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PDE heat equation (inconsisten problem)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93177] PDE heat equation (inconsisten problem)
  • From: Matteo Calabrese <calabrex87 at hotmail.it>
  • Date: Thu, 30 Oct 2008 02:01:29 -0500 (EST)

Dear Mathematica Friends,

I'm trying to solve this simple problem: I've got a silicon bar in 1D resolving fourier equation of heat. With these Boundary Condition, mathematica gives me this kind of error. however, solution seems consistent with the problem. Could anybody explain ad resolve it??

thank you in advance,

Matteo Calabrese

University of Physics

Turin, Italy


(*Mathematica Vs 6.0*)

 

kappa=1.;

ro=1.;

c=1.;

k=(ro*c)/kappa;

h=1.; 

side=1.; (*silicon bar length *)

tmax=1;

to=20.; (* room temperature*)

 

eq={Tx,x[x,t]==k*Tt[x,t]}; (*Fourier's heat equation 1D*)

(*Initial condition*)

 ic={T[x,0]?If[x>0,0,40]};

(*Boundary Condition*)

 bc1={T[0,t]?40.}; (*dirichlet condition*)

 bc2={Derivative[1,0][T][side,t]?-h (T[side,t]-to)} (*Newton-Robin condition*)

 

 sol=NDSolve[{Join[eq,ic,bc1,bc2]},T[x,t],{x,0,side},{t,0,tmax}]

 NDSolve::ibcinc: Warning: Boundary and initial conditions are inconsistent. ?

 {{T[x,t]¢çInterpolatingFunction[{{0.,1.},{0.,1.}},<>][x,t]}}

 

(*If you plot the Interpolating function, it seems a good solution*)

 

 

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