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Using boundary of 2D domain into 1D input for NDSolve PDEs

Posted 22 days ago
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I am trying to solve three simultaneous PDEs, where the first two are 1D in spatial and the third equation is 2D. $$T_f[\tau,z] = T_g[\tau,z,0.05]$$

When I try to use the above equation within the NDSolve I get the following error

Function::fpct: Too many parameters in {[Tau],z,r} to be filled from Function[{[Tau],z,r},10][[Tau],z].

Tfin[\[Tau], z]==Tg[\[Tau], z,0.05]

$$ T_g[\tau,g,r=0.05] $$ is unknown of the 3rd PDE. Can someone help how to overcome this problem.

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