A Little Aside On Radiance

I’ve sort of covered this topic buried in various Buildhub 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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