Now, we have all the ingredients to that model of a wildfire.
The heat equation in 2D to describe the diffusion of heat. We have a model for heat loss.
We can describe the effect of wind at least in one dimension, but that would be easy to generalize
to two dimensions, and we have a simple model for combustion.
In the homework, you're going to put all of these together to model a wildfire.
This boils down to adding the different contributions to a rate of change of temperature.
This is what the result could look like.
In the region where the fire has started, the wood is depleted so they can't be any combustion going on.
The fire has advanced to the right, a little to the left, and to the top.