3D pipe flow+Buoyancy+Variable properties
 

Hi
I'm writing a 3d cylindrical transient code to finally solve the laminar buoyancy effected flow which fluid properties are variable temperature dependent.
I have written the code step by step. First step, results of flow without gravity are reasonable. Only u_axial and u_radial exist and u_tangential is totally zero.
At second step I added gravity as a source term to Radial and Tangential Navier-Stokes equation, gSin(teta) and gCos(teta) respectively, but the u_tangential domain is not as well as I expect it to be. Against being zero after entry length, it has some (symmetrical) values. I should add to my expression the boundary conditions.
I considered velocity inlet, known temperature at inlet, constant heat transfer on walls and at outlet boundary condition which some doubts are on it. I made two different conditions for outlet, Outflow and pressure constant at outlet boundary.
Outflow:
1- u_axial(end)=u_axial(end-1)
2- u_radial(outlet boundary)=u_radial(end)
3- u_tangential(outlet boundary)=u_tangntail(end)
4- Pressure totally is calculated on all nodes
Pressure constant:
1- u_axial(end) calculates according to continuity equation
2- u_radial(outlet boundary) extrapolates from u_radial(end) and u_radial(end-1)
3- u_ tangential (outlet boundary) extrapolates from u_ tangential (end) and u_ tangential (end-1)
4- Pressure totally is calculated on all nodes except last series of physical nodes near the outlet boundary that is considered P’(end)=0 and P(end)=constant
None of above options did not guide me to correct results. At first one, the tangential velocity domain must be zero after entry length but here it is not. If there is someone who can help me, give me her/his email. I will send my result.
At pressure constant condition, the tangential velocity domain is near zero except near outlet boundary condition which there is some huge gradient of velocity.

I kindly appreciate your time and consideration.
Best, SNA