I'm trying to do a simple simulation of a solar panel coupled through some piping to a boiler, with the aid of a pump. My input constants could be something like: volume of liquid inside the panel, volume of liquid inside the boiler, pump transfer rate.
For simplicity I can assume that connective piping does not absorb any heat, so panel and boiler are coupled next to each other through some hole and thermally insulated from another.
Possible constants: ambient temperature, heat loss (depends on ambient temperature).
The variables: panel temperature, boiler temperature, whether the pump is running or not.
What I'm doing right now is like linear estimation, applying some energy to the panel (raises the heat linearly), running the pump transfers linearly energy from one vessel to another (temperature increase/decrease is inversely proportional to volume of liquid), heat transfer to boiler raises its energy linearly.
I would like to have some thing like: estimating the rise and fall of temperature in both vessels given the above constants and variables. It doesn't have to be scientifically exact, but I know that linear aproximation is wrong as the temperature increase is somehow inversely proportional to absolute temperature (i.e. it 'tapers').
The end result will be like: apply xxx units (Joules) of energy to solar panel for 1 minute > temperature rises by y degrees; start pump (open valve) for 1 minute -> temperature in boiler goes up by z degrees, temperature in panel goes down by w degrees.
Any graphs or formulas will be helpful, I can continue from there. This is not a homework or scientific study, just something for personal use.
Also some explanations about differences between water and oil energy absorbtion would be nice.