Heating the Slab – an overview

I have no idea whatsoever what you are talking about in your topic thread on modelling your slab? — joe90 on the Buildhub Forum 27/01/2017 at 09:52 [link added -TE]

We have a passive-class house where the net heating requirement to keep the house warm in the coldest winter months is approximately 1kW.  The only heating system for doing this an underfloor heating (UFH) system base on 3 ~100m UFH loops buried in our passive slab.  That’s it; no upper floor systems; no towel rails; nothing.  The reason for this is that our timber framed house is super insulated and air tight so there is very little temperature variation throughout the house, but that’s all been covered in earlier posts.  What I want to do in this post is to provide a simple explanation of how I am going to heat my house and how this works so that John (@joe90) and other forum members understand my approach.

This basic heating strategy was first evangelised by Jeremy Harris), but variants have been adopted by other forum members and their consistent experience is that it works and works effectively for this class of passive house.  However, what I am doing is a slight variation on Jeremy’s approach:

  • I am using the slab itself as my main heat store, so no buffer tank.
  • I will be heating it by circulating warm water through the UFH loops and this water will be heated by a simple small inline 3kW electrical heater element.
  • The heating charge will normally be done as a “chunk” once per day during the E7 cheap rate period to take advantage of low tariff rates.
  • However, I am also including in the design provision for the later addition of an ASHP, should the heating data collected over the first year show that there is a 10-year payback in doing this.

As I said, Jeremy’s approach has been well documented by him in his blog and by others.  He has recently described that his system settles down into a repeating pattern over the colder winter months winter where his heating comes on for a few hours once a day in the early morning, and the heat in the slab is topped up during this period.  This is broadly what I call “chunk heating”: unlike a traditional house central heating system which is turning on and off pretty continually, the heat losses in our type of house are so small and the house has such a high thermal inertia that you can heat the it practically with a single daily top-up to the slab; this heat then “trickle feeds” into the house over the day.  Yes, there is a slight residual ripple on the temperature in the house, but this is less than a 1°C undulation over the entire day and so this isn’t really perceptible to the occupants.

I am adopting this same approach, but shifting my heating period earlier so that it ends at the same time as the E7 low rate tariff ends.

The main difference in my implementation is that I am heating the slab directly without a buffer tank. I wanted to get my head around this before committing to this decision,  so I modelled this in some detail and covered all of this physics and modelling stuff in my Boffin’s corner thread.  This modelling has persuaded me that the mechanisms and dynamics of heating are pretty simple, and so in this post I want to cut out all of the equations and stuff (with one exception) and focus on describing what happens in plain terms.

First, I am using a small 3 kW electric element to heat the water circulating in the UFH loops (the same type is used as a hot tank immersion heating element).  Just like an electric shower this heats the water stream a step in temperature. Sorry I am a boffin, so I will call this temperature change ∆T.  (BTW, the triangle is just the Greek letter D and is short for difference; blame Isaac Newton for that one.)  Just like an electric shower, double the power and ∆T doubles; double the flow rate and ∆T halves, and if I do the sums for a typical flow throw my UFH loops, and for a 3 kW heater then ∆T works out at about 1.6°C for my system — a lot less than a typical gas-boiler fed UFH installation, but my heater is puny in comparison.

So if I start pumping 3kW of heat into my slab, then the system settles down after about 10mins and the heat output is pretty much the same along the entire  3 × 100m runs of UFH pipe, pipe work, that is each 1m of pipe dumps about 10W of heat into the concrete.  This lifts the temperature of the concrete, and at the same time cools the water in the pipe pretty steadily along its length so it comes out at 1.6°C cooler than it went in.  But cooler or hotter than what?

The heat flows radially away from the UFH pipe creating a thermal gradient. [Boffin bit warning, and the only one] this gradient is pretty close to what is known as the steady state radial solution to the 1-D heat equation, which has a formula Tr = Tp – A.log(r/rp). where T is the temperature and r is the distance from the pipe centre, with the p subscript relating to the pipe/concrete interface. The A term is a function of the amount of heat flow.

The main thing to note here is the general shape of this gradient: the temperature of the water ends up roughly 4-5°C hotter than the slab average for this sort of 10W/m value, and the temperature in the concrete falls away rapidly as you moving away from the pipe towards the average slab temperature.  Since the volume of concrete goes as r2, the actual proportion of the concrete more than 1°C hotter than slab average temperature is small.  So the overall effect of the heating is to slowly lift the average slab temperature.  There is also a general heat gradient along the water in the pipe but once you get more than a few cm from the pipe centre the concrete is all within 1°C or so of the slab average.  There are also local hot regions around the UFH pipes up to 5°C or so hotter than the overall average slab temperature.  However, this is factors less than you will get with a conventional UFH system.

A key difference of Jeremy’s approach is that the water continues to recirculate after the heating is turned off, and now the water flow acts to redistribute the heat rapidly along the pipe levelling the previous 1.6°C gradient; at the same time (without the heat being pumped from the UFH pipe) this central warmer region rapidly flattens out as the heat flows outward, and within an hour or so hardly any heat variation remains and the entire slab is within ½°C of the slab average temperature.  A good analogy here is pouring water into a bucket: the surface level steadily rises as you pour it in and the surface itself is a bit churned up by the act of pouring, but as soon as you stop pouring, it rapidly levels out to flat surface.

OK in a real slab this is also complicated by the deep elements (the unheated ring beams in my slab are over a third of the total volume) and the heat does flow into these largely thanks to the high thermal conductivity of the rebar.  But overall, the slab is acting as a heat battery soaking up the power that you pump in.  The trick is not to put a somewhat arbitrary limit of the maximum input water temperature (say 25°C) as this will limit the amount of power that you can apply.  This heat gets quickly spread uniformly throughout the slab.

By the end of the heating period, the slab is 2°C (or whatever) warmer than the room temperature, and is starting to transfer heat into the room fabric at ~15W/m² whilst itself slowly cooling.  This is more than the external heat losses in the house, so this heat both warms the air and the rest of the wall fabric.  This creates a very slow rise and fall in the room temperature over the course of the day — of roughly 1°C.  But so long as you put in enough heat each night, the overall house temperature remains stable.

So how much is “enough” heat?  In my case I use a very simple strategy.  I am using the UFH circulation temperature at midnight as my test.  If it is less than the previous night, then I add a bit more heat than last nigh and v.v.  Simple really.

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