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Thin liquid film with thermal gradient in contact with air (tpf, ht, ALE, AMR)

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Dear all,

I am modelling a thin film liquid in a rectangular channel (2mm), as well as the air on top of it. At the initial condition everything is within room temprature (Tc) then one side of the heater reaches a higher temprature (Th).
Therefore I am using the laminar two phase flow integrated with heat transfer in fluids for this problem.
Now I want to model the thermocapillary effect at liquid interface with air. I expect to see the deflection and change in height of the liquid and finally attain the liquid surface velocity.

I have attempted to formulate this problem in 2D by using the incompressible NS and adaptive multigrid meshing since the zone of interest is mainly the interface. Here are the setps:

1) Thermal insulation at the bottom wall of the thin film liquid.
3) IC: all sides are at Tc
2) BC: right side is at Tc while left side is at Th with deltaT higher ( 25°C).
4) Outflow (the air also consider as another 2mm layer) so the upper boundry is considered as outflow
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5) Wall1: is the lef and right sides of the channel which are considered as wet walls with pi/2 contact angle.
6) Initial values for both fluids U=V=0, p=0.
7) Initial interface: a line for the surface in between air and thin film liquid.
8) Wall2: top and bottom wall no-slip condition.
9) Pressure point constraints two top corners
10) Volume force to consider the effect of gravitional force. (rho.g.dt.alpha)

Here is the problem, by solving this I get the velocities but not the one which I want at the interface, it takes a very long time to solve (converge) even with a extremly coarse mesh and medium level of tolerance, therefore I thought of ALE application mode which is in progress. But using initial interface is the best way to consider the surface between liquid and air? And how to insert the change of height with respect to temprature in the problem? (dh/dy ~ dT/dx).
Do I need to consider another body force in air since the marangoni effect happens in the air too? (conductivity of liquid is very small)

Thank you in advance for sharing your opinions with me.

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