| Author | Message | ||
     qiqiapr (qiqiapr) New member Username: qiqiapr Post Number: 1 Registered: 06-2006 |
Hi, I am simulating such a problem: Apply voltage on an unregular wire, the current flow will generate power(heat), which will introduce temperature distribution. The electrical conductivity is effected by the temperature as a feedback. First I wrote 4 equations for this problem, V: div(eps*grad(V))=0 {potential equation } Power: Power = eps*grad(V)*grad(V) {define the power density } Temp: div(K*grad(Temp))+ Power= 0 {heat flow equation} eps: eps_pd=eps(1+alpha*(Temp-Temp0)) (temperature dependence of conductivity) But flexPDE told me "operands are not of the same type" in the first equation. If I don't write the fourth equation(without consider temperature dependence of conductivity), there's no such problem. Later I delete the fourth equation from here, and put it in the Region segment instead, flexPDE seems ok, but it takes forever to finish. Could you please tell me how to solve this problem? Thank you so much. It's urgent. | ||
| qiqiapr (qiqiapr) New member Username: qiqiapr Post Number: 2 Registered: 06-2006 |
the fourth eqaution in my previous post should be eps=eps0(1+alpha*(Temp-Temp0)) | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 628 Registered: 06-2003 |
1. The diagnostic should have tagged the second equation, because you can't multiply vectors. You must use one of the vector operators DOT, MAGNITUDE, etc. 2. Power and Eps should not be declared as variables, because they are not defined by PDE's, but simply as algebraic functions of the variables. 3. Professor Backstrom has an example of exactly this problem in "Backstrom_Books | Fields_of_physics | d_Heat | heats2.pde". Take a look at that example to see how he did it. |