I posted this on the envirotalk forum but no responses yet - anyone here interested ?

I'm having a play with a spreadsheet to simulate a building energy/temp performance. Its just a really simple box at present, 4x4x2m, wall R value 2, roof Rvalue 3, Floor R value 2 but with constant ground temp of 15C. Outside temp I've modeleld as a sinewave with parameters for max and min. MinT at about 6am, max at 6pm (due to regular sine wave shape). My model just estimates the heat flows though walls every 5 mins and re-calculates internal temp.

With no heating the internal temp pretty clsoely follows the external temp - with outside min = 5 the inside drops to 8 and max 25 the inside gets up to 22 - with a slight delay of about 20mins. I'll try to work out how to insert charts.

I'm wondering though if my simple model of heat conduction through the walls is correct. I just use the standard formula P = A *deltaT / R. I know there is a lot of debate though about walls with high thermal mass/heat capacity vs walls with maybe the same R value but low heat capacity. How would I incorporate the wall heat capacity in my model ? It seems that if we just assume heat conduction through the wall then all that matters is the R value, but then as the outside air cools, the outside of the wall starts to radiate/coduct/convect heat away to the outside air. So the thermal gradient through the wall increases, heat flow out increases and internal temp falls. But the wall average temp is also falling, meaning the energy stored in the wall is also decreasing - i.e. is the wall supplying some of its heat to provide the external heat flow and thus buffer the inside air from supplying all the increased heat flow ? I guess this would back up the argument that high heat capacity delays the loss of heat from the inside.

Once the outside air starts cooling, the temp gradients inside the wall can only stay the same or increase, so the flow of heat from inside at best will stay constant. My current model with no heat capacity assumes that as soon as the outside temp drops, deltaT increases so heat flow from inside to out increases. I guess the correct answer would need a model of the temp profile across the wall which probably wouldn't be linear as I'm assuming in my simple model. Maybe I could calculate the average temp of the wall (Tout+Tin)/2, calculate how much energy would be lost to the outside from such a temp change, and subtract that from the calculated conducted heat from inside to outside. With high heat capacity though, that could be more than the heat being conducted from inside, i.e. the wall average temp is higher than a simple average - I don't want to start iterating for a solution though !

Stage 2 ....

Well that idea didn't last long. Today I looked at just how much energy is stored in the brick walls. If I have all the numbers correct, then the energy in the wall far outweighs the small energy flows that I've been considering. Without the wall heat capacity, I calculated that the total energy flow in 5 mins through all the walls and roof of the room for a 5 deg difference between inside and out would be 44kJ. This is sufficient to cool the room down almost to ambient overnight, so it sounds about right - in fact maybe a bit too much. In that first 5 mins, the wall temp (simple average of inside and outside) dropped by 0.6deg. But for a 4x2m, single brick wall, Cp 0.8 kJ/kG/K and with a mass of about 200kg/sqm, this would represent a drop in energy of 816kJ !! This suggests the wall temp would hardly drop at all as the outside temp drops and still be able to keep the conduction heat flowing to the outside.

As another estimate, I calculated that the total heat capacity of the air in the room is only 832 kJ, assuming it will drop from 20 to 0 deg. Thats similar to the energy in 1 wall with a 0.6deg change. Does this mean that the walls would be able to hold the room temp constant for the whole night ? Or at least until the room temp dropped to the wall temp and then stabilise ?