| Author | Message | |||
     Andrew Green (a_green) New member Username: a_green Post Number: 1 Registered: 12-2005 |
Hi I am wanting to use flexpde to calculate the power loss in a loop of wire driven by a known AC current. My understanding is that the problem is an integro-differential one of the form div(1/mu*grad(A)) + sigma*dA/dt - J = 0 area_integral(-sigma*dA/dt + J) = I where A the magnetic vector potential is unknown and J the current density in the region of interest also an unknown due to the skin and proximity effect. I is the current in the wire, sigma the conductivity. I know I have to write this in terms of separate Real and Imaginary variables ie., 4 unknowns Can flexpde solve integro-differential problems? If not direct, can I rewrite the integro part as an integral constraint + say a second pde? If so how? Certainly if I put the two integral equations direct into the equations part of flexpde, the program aborts immediatly with a " Singular Diagonal Block" error Hope someone can help me. | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 501 Registered: 06-2003 |
If J is a single number, then you should be able to do it by making J a GLOBAL VARIABLE (SCALAR VARIABLE in earlier versions) and using the integral as its equation. See "Samples | Misc | Heaterti.pde" for an example of this kind of problem. If J is a distribution, then it would appear there is not enough information to distinguish an infinite number of partitions of dA/dt and J. | |||
| Andrew Green (a_green) New member Username: a_green Post Number: 2 Registered: 12-2005 |
Thanks for the tip Robert. After much playing around and reading papers I finally got some sensible results. The key to the problem is recognising that for 2D type problems where cross section of the conductor is uniform the source current density is uniform over the cross section and can be determined by integrating the Magnetic Vector Potential over the conductor area normal to the current flow. I have attached a commented .PDE file for those interested in exploring this problem area with FlexPDE.
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| Andrew Green (a_green) Junior Member Username: a_green Post Number: 3 Registered: 12-2005 |
Ooops - I forgot to note the model is a regular XY type. I have yet to try an axisymmetric one, despite the title of the thread indicating otherwise. |
Skin and Proximity Effect in Parallel Conductors