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From: Torsten Hennig on 25 May 2010 22:40
> Hello everybody.
> I am programming a .m-file that computes the
> temperature distribution in a cylinder that consists
> of 4 layers each one having different specific heat
> capacities / densities / thermal conductivities. The
> inner temperature is constant, whereas the outer wall
> is giving heat via conduction to the environment.
> However when I let the programm to give me the values
> for t=> infinity, I dont get the correkt values like
> in the steady-state-model :S any help would be
> appreciated. Here is the m.file:
>
> function pdex2
> m = 1;
> x = linspace(0.295,0.655,40);
> t = linspace(0,8e+7,40);
> sol = pdepe(m,@pdex2pde,@pdex2ic,@pdex2bc,x,t);
> u = sol(:,:,1);
>
> surf(x,t,u)
> title('Numerical solution computed with 40 mesh
> points.')
> xlabel('Distance x')
> ylabel('Time t')
>
> figure
> plot(x,u(end,:),'r')
> title('Solution at t = oo')
> xlabel('Distance x')
> ylabel('u(x,oo)')
>
> %
> ------------------------------------------------------
> --------
> function [c,f,s] = pdex2pde(x,t,u,DuDx)
> ri=0.295; lambdai2=1.685; rocpi2=1600000;
> r2=0.395; lambda23=0.176; rocp23=800000;
> r3=0.520; lambda34=0.13; rocp34=400000;
> r4=0.645; lambda4w=52; rocp4w=7850000;
> rw=0.655;
>
> lambda=stepfun(x,ri)*lambdai2+stepfun(x,r2)*(lambda23-
> lambdai2)+stepfun(x,r3)*(lambda34-lambda23)+stepfun(x,
> r4)*(lambda4w-lambda34);
> rocp=stepfun(x,ri)*rocpi2+stepfun(x,r2)*(rocp23-rocpi2
> )+stepfun(x,r3)*(rocp34-rocp23)+stepfun(x,r4)*(rocp4w-
> rocp34);
>
> c = rocp;
> f = DuDx.*lambda;
> s = 0;
>
> %
> ------------------------------------------------------
> --------
> function u0 = pdex2ic(x)
> u0 = 400;
> %
> ------------------------------------------------------
> --------
>
> function [pl,ql,pr,qr] = pdex2bc(xl,ul,xr,ur,t)
> pl = ul-400;
> ql = 0;
> pr = (ur-20)*10/52;
> qr = 1;
>
>
>
> THANKS ALOT FOR ANY HELP

pdepe is not the suitable tool to solve layer problems
because it does not take into account the interface
conditions
T+ = T- ; lambda+*(dT/dn)+ = lambda-*(dT/dn)-
(continuity of temperature and heat flux)

Best wishes
Torsten.
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