Would anybody have any information on the solar absorption (say W/m2) of a concrete slab??
peter
Would anybody have any information on the solar absorption (say W/m2) of a concrete slab??
peter
It's related to the emissivity.
http://en.wikipedia.org/wiki/Emissivity
http://www.engineeringtoolbox.com/emissivity-coefficients-d_447.html
And the conductivity and thickness.
Hi Peter,
Not sure of your background but it's not easy maths unless some massive simplifications are taken http://en.wikipedia.org/wiki/Heat_absorption
The simplest form is
reflectivity=1-emissivity
used as a multiplier of the incoming energy and ignoring effects of different wavelengths (infrared,visible,UV).
So using ghostgums link and taking the 0.85 value for "concrete" (where polished concrete is probably a somewhat lower value) you could take a basic stance that it absorbs 85% of the incoming energy, or 850w/m2 when perpendicular to the sun with the usual base assumption of sun energy.
Interesting seeing on that wikipedia page "Rigid fiberglass, a common insulation material, has an R-value of 4 per inch, while poured concrete, a poor insulator, has an R-value of 0.08 per inch."
You have oversimplified the calculations.
Radiant heat transfer is bidirectional - in fact all objects radiate heat unless they have zero emissivity or at absolute zero degrees.
Thhis obeys the Stefan-Boltzmann formula which is a function of surface temperature and emissivity.
The important number is the net radiant transfer between the objects.
If the surface temperature rises too quickly then it can re-radiate the thermal energy as fast as it is being received. Even at room temperature, the mass can be radiating 400W/m2 compared to the 500W/m2 of winter solar insolation - in effect only a 100W net gain. However there is a practical limit to how much solar radiation the mass can be exposed to due to the rate of thermal conduction away from the surface. Too much sun exposure would result in the room overheating.
For the mathematically inclined you calculate the net rate at which energy can be transferred to the concrete mass
You need to know
a) Initial steady state temperature on the surface of the mass at the beginning of the day
b) Initial temperature on the other side of the mass (probably close to ground temperature if it is a slab - varies according to district)
c) thermal conductivity of concrete (1.7W/mK)
d) volumetric heat capacity of concrete (2060 kJ/m3/K)
e) thickness of mass
f) emissivity of mass
g) solar insolation (~500W/m2 - winter, ~1000W/m2 - summer)
It is probably solvable as a simultaneous equation using calculus but my maths is too rusty nowadays to do this. I have to dig around in my Year 12 maths notes.
Alternatively, you probably can do a brute force simulation with a computer program using the Stefan-Boltzman formula and the thermal conductivity equation.
Thanks for supporting my statement Dymo
"it's not easy maths unless some massive simplifications are taken"
If anyone REALLY needs/wants an accurate answer, the company I work for does this type of analysis through various engineering software packages.
Good to know there is a real engineer around these forums. Since we are on this topic, do you know how accurately AccuRate and NATHERS model the hour to hour effects of solar gain on thermal mass with regard to indoor air temperature and mean radiant temperature.
dymo - No, I'm not familiar with those. We do first principle analysis for industrial applications.
Peter - If the solar absorption is your starting point, what's the end point you're trying to get to?