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Modelling Thermal Lag



I was really unhappy with my discussion of this on my last blog entry, so I want to get a better quantitative understanding of how this would impact my house design, so I decided to write a simple 1-D explicit form finite mesh simulation which could be used to explore various wall and roof profiles. I initially intended to do this as a spreadsheet so that others could have a play with their own designs but without needing to get into code and programs, but stability issues means that the mesh size was just too small for this to be usable, so I ended up coding this up as a program.  (Save this wall-thermals_c.txt as a C file.)  The source is fully documented inline so I won't repeat this here. It's simple to compile and run on any system with a C compiler, e.g. Linux / Mac / Windows with MinGW. If it is useful and there is a consensus for an alternative language then I'll port it.


If anyone is interested, then I can post some sample graphic analysis, and also reflect any comments later. But some general observations:


  • The thermal lag through my walls is measured in days not hours. The wall acts as a huge filter to remove even daily fluctuations, so don't worry about sizing heating for worst night-time conditions for ~0.14 U-value or less walls. You need to think of time averaging any external temperatures over days not hours.
  • You really don't want to think about saving heating, when you go away on holiday. I looked at how long it took to heat the walls up on a typical February day from cold limiting the heating to 6kW. The walls just sucked that heat in and it took over a week to get the to the point where they were still warming towards a steady-state thermal profile but at double the base heating load!


These are a couple of profiles for a daily 0 - 10°C external cycle. Note that I will have an external stone skin which does nothing in terms U-values, but does act as huge thermal damper of heat variations. There are significant heat flows in the walls, but the second plot show the "one sigma" for these as a function of depth in the wall. There is bugger all ripple getting through to the internal walls. (Windows have no thermal lag so if you have large areas of window in your house then this won't be the case.)


TermperatureByDepth.png  HeatFlow-StdDev.png

I still want to do a bit more playing to look at the effects of solar gain, etc., but anyway if you can read C (the code should be understandable to anyone who knows Fortran / Basic, etc.) or the code documentation, then have a browse and tell my what you think.

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Here are the key elements in the discussions following this post:


jsharris Posted 26 October 2014 - 09:28 AM

This tallies well with my direct experience. Our internal wall temperatures don't show any diurnal variation that I can detect by ad hoc testing with an IR thermometer. There is very little difference in wall temperature between the North and South internal walls, for example, The house seems to be exceptionally temperature stable as long as the external doors and windows are kept closed, with the exception that solar gain does have a significant impact in heating the house through the windows at times.

I'm coming around to the view that floor temperature control may not need to be very sophisticated, and almost certainly doesn't need weather compensation. I suspect that just manually setting the floor to close to the desired room temperature (maybe a fraction of a degree warmer in winter) and then letting the active bit of the MVHR do the fine control will be the best strategy. The active MVHR can warm the house by half a degree pretty quickly when needed, I've found, even though the air flow rates are modest. I tested this last week, after I'd left the front door open for 20 minutes or so whilst cutting some skirting out in the garage and found that the house had dropped to around 19 deg C. The floor was at around 19.5 deg C and when I would the MVHR thermostat up to 20.5 deg and turned the fans to speed 3 the house gained half a degree in around 20 minutes or so, such that I turned the MVHR back down to passive mode, trickle ventilation and the house then sat at its usual 20 deg C or so.

This shouldn't be surprising, as the effect of the additional heat from visitors is easily detectable (as anyone who'd visited may have spotted). An extra person or two in the house tends to increase the temperature slightly after half an hour or so, just from their body heat.

TerryE Posted 26 October 2014 - 11:03 AM
One of the things that isn't covered in the discussion of wall specs is this thermal lag effect. Clearly we need to balance overall U value with the wall thickness (which in effect removes usable living space) and unit cost of the wall itself. But the thermal lag is largely dictated by the ratio of the specific heat to thermal conductivity. Cellulose filler is a very good material in that it has a very high specific heat for its conductivity (compared to PIR say). This gives it excellent lag properties. Once the lag through the wall is over a day or two, as you observe there is almost no observable diurnal variation observed on the inner wall.

Another thing which isn't immediately obvious is that whilst clear cavity gaps have almost no effect in U value calculations, they are important in acting as a rate limiting barrier for heat flow. You can see this in my Std Dev of thermal flow where my airgap is at 30-35cm between the stone outer and the frame inner. In the case of your wall profile, Jeremy, the stand-off between the wood cladding and the frame helps limit excess solar gain through the wall fabric itself.

