Hi

I tried to follow up your indication, without success unfortunately.

I’m in Maple since May of this year  that is way I can’t construct right numeric solution.
It frustrated me very much.

Lets simplify the problem to steady state.
1^st wall: x from 0 to x1;

2^nd wall: x from x1 to x2;

Equation: diff(T(x),x,x)=0;

BC1 = T(0)=1200, #heated side

BC2 = diff(T(x2),x)=-(h/lambda2)*(T(x2)-Tamb) # cooling side
…
and …

BC3 = lambda1*diff(T(x1)=-lambda2*diff(T(x1),x)  #interior boundaries.

If it is no problem for you, please advise me, how to using piecewise transformation according your previous answer.

Regards
wzelik

Hi

I tried to follow up your indication, without success unfortunately.

I’m in Maple since May of this year  that is way I can’t construct right numeric solution.
It frustrated me very much.

Lets simplify the problem to steady state.
1^st wall: x from 0 to x1;

2^nd wall: x from x1 to x2;

Equation: diff(T(x),x,x)=0;

BC1 = T(0)=1200, #heated side

BC2 = diff(T(x2),x)=-(h/lambda2)*(T(x2)-Tamb) # cooling side
…
and …

BC3 = lambda1*diff(T(x1)=-lambda2*diff(T(x1),x)  #interior boundaries.

If it is no problem for you, please advise me, how to using piecewise transformation according your previous answer.

Regards
wzelik

Thank you very much for help.

Regards
wzel

Thank you very much for help.

Regards
wzel

Hi again!

Something wrong with my question?  ...or the problem is in pdsolve? :-) :-) :-).

Please for any adivice!

Regards
wzel 

Hi,

The problem is that I don’t  have idea how to set up pdsolve!
I have solved problem  for one domain. It was easy.

PDE := diff(T(x, t), t) = a*(diff(T(x, t), x, x));
a := 9.245*10^(-7); L := .3; h := 10; lambda := 3; `epsilon;` := .85; sigma := 5.6697*10^(-8);
IBC := {T(0, t) = 1000, T(x, 0) = 298, (D[1](T))(L, t) = -h*(T(L, t)-298)/lambda+`epsilon;`*sigma(T(L, t)^4-298^4)};
pds := pdsolve(PDE, IBC, numeric, timestep = 50);
p1 := pds:-plot(t = 100);
p2 := pds:-plot(t = 36000);
plots[display]({p1, p2}, title = `Heat profile at t=100 and 3600 seconds`); 

But I’m looking for solution from two or three domain, for classical multilayer transient heat transfer.
I know there are another numeric possibility, finite element, finite differences,
but I wonder if it possible with Maple.

Regards wzel
 
PS:
In the previous post I made typing error in BC2, sorry for that.