| Author | Message | |||
     Barnabas Kipapa (yenrab54) Member Username: yenrab54 Post Number: 16 Registered: 07-2007 |
So far we've been successful in defining the problem a specific resistor. The goal of the simulation is to find it's equilibrium temperature. The resistor is in vacuum and comes to equilibrium via radiative dissipation. The only radiation sample-problem has to do with transfer between two materials where the domain is already in a state of equilibrium(radflow). So, my question is whether and how a vacuum can be defined along with dissipation? thank you in advance | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 911 Registered: 06-2003 |
The full moments approximation for radiative transfer with E the radiation energy density and F the radiant flux vector, is dt(E) + Div(F) + c*sigmaa*E = sigmap*a*c*Temp^4 The flux can be approximated as F = -beta*c*lambda*grad(E) Combining gives dt(E) -beta*c*Div(lambda*grad(E)) + c*sigmaa*E = sigmap*a*c*Temp^4 Here beta is the proportionality between radiation energy and radiation pressure, and is 1/3 for opaque materials and 1 for tenuous materials. sigmaa is the absorption average cross section sigmap is the emission average cross section (equal to sigmaa in opaque materials). lambda is the transmission average mean free path c is the speed of light a is the radiation constant, related to the Stefan-Boltzmann constant Sigma by a=4*Sigma/c (=7.5634e-15 erg/cm3/degreeK^4) If the material equilibrates instantly with the radiation, you can use E=a*Temp^4 to eliminate Temp. Otherwise, you need to add the material energy equation, something like rho*cv*dt(Temp) = c*sigmaa*E - sigmap*a*c*Temp^4 This formulation embodies a multitude of simplifications, including: 1) averaging the absorption, emission and transmission properties of the material over radiation frequencies. 2) assumption that the angular distribution of radiation can be approximated as I(mu) = A + B*cos(mu) + C*sin(mu). (ie, no directed beams and shadowing). Vacuum propagation is not a problem, simply set beta=1, sigmaa=sigmap=0 and lambda=some number larger than the domain. But you should not take my word for all this. You should consult a radiative transfer text. There are lots of ways to approximate radiative transfer, depending on how much detail you need to know and how absorbing your media are. Nor do I guarantee that I have all the constants right in the discussion above. | |||
| Barnabas Kipapa (yenrab54) Member Username: yenrab54 Post Number: 17 Registered: 07-2007 |
I'm having trouble locating these formulations in the texts I have in front of me. I'm looking at Siegel and Howell's Thermal Radiation Heat Transfer as well as Kaviany's Principles of Heat Transfer. Do you have any suggestions of which text I should refer to? | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 913 Registered: 06-2003 |
I may have jumped to some conclusions as to what you need. What I wrote before may be overkill. You might be able to get away with a heat conduction equation with a high conductivity in the vacuum. Do you need to calculate the heating of a remote reservoir? If not, you can merely use a conduction equation with a boundary condition loss term of emissivity*(Temp^4-Tambient^4). The equations I presented before are essentially a high-temperature gas model that you may not need. I reconstructed them from notes and old reports. I used to have a book "Equations of Radiation Hydrodynamics" by Pomraning that may summarize the equations the way I did. (But I can't find the book in the boxes where everything now resides after our move....) The book is available on Amazon for $15.56. | |||
| Barnabas Kipapa (yenrab54) Member Username: yenrab54 Post Number: 18 Registered: 07-2007 |
i'm attempting to simulate an effective heat sink that in reality would be a vacuum. i want to get as close to simulating radiative dissipation as conveniently possible. i'm not sure what you exactly mean by remote reservoir, but i'm going to try the boundary condition loss term approach in the meantime. also,we've got a pretty awesome science library here at UC, so i'll check there for this book. | |||
| Barnabas Kipapa (yenrab54) Member Username: yenrab54 Post Number: 19 Registered: 07-2007 |
Hey Mr. Nelson, Our library owns the book, but it's on an indefinite loan. My goal is to simulate the temperature stabilizing in a particular resistor design. From what I've been told, such a resistor's temperature will stabalize within ten and twenty minutes. I tried the high conductivity suggestion with many, many different values for each of my property values, but instead of stabilizing, as time goes on, the change in temperature increases. My gut tells me this problem shouldn't be hard to formulate, so I assume I've made a critical error. Could you peruse my descriptor to see if you notice anything obviously wrong?
| |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 925 Registered: 06-2003 |
1. If you rearrange your temperature equation, you get (in part) dt(Temp) = stuff*Temp^4 This means Temp^4 acts like a source, so the solution will exponentiate in time. You've got the wrong sign on the Temp^4 term. 2. But... The Temp^4 loss term should be a boundary condition, not an internal loss. It looks to me like you should strip the "air" and "absence" materials and put boundary loss terms on the faces. At present, you don't have any boundary conditions, which means that all outer surfaces are perfectly insulating. I doubt that that is what you want. | |||
| Barnabas Kipapa (yenrab54) Member Username: yenrab54 Post Number: 20 Registered: 07-2007 |
Ok, so I tried it two ways. The first with just natural BC's on every surface and segment equaling ...temp^4. That resulted in the system cooling down instead of heating up. Then I tried it with the BC's equaling ...(temp^4-tamb^4) where tamb is the ambient temperature. This resulted in no change,at all. I then reduced the number of BC's to what I thought were the important surfaces, but this also results in cooling. I read the help on BC's in 3d, so I know where they are applicable, I'm just not sure where they will give the desired effect. Anyway, here's the latest.
| |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 926 Registered: 06-2003 |
You've got far too many radiative surfaces! This is a boundary condition, so you only want it on outside boundaries, not internal interfaces. On internal interfaces, the natural() becomes a surface source (or sink, depending on signs). Also, you should check dimensional consistency of all your equations and BC's, as well as signs. |
temperature stabilization