Fitting multiple RC time constants

[Johnh]

Hi Keith, Thanks for posting the images

So if I'm understanding it, the underlying question is about solving a problem of hear flow in a one dimensional system. Ie heat flows from a source to a sink, controlled along the way by the conductivity and thermal cspacity? So in the RC analogy, the R parts capture length/( Area x conductivity) / and the C's capture mass x heat capacity.

I often work on such issues in the context of transfer of heat in a fire, or in solar problems.

If I'm using a spreadsheet, the easiest way is often just a discrete time step analysis. Maybe divide the whole path into the 10 segments as described above. and at each small time step, just assess the heat flowing into and out of each segment based on its temperature at the previous step and that of the adjacent segments, and work out its new temperature.

For a concrete wall in a four hour fire, I might have a spreadsheet line every 5 seconds. So it's a big file but a simple one., nothing is explicitly solved. It converges well if the time step is small enough for the problem. I've tested it against analytical solutions to check.