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MathGroup Archive 2007

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Re: Other PDE heat equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79737] Re: Other PDE heat equation
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Fri, 3 Aug 2007 06:25:03 -0400 (EDT)
  • Organization: Universitaet Hannover
  • References: <f8pkd4$2vr$1@smc.vnet.net>

Miguel schrieb:
> How can I to resolve the unidirectional heat transmission for a plate
> o slab:
> 
> a=0.03;hc=1890;k=34;L=0.03;
> 
> NDSolve[{a D[u[x,t],{x,2}]==D[u[x,t],t],
> u[L,0]==600,  (* Initial value: the plate has the same temperature *)
> u[-L,0]==600,
> u[0,0]==600,
> (D[u[x,t],x]/.x->0)==0  (* Max. in centre *)
> (D[u[x,t],x]/.x->L)==(-hc/k)(u[L,t]-600)    (* Q convection = Q
> conduction *)
> u[L,t]==u[-L,t]},  (* Temper. symetric *)
> u[x,t],{x,-L,L},{t,0,10}]
> 
> NDSolve::ivone: Boundary values may only be specified for one \
> independent variable. Initial values may only be specified at one \
> value of the other independent variable. >>

There are many. As I see the correct set of equations for your problem is

Specify constants
a=1;
L=1;
hc=1;
k=1;

Equations for first argument in NDSolve

deqs={a Derivative[2,0][u][x,t]-Derivative[0,1][u][x,t]==0 (*PDE*),
u[x,0]==600 (*starting values at t->0 for all x *),
Derivative[1,0][u][L,t]==(-hc/k)(u[L,t]-600) (*right surface current at 
x=L for all t *),
Derivative[1,0][u][-L,t]==(-hc/k)(u[-L,t]-600)(*left surface current *),
}


-- 

Roland Franzius


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