Why a high temperature region is not generating a uphill flow?

Hello,

The domain size is incredibly small (given the velocity magnitude at the inlet), therefore this problem that you are analyzing is not dominated by natural convection.

It doesn’t mean that buoyancy effects are not playing a role in the simulation, it just means that the advection term is too large in comparison.

PS: both approaches that you ran use the Boussinesq approximation, in case you are interested in reading a little bit more.

Cheers