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Heating of a solid cylinder with internal heat generation

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Old   July 13, 1999, 15:17
Default Heating of a solid cylinder with internal heat generation
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Sriram Popuri
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Hi! I have a two dimensional transient heat conduction problem with internal heat generation (exponentially decaying (axially) heat source). It's a solid cylinder. I am looking for qualitative data (temperature profiles) inside the cylinder. This is a pure conduction problem. But, I was wondering if I could use Fluent 4.5 or 5.0(somehow) to get the results quickly in a short time. If someone could give me a probable answer, I sincerely appreciate it. Thanks!
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Old   July 13, 1999, 15:47
Default Re: Heating of a solid cylinder with internal heat generation
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Adrin Gharakhani
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Maybe I'm missing something here, but if the problem is 2D how is the heat source axial? Do you mean radial?

If the boundary condition is not too complex, you can take advantage of the symmetry (and the simplicity) of the geometry and derive the (semi) analytical solution for your problem. Any graduate level book on conduction will talk about various problems (BC's) related to cylinders. You may actually find your exact problem solved in these books.

Adrin Gharakhani
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Old   July 13, 1999, 16:42
Default Re: Heating of a solid cylinder with internal heat generation
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Sriram Popuri
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Hi, Adrin! Thanks for replying. May be I will explain the problem formulation in a little better detail now. The formulation is an over simplification of the actual physical problem. The actual problem involves microwave heating (internal heating) of a compound medium with cylindrical structure (effective properties and power attenuation constants, I have defined with reasonable assumptions). The temp gradients are functions of x and r only. So, at time zero the power flux starts heating one face and decays towards the outlet exponenentially (is a function of x). The power flux will not appear as a boundary condition. The bcs are convective and for simplicity are made zero from all the faces. Of course, I have the symmetry condition at the center line. So, that's basically the problem. I need to find out the axial temp. profiles for t>0 by varying power flux at the inlet. Sounds simple enough. I looked into several grad level conduction texts (including Necati Ozisik's). Ozisik talks about a similar problem. But the solution process, I thought, was too complex. Anyways, if you could give me any further simplifying ideas, I appreciate that. Thanks!
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Old   July 13, 1999, 17:08
Default Re: Heating of a solid cylinder with internal heat generation
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Tom Plikas
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In fluent 5.1.1, you can define a user defined scalar equation. Write user defined functions in C using DEFINE_DIFFUSIVITY and DEFINE_SOURCE (see help section for details) to describe your thermal diffusivity and volumetric heat source respectively. In the user defined scalars pane,, you set the flux function equal to none and allow for the default unsteady function (Fluent 5.1.1 has this option). You now have a unsteady conduction problem with a source term. After properly defined your B.C.'s, turn off the flow equations in solution controls panel so that you just solve the scalar equation. Although I have not tried the above mentioned procedure, this should work Good luck Tom
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Old   July 13, 1999, 17:16
Default Re: Heating of a solid cylinder with internal heat generation
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Sriram Popuri
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Thanks, Tom! I don't have Fluent 5.0 not 5.1.1, but I am assuming it's possible with 5.0 also. I will take a look at that.
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Old   July 13, 1999, 17:21
Default Re: Heating of a solid cylinder with internal heat generation
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Tom Plikas
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I don't think Fluent 5.0 allows for a unsteady term in the scalar equation. Fluent 5.1 does. You'll have to check.
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Old   July 13, 1999, 18:09
Default Re: Heating of a solid cylinder with internal heat generation
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Sriram Popuri
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Tom! I only use Fluent 4.5; I will take your word for it about 5.0. I will try to get 5.1 if I could. thanks
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