Discussion Forum

Hi Davide

well your problem is in fact a rather complex one !
Normally when one talk about "Convection heating boundary" one means an external wall/boundary exchanging with an infinite large volume at temperature T, but this large volume is not modelled, only the heat exchange over the boundary where you define a heat exchange value in h[W/m^2/K] is used.

In your case the hot surface is heating up the air that starts some turbulences and flow and then transfers the heat to the second wall, which itself is cooled by a flowing water pipe. This convection exchange depends heavily on the geometry, the time to build up, the fluids ... and is not that easily defined, nor modelled.

COMSOL has some other boundary conditions to exchange heat for vertical and horizontal ... walls, based on known heat equations but I do not remember if they comprises a given air gap, take a close look, in which case you would not need to model the air at all, it would "just" by a boundary physics (resistance) between two solid domains.

If your air layer is thin < 1 mm you can say you hardly have any convection and you can consider the air heat conduction of the air alone, but from the moment the air path is larger you will have a mixture of bulk heat conduction and mass transport i.e. convection (and air buoyance effects due to density changes ...)

Normally you need to set up a full Conjugated heat flow model with two solids and two fluids, one flowing and with all the corresponding boundary conditions.

To start with you could only consider conduction in the air, and no mass transport and exclude the air from the flow model, at least that will give you a minimal exchange value, normally the convection/mass transport can only improve the heat exchange

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Good luck
Ivar

Hi Ivar,

First of all, thanks a lot for your reply.
I asked this question because it looked weird to me that Comsol didn't have a model for this kind of heat exchange. In my opinion the problem is not that bad. There is a convection between the two walls which is a function of both the temperature difference between the two walls and the convective heat transfer coefficient (h), which is itself a function of that temperature difference.
I really can't see why Comsol is not able to solve this problem. For a simple 2D geometry like this one you could even solve the problem in Matlab, as it is nothing more than a simple system of nonlinear equations.

Anyway, thanks again for your reply. I will try to find a solution for it.

Hi

COMSOL can absolutely solve it, no problems there, but it depends on the level of details and "true" physics you want to involve, and which hypothesis of simplification you will accept => hence the time & effort you have at disposal to get the solution.

You can even write your equation to link the two opposed surfaces, assuming the air exchanges a value of h[W/m^2/K] between the two surfaces, the only thing is : how do you want to link the x,y,z positions along the two metal boundaries across the air gap, for bidirectional coupling ?

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Good luck
Ivar

Hi Ivar,

Yes, you are perfectly right. So, let's say I would like two have two different solutions:
1) the first one describing the "true physics" of the phenomenon, with the air moving and transporting heat from the lower plate to the upper plate. In this case I also want to have the flow velocity as output;
2) the second one only describing the heat transfer. So in this case at the end I only want to know the temperatures of the air, of the plates and of the water.

How would you set the BC for both cases?

Thanks.

- Davide

Hi Davide

Well I do not know exactly your model, but the "true" physics means you need to define correctly the three-four domains and their shapes, define the materials (and their temperature dependence) define the inflow and pressure/ velocity/temperature of the liquid, then I assume your air region is closed, else how to define the heat and mass exchange through your open boundary !?
the heat flux inflow on your "hot" Domain and solve the system either with a time solver or with a stationary solver (but it might have some difficulty to converge so you could solve only for the fluid alone, and use the stationary results of the fluid flow as starting point for your full model)

When you talk about the "simplified" model you already talk about "the" air temperature hence you assume its constant, no spatial distribution (apart from a gradient across the air gap I assume ?) You could add a point, lump in the air mass heat capacity and average temperature and link the two surface through this "point" with some "resistance", one way I assume should work is to add a dependent variable for total heat flow and have COMSOL adapt and solve for it with a global "h" of some defined value linking the two surfaces. Still I'm not sure how "representative" this simplified model is really.

Finally modelling is making a lot of hypothesis on how the real world is, so you should validate your model rapidly with some representative measurements on a physical mock up test model

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Good luck
Ivar

Hello Ivar Kjelberg ..

Hope everything is going well with your side.

I am doing thermal simulation of my Inductor with ferrite material.
Please I have same issue in thermal simulation ( ' how to define the physic to the problem).
I will be very thankful to guide me .

Thanks
Best regards
Zeeshan