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Hello Wieslaw Zelik

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Hi all
i must say this is like the 5th thread i see dealing with natural convection and problems with the analysis.
this is also not the first time i have seen reference to "natural convection must be solved under transient solver".

well, the solution to the whole natural convection problem is complex but possible in both STATIONARY and TRANSIENT (i personally prefer for engineering application to use the stationary solution unless i am interested in the "Ramp-up" process) if only you define the physics properly , see below:

the system:
1. you need to create a large enough volume of fluid around the object to make sure that you don't get artifacts in the computation field due to the boundaries (usually 2-5 times the nominal dimension of the object in length in all directions)
2. define the fluid field: under 'absolute pressure' choose "pressure(nitf/fluid1)" , and as reference pressure enter the ambient pressure.

Mesh:
1. choose a "fine" mesh for most cases where the geometry is more elaborate then cubic presentations (you need a fine enough mesh to capture the fine temperature gradients in the near wall region, as well as the sharp directional acceleration gradients of the velocity field from the entrainment into the plum)

Boundary conditions:
1. the face where the plum (the heat plum raising from the object) is to be defined as "outflow" (under heat transfer BC) AND "outlet" (under laminar BC - set P0=P, ambient)
2. the faces where the fluid enters the system (to satisfy the entrainment of the plum) is to be defined as "open boundary" (with "no viscus stress" condition and T0=T, ambient)
3. Volume force, is to be defined as "-g_const*(nitf.rho-rho_ref)"
4. heat source, what ever is relevant to you system.

summation of BC:
1. volume force
2. open boundary
3. outflow
4. outlet
5. heat source

Solver:
1. choose the stationary solver and change
under study>solver configurations>solver1>fully coupled 1 , change the 'damping and termination' definition to being "automatic highly non-linear"

regarding convergence in Stationary studies:
as we all know and like you can find in many places in the literature, indeed natural convection has a transient element to it, as the plum and flow field fluctuates along the heated surface, HOWEVER, there is still the possibility to achieve a Stationary study that complies with the system.

the thing is, should you run a stationary solver, you will see that after some iterations as the convergence 'green bar' goes all the way to 90% it will then drop sharply to approximately 50%... this phenomena will fluctuate back and forth ENDLESSLY!
what you need to understand it that this is happening because the solver set on one solution then loss stability as it "moves" to another.

What you need to do: let the solution fluctuates aback and forth 1-2 times, once you see the pattern - stop the solver, and there you have it!!! - your solution (you will see that should you stop the solver at a different fluctuation the flow filed will look slightly different 'Plum-wise' but the temperature will be identical)

i have attached a working example, that has been lab tested to make sure the solver results are accurate.

Best regards to all
M.sc Yoav matia.