My views re windows echoes yours: windows are necessary if you need the light or if you want to see a "to die for" view, but don't put them in just to have a view of the neighbours gardens or houses. Thermal gain though windows is totally uncontrollable as are the thermal losses.
TerryE  Posted 26 October 2014 - 06:10 PM
I just looked at the impact of sunshine on the surface of my wall. Roughly 99% of the energy gets re-radiated or convected back off the wall surface, and again roughly 1% ultimately makes its way through the insulation to the inside and warming the house, or more strictly the extra heating reduces the otherwise heat loss, but the mode delay is 6 days!!

jsharrisPosted 26 October 2014 - 06:15 PM

Compare that to a really good window....................

TerryE  Posted 28 October 2014 - 09:27 PM
Jeremy, I think that I might be getting too anal here, but I've think got a pretty good handle on the whole thermal lag issue now: it's just so large that you can almost just ignore any daily temperature variation and you really need a material step change in temperature of days for it to start to make any difference. As we've just said, the main control challenge in terms on unpredictable variations in heat loss are the solar gains from an windows -- and black-body radiation out of them at night.

What I have been trying to get a better handle on are the feedback mechanisms relating to unpredictable variations in internal heat sources -- your vacuum cleaner challenge. It seems that we have two overall feedback mechanisms: surface coupling and air control.

In terms of surface losses, I will typically have ~1 W/m² heat loss though my walls (including sloping roofs) in the milder winter months, and maybe 10x this through my windows (albeit with less than 10x the total area). This surface transfer is a mix of radiative and convective heat losses. The radiative loss is essentially driven by the Stefan–Boltzmann equation. The T^4 delta is practically linear for small ΔT around 20°C (293K), and cranking the numbers for black body radiation gives 5.72 ΔT W/m²K. OK, wall plasterwork isn't black body, but for most matt surfaces it will be 60-80% of this.

The convection element seems to be another "proportional" to ΔT rule of thumb, except that the "constant" is itself a function of ³√ΔT for a still air assumption. Even so, the linear term dominates for small ΔT around the ~1 W/m² heat loss centre point, and typically maybe 40-60% of the radiative amount, giving an overall ballpark of 8 ΔT W/m²K, or roughly an eighth of a degree delta between the wall and air temperature at steady state. The actual value (8 quoted here) is pretty much secondary as if this was only 4, say, then the wall surface temperature drop would be a whole 2x greater at ¼°C! The main point is the the linear term dominates in this feedback, and that the rough scale is as I've discussed.

Our living room has roughly 50m² of wall and ceiling and another 20m² slab under foot, so an extra couple of warm bodies would raise the temperature maybe ½°C before reaching dynamic equilibrium again. My answer to the hoover effect is that we're getting a couple of Dyson battery cleaners -- less power and less time before the battery runs out

However the time constants are sufficiently separated from those of an active MVHR (even with 0.5 ACH, say) that as you say, setting the slab setpoint weekly, say, depending on overall weather trends and using active heating/cooling of the MVHR input -- or even just controlling the bypass mix should give an adequate level of control.

SteamyTea  Posted 28 October 2014 - 10:48 PM
I have been looking at this very issue for years. I soon seem to go around in circles.  Some analysis of temperatures, solar radiation and windspeeds I did over on the 'other place' seemed to show a better fit between windspeed and temperature loss that anything else. Trouble was I bored people with it and was not getting feedback.

I am willing to see how long it takes to raise the temperature by running my vacuum cleaner tomorrow. I need to tidy up as I have been fitting multiple temp and RH sensors around the place, along with a weather station and a more accurate energy monitor. So should be able to get the data.

I do seem to remember that the equation for thermal inertia is very sensitive to 'shape'. Physicists will make any shape a sphere to make life easy.  I do have my 5 sided box made, the 6th side is for testing materials and their properties. Just been sidetracked for the last few weeks with other things. But willing to share data and experiment design if it helps.

TerryE  Posted 28 October 2014 - 11:58 PM
I am fairly comfortable with the cp, ρ and K coefficients and the 1-D finite element approximation. It's getting a handle on the surface transfer modelling and how that's going to interact with the variability of heat inputs and the consequential air temperature.

In one aspect I differ in my personal tastes / tolerances from Jeremy: I have a place on a Greek Island where I spend 3 or so months a year: I am used to living temperatures in high 20s and low 30s indoor. I don't really see a 2-3 variation in room temperature as a big issue -- but as Jeremy will no doubt point out: anticipation isn't the same thing actual experience.

I'll still be interested in your vacuum tests. You could even stick your wall profiles into my little C program to see if its response curves are similar to what you find with your house :)

SteamyTea  Posted 29 October 2014 - 07:20 AM

When you put the wall surface in, do you take into account the texture. This could easily add an extra 30% to the area of an external wall.

