Implementing custom boundary heat source with local x coordinate

I want to insert a custom boundary heat source which depends on position x along an edge.

I have two questions on how to implement this:

How can I create a local x coordinate along this edge? Something like xedge_1

How to insert this local x coordinate inside my function, is it as easy as y(x) = f(xedge_1)?

For reference purposes, I included the function, dependent on x and also the specific boundary. A general description on the above two steps would suffice.

Kind regards,

Marvin