Modeling Heat Generation in 2D

[PaulTherm]

Hey All,

If I want to model a cylinder that has a heat source (a heater) at the bottom. I want to model it using the heat equation in 2D (in the radial direction), how can I account for the bottom heater? I need to find a relation between the bottom heat flux and the volume heat source. I appreciate any help!

Paul

 

[IRstuff]

How is it a 2D problem? Doesn't the fact that you refer to a "bottom heater" and "radial direction" explicitly demands a 3D solution?

What do you mean by "account for?"

What "volume heat source?" Is there another heater besides the "bottom heater?"

Is this for school? Student posting is not allowed.

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[PaulTherm]

Hey,

Thanks for the answer! It is a 2D problem because I want to analyze the radial direction. If we look at a 3D scenario, the bottom heater (which is the only heater of the system) gives a heat flux at the bottom and some of energy is conducted and stored in the volume, while the rest is dissipated by convection through the surfaces. Now, looking at a 2D geometry in the radial direction, I want to account for the heat flux that enters the system at the bottom and use it for the analysis. Basically, I need a relation between the heat flux at the bottom, the heat storage and the heat flux that is leaving the radial direction. I have the option to include the heat flux as a volumetric heat source. That is, the heat flux (W/m2) at the bottom should be expressed as a volumetric heat source (W/m3) by using some artifices that I'm not sure yet how to express. The problem is also time dependent and that gives more headache.

P.S. t is not for school. I don't think this is a class problem

 

[IRstuff]

The heat flow from the heater would seem to be heavily driven by vertical convection, so I don't see how you can assert that it's a purely radial problem.

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[PaulTherm]

Exactly. Well, it's not an easy task, but I'm sure that there are some artifices where the fluxes can be combined and use them in relation to the bottom heat flux, Cp and rho. Again, the problem is when dealing with the temperature difference because it's a dynamic one. I was thinking that someone already went through something like this. I will come back with an answer if I find one. Thanks anyways

 

[IRstuff]

There are no practical solutions for a 3D fluid; you'd have to do some sort of FEA. There are some solutions for a 3D solid, but they'd only be approximations of your case.

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[PaulTherm]

It is FEA and it is a solid body. I don't expect an exact solution anyways. By performing a study on the 3D, I can see that by taking the bottom heat flux (x W/m2) and inputting as a volumetric heat flux (x W/m3) in the 2D doesn't give such a big discrepancy when evaluating the temperature, therefore I can continue my study like this. It was a good sanity check! For the conditions that I have, the heat conduction inside the body is so fast that the source can be for entire volume.

 

[IRstuff]

OK, that's new information. Might have been nice to know that up front

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[corus]

It's a cylinder so 2D axisymmetric geometry would allow a solution to represent 3D. In FEA you'd simply apply a surface heat flux to the bottom surface and run a thermal transient analysis. The main problem is likely to be determining the heat transfer coefficients to the surfaces and heat loss by radiation. With an open cylinder you could calculate radiation view factors to the outer ambient, but some codes will let you define a cavity to allow radiation between all surfaces and to the ambient temperature, if required.

 

[PaulTherm]

I was thinking about axisymmetry as well. The problem is that it will be in more complex system, where the cylinder will be fixed in some rectangular bodies and that's why I can't use that. That's a good idea, though! The heat transfer coefficient is easy to evaluate if you know the ambient properties and temperature. Radiation is always tricky. Now even though I found that having a volumetric heat source with the same power gives the same results, it would still be interesting to find that relation between the bottom flux and a volumetric one that accounts also for the specific heat and density.

 

[IRstuff]

Since your Biot number would apparently be very low, then the bottom can be cannot distinguishable from the volumetric by the temperature distribution in the height dimension. On the other hand if your Biot number is high, there will be a noticeable temperature difference between top and bottom.

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[PaulTherm]

Exactly. Apparently I'm good for now for a wide range of heat fluxes and temperatures. Anyways, thank you guys!