How can I incorporate gaseous conductance into my COMSOL model?

[1lai]

My COMSOL model consists of a suspended membrane supported by two arms. At low pressure, the membrane temperature will increase upon thermal irradiation. I want to simulate the temperature rise as a function of pressure but don't know how to include the gaseous conductance. Any suggestion?

Thanks.

 

[PerennialII]

Hi 1lai,

I was left wondering about a couple of things with respect to your problem, and how to approach it. First whether you'd like to treat the conductance as a more complex than average heat transfer boundary condition in your problem (a boundary condition which is time, pressure, etc dependent) or whether you wish to do a coupled model, where you'd essentially introduce the gas flow problem into the model itself and solve these in a more general setting? Both can be naturally done in Comsol, depending on how much information & familiarity you've with respect to the problem and how much effort you're willing to put into it (and what are your requirements with respect to the accuracy of the results you'll receive).

 

[1lai]

Hi PerennialII,

At this moment, I want to solve a simple problem using a only pressure-dependent, average heat transfer boundary condition. Since I am not very familiar with Comsol, could you please teach me how to tell the model an additional thermal conductive path to the ambient?

Thanks a lot.

 

[PerennialII]

Ok, that sounds very doable. One of the best things about Comsol is that pretty much everything can depend on nearly everything and it gives the user lots of tools to solve complex problems.

For example one can define a boundary condition, say for an edge, as a function of time by simply writing the boundary condition as a function of time to the appropriate cell, when have opened the "boundary condition" window. So you can define all sorts of dependencies straight to the respective "cells" in the GUI (like if you take a look at boundary settings in a heat transfer problem you'll see a selection of boundary condition options [heat flux, temperature, isolation etc.] which you can then define as you like) as a function of whatever you want (pretty much the only limitation being that the problem remains solvable and everything is 'defined') using the matlab-like notation of Comsol.

For example, if I'd want to define a linear boundary condition as a function of time, I'd just specify a+b*t (a,b constants, t in comsol is reserved for time) for that boundary in question for what quantity I'm interested in specifying.

So I'd think the next question is how well is your boundary condition defined at the moment, do you have it already written down well enough that it would "just" be about inputting it or does it require an additional solution of some sort or coupling to the solution of the thermal problem (like do you have a known pressure variation with time etc. which could be used to define it)?

 

[1lai]

Thanks a lot. I chose the right model (heat transfer-conduction is different from heat transfer-conduction and convection) and set the boundary condition according to your suggestion and it worked. however, to best define the boundary condition, I should specify h=C1*A where h is the heat transfer coefficient, C1 is a parameter~5.3e-12, and A is the area of surface. Could you tell me how to give a right expression of A?

 

[PerennialII]

...nice going! Is it a 2D or a 3D model? If 2D treating the edge as being of unit thickness (2D ~ model having an unit thickness, thickness = 1) and then the area being 1*edge length sounds like something would try 1st.

There are a number of step-functions and like (and you can use "if" sentences in your boundary conditions) in case you need to define time dependencies (or any other dependencies) for the bc (or the interpolation property if want to input something in tabular form and let comsol do the interpolation).

 

[1lai]

I have a 3D model. The heat transfer from the model to ambient is propotional to the surface area of the model. It seems the total amount of heat should be integrated, or I can issue an expression of h=C1*ux*uy. however, COMSOL does not know "ux" or "uy". What are the right symbols for coordinates?

Thanks.

 

[PerennialII]

For coordinates the notation reserved for the global system is x,y,z, for the subdomain a face system can be defined (parametrization variables, tangent variables) as t1k, t2k (k=x,y,z) (the manual has the detailed specs about the convention). Working with the heat transfer coefficient is probably a good idea so don't have to work with properties of the whole face or integration of it all.

 

[1lai]

I guess everything is OK now for the stationary analysis using the heat transfer coefficient w/o integration. The results fit reasonably with some of our experimental data.

We did vacuum packaging of our MEMs device and measure its time constant for estimating the vacuum level inside the chamber. Theoretically, the time constant is inversely proportional to the total thermal conductance. However, I cannot get an right solution of time constant in COMSOL. I set the solver parameters to transient analysis and find that the temperature rise vs time is almost identical for all different pressure. This does not agree with the experimental data and theory. Did I miss something in transient analysis? Does the model automatically update the (mesh) temperature and boundary conditions after each time step?

Thanks.

 

[1lai]

Could you please show me how to apply BC, for example, a sawtooth heat or a heat impulse, using "if" sentence? Thanks.

 

[1lai]

All done. Thanks.

 

[PerennialII]

Nice work!

I guess everything is OK now for the stationary analysis using the heat transfer coefficient w/o integration. The results fit reasonably with some of our experimental data.

We did vacuum packaging of our MEMs device and measure its time constant for estimating the vacuum level inside the chamber. Theoretically, the time constant is inversely proportional to the total thermal conductance. However, I cannot get an right solution of time constant in COMSOL. I set the solver parameters to transient analysis and find that the temperature rise vs time is almost identical for all different pressure. This does not agree with the experimental data and theory. Did I miss something in transient analysis? Does the model automatically update the (mesh) temperature and boundary conditions after each time step?

Thanks.

Yeah, it updates everything with respect to the time-parameter within the analysis all by itself. Hmm, might test whether it works overall by specifying the extremes of heat transfer and seeing whether you can produce a difference. To see that everything is in principle ok and there isn't an order of magnitude type or something there. Although if the stationary works certainly shouldn't.

Could you please show me how to apply BC, for example, a sawtooth heat or a heat impulse, using "if" sentence? Thanks.

The notation is very MATLAB like, e.g. (a+b*x)*(t<2), where the latter part has a value of "1" when time is smaller than "2", otherwise "0". You can also use a classic if(condition, to do when true, when untrue) type notation. Or step functions, which numerically thinking are often the preferable way (there are a number of smoothed step functions, particularly "nice" since there are variants with continuous derivatives and they integrate well) like flsmhs(location, scale), where the scale is used to define the range of transition for the step.