I've recently found myself unable to perform a seemingly simple action in Blender while creating my model. I want to create a "tube-like" edge where 2 of the parts connect together, but nothing I've tried has worked, since extruding the edge results in a plane that I can't scale properly. I'm unsure of what to do, as I'm quite new to Blender and don't fully understand what I'm doing. Explaining what I want to achieve seems a bit hard, so I've added some images! I'd really appreciate some help!
Here is one example:
I started with a cube where I removed the top face and Beveled to look similar to your target shape. I then selected non-Manifold edges (or you can select these manually), 'D' (Duplicate), 'P' Separate Selection (into a new object 'Cube.001'),
I then converted the Cube.001 into a curve that will bend a new mesh:
Then I added a cylinder and subdivided only the vertical edges to make sure it had sufficient edges to bend along the curve,
and then used the Curve modifier to fit it. (you may have to adjust the axis of conformance, and move the cylinder or Object :: Apply :: Location):
You can add the Subdivision Surface modifier to smooth the outcome.