Heat flux calculation on boundaries

[mark smith]

Find attached a 7zip compressed file of a simple thermal problem with a heater and bar, the boundary conditions have one end held at a fixed temperature and convective/diffuse radiation on other surfaces. The hexahedral mesh is included to repeat the calculation if required as is a loadstate file for postprocessing in paraview.

Now In the 12 solvers example for the SaveScalars equation it states:

! This solver computes the total flux in two different ways
! 1) using integration points of the boundary
! 2) summing up the nodal heat loads from the residual, r=Ax-b
! Of these the latter is more accurate.
!-------------------------------------------------------------
Solver 11
Exec Solver = after all
Equation = "save scalars"
Procedure = "SaveData" "SaveScalars"

Filename = $prefix$_tot.dat

Operator 1 = "diffusive flux"
Variable 1 = "Temperature"
Coefficient 1 = "Heat Conductivity"
Operator 2 = "boundary sum"
Variable 2 = "Temperature Loads"
End

In my case the sum of the diffusive flux to 3 decimal places is -0.995 W where as temperature loads gives to 3 decimal places -1.0 W
The total power in the heater is 1 W so indeed it appears that the 2nd method is more accurate in terms of the total but
postprocessing the temperature flux results in paraview integrating over each of the BC faces gives results which are very similar to the
diffusive flux results given by SaveScalars and Comsol using the same mesh agrees closely with these results rather than the boundary sum results?
The convective/radiative flux results from the side faces by the 2 different methods in SaveScalars differ my more than a factor of 2?

To be able to postprocess in paraview you need to be able to look at the results in the direction of the surface normal, so if you place all 4 side
surfaces in 1 boundary condition (or indeed have a curved surface) then the integrate variable will not give the correct result since you need to sum the normal component for each elemental face, how might this be achieved?

Regards
Mark