cross-section averaged fluid temperature as a function of flow direction

Hi,

I am modeling 3D laminar flow with heat transfer in a channel of rectangular cross-section.

How can I implement the attached formula for mean fluid temperature?

I would like to determine the mean fluid temperature at each cross-section as a function of the flow direction.

I am currently using T_mean = mod1.intop1(u*T)/intop1(mod1.u), which gives me the average temperature at the inlet cross-section (x=0), since intop1 is the integration over the inlet face.

The documentation mentions a function called linear projection but this appears to be for line integrals. I get an error when I use this function.