weather station. Here the outdoor design temperature is -4.3ºC. On Wednesday 14th at 8pm December 2022, it started to get really cold, getting as low as -8.7ºC. The temperature goes up and down a bit, but only really warms up on Friday at 11 in the morning. 

These drops are usually quite short lived events of a few hours, the one I chose here was the longest and coldest period I could find for Birmingham in 2022. 

I imagined there were 14 tonnes of bricks in the internal walls with a surface area of 85m² which probably isn’t that far off of the internal walls of some brick townhouses.

The U-value of the bricks is a limiting factor. The brick potentially contains 3.27 kWh of heat for every degree of temperature difference. But the maximum transfer rate turns out, for the area of the walls being modelled here, to be 0.4 kWh per hour, per degree - so there’s a source of heat there, but it just can’t get out very fast.

Next I compared that to pillars of water in copper tubes, 400mm in diameter and 2.5m high. Just the water in these would weigh 6.3 tonnes, and have a surface area of 21m².

There are two reasons I chose copper pillars of water. Water has a high specific heat capacity - it takes a lot of energy to heat it up, 5 times more so than the brick, and once it’s hot there is a lot of potential energy there. Both copper and water conduct heat very well, more than twice as well as the bricks. 

For the copper pillars we have the opposite relationship between the potential energy they contain and the transfer rate. They potentially contain 7.33 kWh of heat for every degree of temperature difference, but the maximum transfer rate exceeds that at 8.29 kWh/hr/degrees - so the potential heat from the copper pillars of water can move much more quickly into the house. 

We can see from the graph that as expected the thermal mass slows the speed at which the building cools down, and means that it doesn’t get as cold. 

Whilst the water columns in copper do end up making a significant heat contribution to the building, it also seems unlikely that many people will incorporate those into their home. Using the thermal mass of the materials that make up the house on the other hand seems a much more practical solution. When we want to make use of the thermal mass of a material like bricks in a building, then it’s helpful to remember that the surface area is crucial as that is the limiting factor to how fast that heat can move in and out. 

In this very simple modelling at the coldest point when it’s -8.7ºC outside with no thermal mass the indoor temperature drops to 15.3ºC, with the brick it is 16.4ºC, and with the water in copper cylinders it’s 17.65ºC; quite a difference. 

Of course the thermal mass also slows down the rate at which the building warms up again afterwards, but then as it also didn’t get as cold inside in the first place, perhaps that is the lesser of two problems?

Two things that are of note to me, and sort of obvious once you consider them are: 

1

The rate at which heat can get from the thermal mass into the building can be a limiting factor. To increase heat transfer you would either increase the surface area, or change the material to a type that transfers heat faster. 

2

You have to allow the building to cool down to get the benefit. For example a night time setback achieves that, and/or slightly undersizing the heat pump would too. 

Next I plan to delve a little deeper into some real energy monitoring data to see if I can find any tell-tale signs of thermal mass at play.