modelling flow through a hole
 

I have a hexagon tube with a heated plate in the middle of the tube with a single hole in the center of the plate. I have laminar flow, and have set the boundary conditions such that the inflow is 100k, and the plate is 400k. I am trying to determine how much heat the fluid(air) picks up as it flows through the hole at various laminar velocities. My problem is that the tube and exit region/temperature(pressure outlet) are affecting the temperature of the fluid after the plate. Is there any way to correct this? I don't want the walls after the plate to play any role in the temperature of the fluid. I am ultimately trying to get the convective coefficient for the frontside of the plate. I am determining the temperature by doing an average area weighted report on an exit plane.

Thanks