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How to treat point heat sources?

Roberta Mongillo

Posted 4 years ago

Hi everyone! I have to solve a 2D-PDE transient heat equation that contains point heat sources. I'd like to know if I wrote the following equation correctly: q0 = 1; Subscript[Q, 0] = q0(DiracDelta[x - x1]DiracDelta[y - y1] + DiracDelta[x - x1]DiracDelta[y - y2]DiracDelta[x - x2]* DiracDelta[y - y1] + DiracDelta[x - x2]DiracDelta[y - y2]); heqn1 = Subscript[k, CLS](D[Subscript[T, D][x, y, t], x, x] + D[Subscript[T, D][x, y, t], y, y]) + Subscript[Q, 0] == Subscript[\[Rho], CLS]Subscript[Cp, CLS] D[Subscript[T, D][x, y, t], t] I haven't considered the heat source as time-dependant just yet to simplify just a bit. Thank you in advance!

Hi everyone! I have to solve a 2D-PDE transient heat equation that contains point heat sources. I'd like to know if I wrote the following equation correctly: enter image description here

q0 = 1;
Subscript[Q, 0] = 
  q0*(DiracDelta[x - x1]*DiracDelta[y - y1] + 
     DiracDelta[x - x1]*DiracDelta[y - y2]*DiracDelta[x - x2]*
      DiracDelta[y - y1] + DiracDelta[x - x2]*DiracDelta[y - y2]);
heqn1 = Subscript[k, 
    CLS]*(D[Subscript[T, D][x, y, t], x, x] + 
      D[Subscript[T, D][x, y, t], y, y]) + Subscript[Q, 0] == 
  Subscript[\[Rho], CLS]*Subscript[Cp, CLS]*
   D[Subscript[T, D][x, y, t], t]

I haven't considered the heat source as time-dependant just yet to simplify just a bit. Thank you in advance!

POSTED BY: Roberta Mongillo