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A Little Aside On Radiance



We've sort of covered this topic buried in various earlier threads, but since I need to use this info for my heating calcs, I thought useful to cover this in a short summary post.

Characterising the components of heat transfer across a solid / air surface really does come down to basic physics and we just need to crank the numbers into the two main factors at play in this:

  • Radiation. Any surface is radiating heat but is also simultaneously absorbing similar radiation from everything in line of site. If everything is at the same temperature, then this all cancels out and no net flow of energy occurs. However even with a small imbalance in temperatures, because of the amount of radiation being transferred, results in a net energy flow. The physics depends on the Stefan–Boltzmann law, and when you crank the numbers for a surface at roughly 20°C, this works out at ~5.7 W/m²K. OK, this has to be factored by something called the emissivity which can be as low as 0.03 for a mirrored aluminium surface, but for normal painted surfaces like house walls, it's nearer to 0.9. Also remember that the whilst the area can easily be calculated for very smooth surfaces, any texturing (like clothes or carpet pile) can dramatically increase this. Nonetheless, a good general rule of thumb is to assume 5 W/m²K.
  • Conduction. This is atoms of air bumping into the walls and transferring energy that way. Air, being a gas, is light on atoms compared to the solid wall, and so is a poor conductor, but it is also free to move and so the air region in contact with the wall is continually replaced due to any air movement. Once the temperature difference between the wall and the air is more than a couple of degrees, then the heating of the air itself generates convection and this make the heat transfer even more efficient. However in internal spaces, where there are no major drafts or temperature induced convection differences, this conduction makes a relatively small, say 30%, contribution, and radiation is the dominant component.


So a good overall figure for bare surfaces is ~7W/m²K and this is what I use in my active slab calculations.

This means that when doing U-value calculations, I can treat any material/air interface as having an effective thermal resistance of its reciprocal, that is roughly 0.15 m²K/W within the R-value calculations. Note that the references often assume some level of internal air movement, and so quote a lower thermal transmittance value of 0.12 m²K/W. Also if the surface includes a reflective / foil layer then the emissivity can drop significantly (though not to the 0.03 figure that I quoted earlier unless a high-spec multi-layered material is used); a typical foil-backed plasterboard might achieve an effective emissivity of around 0.3 which is why this is often quoted as having a transmittance value of 0.4 m²K/W.

The bible which gives all of these magic figures is the BRE Conventions for U-value calculations document and the data given therein broadly corresponds to the above.

Incidentally the average human has a surface area of roughly 2m², so radiates 5 x 2 x (33 - 20) (=130) watts if naked in a room at 20°C. Clearly the more clothes that you wear, the less your effective surface temperature, and the less your radiant heat losses; so with a light covering and a jumper on the torso, this might drop to 100W or so. This echoes a point made in one of Jeremy's earlier posts: how cold you feel in a house relates to your overall heat loss and in still air maybe 60-80% of this total is due to radiant losses rather than conductive/convective ones. So the temperature of the wall surfaces is just as important as the air temperature in determining this comfort level. Being in a room with walls and air at 20°C can feel just as comfortable as being in a room with walls at 17°C and air at 24°C.

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No comments from anyone else (maybe as a refection on my decision to post this on New Year's Eve!) apart from my own footnote on 28 Jan 2015 02:29 PM:

As a codicil to this, a friend who is an electronics engineer came for a visit and we got around to chatting about my new house plans and how the Active slab will work.  His reaction was: it can't possibly work because of the layering effect of air above the slab, "heat rises in air".  A couple of points to emphasise again:

  • The 7 W/m² figure is nothing to do with the air in the room.  It's a net radiance; it would be the same figure even if the room was in a vacuum.
  • Yes, the air column will tend to be stable is the floor is colder than the air above it.  The physics of convention and its onset is complicated, but the headline you can pretty much ignore any convection effects if the slab is only a couple of degrees warmer than the air mass.  This isn't the case for conventional UFH, but this is the case for an active slab.
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Isn't the distances between the emitter and the receiver important when it comes to radiant energy transfer?

If it wasn't the surface of the Earth would be a lot closer to the temperature of the Sun's surface.

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@SteamyTea, Nick, thanks for the response.  I miss having JSH around for this type of dialogue :( but you will keep me on track :)


Yes for a point radiant source, but no for a semi infinite one.  See Olbers' paradox. Consider a six sided box (sometimes called a room) with 5 sides at 20°C and one side at 23°C (the floor).  Consider a small area on the floor.  It is radiating according to Stefan–Boltzmann law and is receiving heat from the walls and ceiling ditto.  There is an inverse effect between the emiting and receiving surfaces, and well as the incident angle, but this needs to be integrated over the entire floor to calculate the actual radiant energy and v.v for transfer of radiant energy from the other surfaces to the floor     So the major heat transfer is actually directly from the floor to the walls and ceiling. 


