[Gmsh] calculating a boundary flux

[Geordie McBain]

Hello.  I'd like to calculate the integrated flux of a vector field
through a patch on the boundary.  For example, after solving say a
Laplace equation for temperature, I'd take the gradient of the
temperature, and integrate the normal component of that over some part
of the boundary (a Physical Surface in 3-D or Physical Line in 2-D)
over which I'd specified the temperature with a Dirichlet condition in
order to get the heat transfer rate.

I read that Plugin(Integrate) `integrates...the circulation/flux of
vector fields over line/surface elements', so that looks ideal, but I
guess I'm not calling it correctly.

For example (to avoid posting a lengthy data file) say I load the
tutorial t7.geo, then use Plugin(Gradient) (on the `background mesh'
view) to generate a vector field.  If I save the `background mesh
Gradient' view as a Gmsh msh, it's only got the triangular domain
elements, not the linear boundary elements.  If I save the mesh though
(Ctrl-Shift S or File/Save Mesh) it does have the linear boundary
elements.

Anyway, when I apply Plugin(Integrate) to the background mesh Gradient
and then save that as a Gmsh msh, it contains a single point element
at the centre of the domain and the scalar value 0.

1. What does the scalar value 0 mean?

2. How do I get the integrated flux of a vector field through each
Physical Line/Surface boundary patch in two/three dimensions?

Thanks.