Inlet outlet mass flux is not identical

Hi all,

I am trying to measure the bulk temperature, but initial testing on the conservation of mass failed as it gave me different results between the inlet and the outlet mass flux. This result makes me doubt all my simulation results so I would like to know what's going on. The model is a rectangular duct flow with 1) heat transfer on one side and 2) prescribed temperature at one of the walls and the channel inlet.

I used two 'general projection' planes to measure the mass flow rate over the entire channel length. As you can see in the graph, there is a sharp rise at x=0 (not to mention the fluctuations. I would say it's a numerical uncertainty due to the meshing). I don't understand why this is happening as this happens even if I refine the mesh, which is very concerning.

Any suggestions on why there is a discrepancy in the mass flux along the channel? Please let me know if there is any mistakes in my model.

Thanks!

Best,
Tae Jin Kim

ps: I also quantified the bulk temperature based on some discussions threads and extensive trial and error. At this point, I think it's almost correct, but please let me know if there is an error.