baracoda said:
@russ_watters thank you very much for this example, it is much more clear to me than those complcated equations. Using ths method I can adjust the data as I want and also use it to predict how the temperature will drop if I will turn the heater off (I will have to look at the plot the other way as I think).
You're welcome. FYI, the basis of this is Newton's Law of Cooling:
http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/diffeqs/cool.html
So yes, it works for both heating and cooling. Reading the full explanation of how it works may answer some of your questions, but...
1. By 0C weather you mean temperature outside?
Yes.
2. What is the differenece between temperature and room heat?
So, first a little mea culpa. "Room Heat" and "Available Heat" were somewhat redundant, or, rather, "Room Heat" was actually meaningless. I'll explain in more detail below, but here's a corrected spreadsheet, showing only "available heat" (notice the result is pretty much the same -- the "Room Heat" column wasn't really doing anything useful).
Newton's law of cooling is like emptying a bucket of water, except that instead of water, you have a container full of heat (thermal energy). "Available Heat" is the amount of heat that has to be added to the room in order to bring the temperature up to the desired 20C. "Room Heat" was intended to be the increment of change when it gets 1C warmer, but it was unnecessary and I didn't do it right anyway, so you can ignore that (and I've removed it). Temperature is just the temperature of the room at each time.
However:
3. What doest it mean that available heat is -20?
This is somewhat moot now, however please note that an iterative method like this is not exact. It has errors. Namely, it assumes a constant heat flux for an each 1C step, which isn't true - the reality is that the heat flux changes continuously. With the new version of the spreadsheet, the error is hidden, but note that in the true version of Newton's Law of Cooling you don't ever get exactly to your target temperature: the last line of the spreadsheet is always very significantly wrong. In the rest of the steps, the errors are relatively small.
4. If I understand correctly the input data is in columns Temp, Room Heat and Heat Flux. The rest you calculated using some formulas. Is it possible that you would send me the excel file with this example as I have a problem with figuring out where did the values came from.
Attached.
5. I am also not sure what is Room K and Room C.
They are my versions of constants that go into Newton's Law of cooling. K is the heat flow rate versus temperature difference: how well insulated the walls of the room are. C is the thermal capacity of the room: how much heat the interior spaces absorb. I believe in Newton's actual Law of Cooling they are combined into one constant.