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     Steven E. Williamson (sew) New member Username: sew Post Number: 2 Registered: 02-2008 |
I would like to be able to perform a static thermal calculation with temperature-dependant thermal contact resistance. I attempted to modify the sample script Thermal_Contact_Resistance.pde (see attachment) by making Rc a simple linear function of temperature, i.e.: Rc(t) = 1/2 + t In order to evaluate Rc at the average of the temperatures on the two boundaries, I used the following boundary condition: contact(Temp) = -JUMP(Temp)/Rc(JUMP(Temp)/2+Temp) This assumes that JUMP(Temp) will be Temp2-Temp1 at nodes in material 1 and that Temp will be Temp1 in material 1 and likewise that JUMP(Temp) will be Temp1-Temp2 at nodes in material 2 and that Temp will be Temp2 in material 2. The argument of Rc then becomes (Temp1+Temp2)/2 in both materials. This seemed to work. However, I noticed that the integrals of the normal heat flux over the "inner" and "outer" boundaries (printed at the bottom of the last two plots) no longer match. For the inner boundary, it comes out to be 1.280 while for the outer, it is 3.562. So I guess my scheme didn't work after all. Is there any way to put in a temperature-dependant thermal contact resistance?
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1068 Registered: 06-2003 |
In "Help->User_Guide->Addressing more difficult problems->Discontinuous Variables" we say: --------------------------------------- JUMP(v) means the instantaneous change in the value of variable "v" when moving outward across an interface from inside a given material. At an interface between materials '1' and '2', JUMP(V) means (V2-V1) in material '1', and (V1-V2) in material '2'. ----------------------------------------- The sign of the JUMP() is different on the two sides of the boundary. Your expression for Rc uses JUMP(), so the resistance is different as seen from the two sides. You should take the ABS() of the JUMP(), so the resistance is seen as the same value from both sides. If you do, the problem converges much more quickly and gives consistent fluxes in the two regions. See attached.
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| Steven E. Williamson (sew) Junior Member Username: sew Post Number: 3 Registered: 02-2008 |
I tried running your script for this problem which uses: contact(Temp) = -JUMP(Temp)/Rc(abs(JUMP(Temp))/2+Temp) instead of the expression that I proposed: contact(Temp) = -JUMP(Temp)/Rc(JUMP(Temp)/2+Temp) In fact, this does NOT work either. If you look at the integrated flux through the surfaces, (the bottom line of the last three plots) you can see that the integrals on the "inner" and "outer" surfaces in the two regions actually give different values (depending on which region you are integrating in): Outer: 3.094545 Inner Region 1: 3.090507 Inner Region 2: 1.999832 You say that "The sign of the JUMP() is different on the two sides of the boundary. Your expression for Rc uses JUMP(), so the resistance is different as seen from the two sides." But the trick here is that I also add in "Temp" after dividing JUMP(Temp) by 2, so that the complete expression: JUMP(Temp)/2 + Temp should have the SAME value on both sides of the boundary. That value should be (Temp1+Temp2)/2 (i.e. the average temperature). To be more explicit: In Material 1: JUMP(V) = (V2-V1) V = V1 JUMP(V)/2 + V = (V2-V1)/2 + V1 = V2/2 - V1/2 + V1 = V2/2 + V1/2 = (V2+V1)/2 In Material 2: JUMP(V) = (V1-V2) V = V2 JUMP(V)/2 + V = (V1-V2)/2 + V2 = V1/2 - V2/2 + V2 = V1/2 + V2/2 = (V2+V1)/2 If JUMP is defined as you say, and if the variable (V or Temp in the .pde) value is defined as I have assumed above, then all of this should work. BUT IT DOESNT. Through trial and error, I think I have discovered an expression that DOES work. If I use contact(Temp) = -JUMP(Temp)/Rc(-JUMP(Temp)/2+Temp) the integrals all come out to be the same (within the precision). The fact that this expression works (I think), implies to me that something was wrong above in my assumptions about the value of JUMP(V) or the value of V in the two materials. Does this make any sense at all? I have attached a .ped script with the above expression for the temperature where contact resistance is evaluated. You can see that the integrals all come out more or less the same: Outer: 1.999558 Inner Region 1: 1.998451 Inner Region 2: 1.999462 I don't particularly like using this expression for evaluating the contact resistance because it does not agree with my picture of how FlexPDE is treating the boundary. It would be nice to have some confirmation (or rejection) of this idea from an expert before I actually use it in a serious calculation. Thanks
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1070 Registered: 06-2003 |
From your experiment, it would appear that the documentation is wrong, and JUMP(V) means (V1-V2) in region "1", not (V2-V1). I will look into it. |
Temperature-dependant Thermal Contact Resistance