TerryE  Posted 29 October 2014 - 11:03 AM

Nope, but it's a good point and could largely balance out the non black-body effects. The main point here is that the heat loss is predominantly of the form h.ΔT. I've played around picking h values between 4 and 12; it doesn't make a material difference to the macro response of the system, just the that the wall is at 19.6 °C rather than 19.8 °C, say, for an internal room temperature of 20 °C.

SteamyTeaPosted 29 October 2014 - 11:23 PM
Have you read this:  http://lup.lub.lu.se...fileOId=2518433 About 100 pages.

TerryE  Posted 30 October 2014 - 10:18 AM
For the benefit for others, this is a detailed academic analysis of the "Possibilities of using thermal mass in buildings to save energy, cut power consumption peaks and increase the thermal comfort" by a researcher from Lund University. The main paper is 50 pages long and it includes as an appendix other paper of a similar size.

Thanks, it's an interesting read. I've just had a quick scan because I am visiting friends at the moment. I'll have to go through it in detail. But it largely echoes what I have discussing here, in various other posts and in my blog entries. I'll have a proper read over the net few days and either post back here or reflect it in my blog. Going for a decent walk with friends now.
SteamyTea  Posted 17 November 2014 - 09:02 PM
Been playing over at the other place and as usual the topic came to inter seasonal storage and how the ground under the house can be helpful.  As I know it can't, and felt I had to show this yet again, I quickly knocked up a little model in LISA, then made a video of it.  Here it is, it shows that there is hardly any thermal penetration: Youtube - Thermal Inertia
TerryE  Posted 18 November 2014 - 01:46 AM

Unfortunately LISA is closed source and windows only. I am wary of the former and don't have any machines running the latter so I can't play with this myself.   However, I agree with your conclusions. IMO the one thing that the ground is good for is as a semi-infinite (at a domestic house scale) heat source / sink that could easily be used as a heat sink for those using a gas heated low-temperature UFH slab to allow summer cool down within the house.

SteamyTea  Posted 18 November 2014 - 07:02 AM

Yes, a large mass is good for keeping a place cool.

jsharris  Posted 18 November 2014 - 07:40 AM

There are some very stubborn folk, who should know better, that have persistently argued elsewhere that the ground doesn't act as a semi-infinite heat source/sink, though. Some insist that the ground under a house can be used as a seasonal thermal store, even. I stopped trying to make the point that the thermal conductivity of soil was such that it simply wouldn't stay warm for long if heated up above the temperature of the surrounding ground, as even an architect was arguing that I was wrong.
SteamyTea  Posted 18 November 2014 - 07:53 AM
I am still arguing with that architect, its fun when there is nothing else to do.

DavidFrancis  Posted 01 February 2015 - 05:01 PM
Terry - I couldn't follow the detail of everything you said above. Would it be much work to produce a small table showing your expected heat losses in your new house assuming an internal temp of, say, 20C and an external temp of zero? The table would show the losses from radiation, conduction and convection for windows on the one hand and roof/ceilings, walls and floor on the other (assuming there's not much difference in any of these three last mentioned elements). And would there be any difference between daylight and nighttime losses if there were no blinds/curtains/shutters?

Many thanks if it is possible.
TerryE  Posted 01 February 2015 - 11:17 PM
David, have a read through my blog posts on my thermal design where I have already given this sort of detail. Ditto Jeremy's. Amongst these and the various discussions in the threads, you'll find days of provoking reading

Do you see how my two graphs in my first post work? What I've done here is to solve the 1-D heat flow equation for my wall profile in the somewhat artificial case where the air temperature is a sine wave from 0-20°C over the day. The result is just the output profile that the model chuffs out. I've got a lot more different analyses, but no one seemed interested in that level of detail. Putting it descriptively the diurnal variation does cause a damping wave of heat flow through the wall profile, but because of its thermal capacity vs conductivity this cyclic flow is almost totally attenuated by the internal layers. The 1 std dev of the heat flow at the outside (as a response of the cyclic air temperature) is 30 W/m² but by the internal plaster layer it is down to 0.0003 W/m² -- that's 5 orders of magnitude less. I also tried looking at the effect of a 3 day cold snap, and it took days before there was a slight response showing itself on the inside. (You can see this delay effect in outer stone skin in the corkscrewing of the heat curves.) This is why I said that you can pretty much use per month average external temperature data for doing your heat calcs.

Yes, of course you are correct in pointing out that the external temperature pretty much directly impacts on the MVHR recovery and the Window losses, but these are roughly a third of my winter losses. We only get solar gain during the day of course, so there is some residual ripple but the thermal capacity of the slab and internal fabric, (plus the slab's active control in Jeremy's and my case) keeps this under 1°C, and most people don't mind their bedrooms cooling slightly overnight.

Yes, having drawn curtains might drop the heat losses, but to be honest IMO the main benefit is a subjective one of not seeing black windows.
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