Re: PDE heat equation (inconsisten problem)

• To: mathgroup at smc.vnet.net
• Subject: [mg93233] Re: [mg93177] PDE heat equation (inconsisten problem)
• From: "Tony Harker" <a.harker at ucl.ac.uk>
• Date: Sat, 1 Nov 2008 05:04:22 -0500 (EST)
• References: <200810300701.CAA00581@smc.vnet.net>

```What Mathematica is telling you is quite right. Your initial conditions
implies T[0,0]=0, and your boundary condition bc1 implies T[0,0]=40,
so they are incompatible. This is a fairly standard situation, and
physicists and engineers annoy mathematicians with their rather cavalier

Tony Harker

Dr A.H. Harker
Department of Physics and Astronomy
University College London
Gower Street
London
WC1E 6BT

Tel: (44)(0) 2076793404
E:    a.harker at ucl.ac.uk

EDUCATION, n. That which discloses to the wise and disguises from the
foolish their lack of understanding. (Ambrose Bierce, The Devil's
Dictionary, 1911)

]-> -----Original Message-----
]-> From: Matteo Calabrese [mailto:calabrex87 at hotmail.it]
]-> Sent: 30 October 2008 07:01
]-> To: mathgroup at smc.vnet.net
]-> Subject: [mg93177] PDE heat equation (inconsisten problem)
]->
]-> 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??
]->
]->
]-> 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.; (* room temperature*)
]->
]->
]->
]-> eq={Tx,x[x,t]==k*Tt[x,t]}; (*Fourier's heat equation 1D*)
]->
]-> (*Initial condition*)
]->
]->  ic={T[x,0]=C5 If[x>0,0,40]};
]->
]-> (*Boundary Condition*)
]->
]->  bc1={T[0,t]=C5 40.}; (*dirichlet condition*)
]->
]->  bc2={Derivative[1,0][T][side,t]=C5 -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. =E2=80=A1
]->
]->  =
{{T[x,t]=C2=A2=C3=A7InterpolatingFunction[{{0.,1.},{0.,1.}},<>][x,t]}}
]->
]->
]->
]-> (*If you plot the Interpolating function, it seems a good solution*)
]->
]->
]->
]->
]->
]-> ________
]->

```

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