Greetings everyone! Junior engineer in trouble and searching for advice here.

For a uni project I'm being tasked with designing a high temperature heat chamber with an arduino powered PID controller from scratch. The development process has been pretty linear so far, but now I've found a hiccup that I can't seem to overcome with my limited experience with termodynamics.

To estimate the power dissipation (and thus the heating element dimension) I've used the simplified model of heat transfer between a slab of insulating material, with the area being the internal surface of the heat chamber and the thickness of insulation given by the height of the firebricks. This gave me a good enough parametric model to play with for the dimensioning of the system, but now I want to take the things a step further.

To get an idea about the expected rise/fall time of temperature, the behaviour of PID controller and so on, I'd like to make a """"""digital twin"""""" (notice the number of quotation marks underlining the possibility of an improper use of the term) of my system in Matlab. Known all the parameters of the system (datasheets of all the involved materials, temperatures, heating power, and so on) I'd like to be able to plot the graphs of temperature over time to evaluate/eyeball the possible PID coefficients (auto tuning coming soon), better define the PWM speed, and so on.

The problem is that I'm having trouble setting up the simulation correctly. Unfortunately coming from electronics engineering I don't really have that much experience or background in thermodynamics, and I'm feeling like running in circles. I've tried to somehow "upgrade" the heat transfer through a slab model, but I didn't get that far.

Thus, I've come here to try to get some advice to get back on track. Can you tell me if the approach is correct, or suggest a better one? Do you have any source/consultation material that can help me navigate this strange world of thermodynamics? Thank you all in advance.

TL;DR:

Input variables: target temperature, PID PWM control of the heating element
System parameters: size of the heat chamber, physical properties of materials involved
Desired output: temperature over time graph of the chamber

How monky spark brain do monky thermo brain things in matlab? Monky really thankfull