Caveat: I know nothing about gas burners specifically. I have a digital background.
In general gas burners are systems that produce a flame with a certain heat and area based on the air/fuel mixture provided. If you can model this with a transfer function or with a state-space model, there are blocks in Simulink that implement those in a generic sense in the Simulink>Continuous library.
Transfer functions* and state-space* blocks don't allow for boundary conditions, but if you model your system directly with integrators, you can impose boundary conditions on the integrators. You might also be able to add input terms to a transfer function that are based on the system output, to introduce nonlinearities.
If you have access to Simscape Fluids, you might find something there that helps you out. I don't have any specific guidance I can offer there, but perhaps that might help you refine your question, or you might find some of the examples in the documentation useful.
I have no guidance on the equations that would be used. Simscape might make you less reliant on a rigorous mathematical model, as I believe it abstracts away a lot of the mathematical underpinnings.
* Note that there are continuous and discrete versions of transfer functions and state-space blocks. You'll want the continuous versions. They don't have "Discrete" in the name, and they can be found in the Simulink>Continuous library in the Library Browser.