If the room was a vacuum then the heat transfer would be entirely directly from the slab to the other surfaces, and mainly to the ceiling which faces it.  The ceiling and internal walls would tend to respond quicker than external walls because of their lower thermal capacity, but once there was a small imbalance start would also start to flow from the other internal walls to the external walls, and the bulk of the heat would soon be being transferred to the external walls and feed the external heat loss through the external walls to maintain the overall house equilibrium.  


Now add back the air.  Temperature differences of a few °C are not enough to initiate convective flow so any transfer of heat to the room air will by conduction.  As I said in my first comment, this is relatively modest. The BRE fiddle factors indicate that this will be maybe 20% of the radiant component for small temperature differences. So any net rise in room air temperature will be nothing like 3°C. 


Sun shining in through a window and onto the floor is a different matter as this will create a localised hot area that will set up a strong convective circulation in the room and rapidly warm the room air.

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Yes, that is the theory for infinite space, and quite possibly for semi-infinite space.

But a room is very far from semi-infinite, and as you point out, the temperate differences are very modest within a room.  Limits have to be introduced to create a more realistic model, and those limits will be small.

I also think that there is not enough consideration taken into account of the emitting frequency, which is really the energy level of the source, not all frequencies are equal (as my cataracts demonstrated).

I am not sure of an easy way to test ideas for radiative contribution to heating.  I do have a radiant heater in my bathroom (never switched it on).  Maybe I could use that and a metal plate on the wall to see what is happening.  Shall think about that when in the bath.


I think that the real problem is that any radiative affect is swamped by convection and conductance and very hard to measure in a meaningful way.

Edited by SteamyTea
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7 hours ago, TerryE said:

Now add back the air.  Temperature differences of a few °C are not enough to initiate convective flow so any transfer of heat to the room air will by conduction.  As I said in my foirst comment, this is relatively modest. 


This agrees with our experience.  In our house, downstairs (where the UFH is) is always warmer than upstairs, despite us having double-height areas and a massive space for the stairs (which themselves are open tread). 

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1 hour ago, SteamyTea said:

I think that the real problem is that any radiative affect is swamped by convection and conductance and very hard to measure in a meaningful way.


Nick, the SB equation is physics.  OK, you need to plug in the numbers and factors for surface reflectivity, roughness, etc, but we had a natural slate floor which will give as close to the theoretical figure of 5.7 W/m²K as you can get by plugging these in.  The 7 W/m²K overall figure for output of a surface with no convection is quoted in multiple sources including BRE, so the difference, which amounts to 22%, is the conductive element.  I would therefore challenge this statement and suggest that the opposite is the true: radiation swamps conduction -- at least in this scenario.  However there are scenarios where this dominance can flip, as in the case of sunlight falling onto a floor which I mentioned earlier, where we can easily get an area of a few m² which is tens of degrees hotter than the room air and this will set up a strong convective transfer of heat into the room.


Still give me another year and I will have hard data by instrumenting my house which will confirm this or refute it.  Jeff's comment supports my analysis, I think. :) 

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However in internal spaces, where there are no major drafts or temperature induced convection differences, this conduction makes a relatively small, say 30%, contribution, and radiation is the dominant component.


Are you referring to houses with a given air permeability level there, or including all houses? I thought part of Ph was that the elimination of air movement was important for comfort... so while the above quote may be true for your house, are we talking all houses?



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@gravelid, I have a passive design house that has been pressure tested and certified to 0.6 ACH equivalent, and to be honest my statements are coloured by that.  With this type of house, if you look at the temperature profile through the external walls (see my modelling Modelling Thermal Lag post), then the walls are within ½°C of the room ambient.  So the room, the slab, the walls are all within a few degree of each other and there are no material drafts other than the MVHR. 


In a more conventional house built with minimum compliance to the 2013 BRegs then heat losses though the walls might 5-10× greater, permeability maybe 20-50× greater, etc. and lots of temperature gradients.  Here you ware going to have a lot more air circulation and convection and in this case I would agree with SteamyTea's comment that convection, etc. will be dominant. 

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That's all fine. I think I didn't parse your sentence correctly. I think I read it without that first comma, thinking you meant *all* internal spaces have no drafts to the extent that would affect the conduction:radiation ratio.

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