Hi there,
I am very new to FEniCS and I am currently trying to model a 2D problem (which I will later expand to 3D), where a block of material is heated by a Gaussian laser source and I should find what the steady state temperature is for the system. I am currently trying to implement different boundary conditions on each face to model the heat flux in from the laser and the heat leaving the material as radiation. To do this I am following the FEniCS tutorial document (specifically Chapter 4). The boundary conditions I want are as follows:
-n.(k grad(T)) = episilonsigma(T^4 - Tam^4) for three sides of a rectangle
Q(x) -n.(k grad(T)) = episilonsigma(T^4 - Tam^4) for the top side of the rectangle
In this case, n is the unit vector, epsilon, k, sigma and Tam are constants and T is the temperature of my system. Q(x) represents the Gaussian heat source incident on the top side of the rectangle.
Following the tutorial guide, I have implemented boundary markers for each face but now I wish to make a python dictionary (called boundary_conditions in the tutorial). However,
in the tutorial, the dictionary is only extended to Dirichlet, Neumann and Robin boundary conditions, all three of which don’t seem to describe the kind of problem I am attempting to describe here (although I could be wrong).
How could one build a dictionary to describe these boundary conditions in a similar manner to what is done in the tutorial? Is there something I am missing?
Thanks in advance,