In[]:=
Quit[]
In[]:=
​​qs=10;ρ=7870;K=80;Cp=450;To=25;​​
In[]:=
L=0.01;Δt=0.01;tt=1;w=0.5;​​A=w*L;nt=tt/Δt;​​Ton=N[To];​​(*
Numerodetram
*)​​nn=9;Print["Número de trams = ",nn]​​(*
Númerodenodes
*)​​NN=nn+1;Print["Número de nodes = ",NN]​​Δx=
L
nn
;Print["Δx = ",Δx1000," mm"]​​Print["L = ",nnΔx," m"]​​(*
Condicionsinicials
*)​​initialcond=Table[
T
i
[0]=To,{i,1,NN}];​​(*
Condicionsdefrontera
*)​​boundarycond=Table[
T
NN
[t]=To,{t,Δt,tt,Δt}];​​Dimensions[initialcond]​​Dimensions[boundarycond]​​
Número de trams = 9
Número de nodes = 10
Δx = 1.11111 mm
L = 0.01 m
Out[]=
{10}
Out[]=
{100}
In[]:=
AW=KA/Δx;AE=KA/Δx;Sp=ρAΔxCp/Δt;​​eq[i_]=(Sp+AW+AE)
T
i
[t]AW
T
i-1
[t]+AE
T
i+1
[t]+Sp
T
i
[t-Δt]+Δxqs;​​eq[1]=
T
1
[t]
T
2
[t]+(qs*A)/(AW);​​eq[2]=(Sp+0+AE)
T
2
[t]0+AE
T
3
[t]+Sp
T
2
[t-Δt]+Δxqs;​​eq[9]=(Sp+AW+AE)
T
9
[t]AW
T
8
[t]+AETon+Sp
T
9
[t-Δt]+Δxqs;​​eq[NN]=Ton;​​eqn=Table[eq[i],{i,3,NN-1}];​​eqns=Flatten[Join[{eq[1]},{eq[2]},{eqn}]];​​MatrixForm[eqns]​​Dimensions[eqn];​​Dimensions[eqns]​​
Out[]//MatrixForm=
T
1
[t]0.000138889+
T
2
[t]
2327.5
T
2
[t]0.0111111+1967.5
T
2
[-0.01+t]+360.
T
3
[t]
2687.5
T
3
[t]0.0111111+360.
T
2
[t]+1967.5
T
3
[-0.01+t]+360.
T
4
[t]
2687.5
T
4
[t]0.0111111+360.
T
3
[t]+1967.5
T
4
[-0.01+t]+360.
T
5
[t]
2687.5
T
5
[t]0.0111111+360.
T
4
[t]+1967.5
T
5
[-0.01+t]+360.
T
6
[t]
2687.5
T
6
[t]0.0111111+360.
T
5
[t]+1967.5
T
6
[-0.01+t]+360.
T
7
[t]
2687.5
T
7
[t]0.0111111+360.
T
6
[t]+1967.5
T
7
[-0.01+t]+360.
T
8
[t]
2687.5
T
8
[t]0.0111111+360.
T
7
[t]+1967.5
T
8
[-0.01+t]+360.
T
9
[t]
2687.5
T
9
[t]9000.01+360.
T
8
[t]+1967.5
T
9
[-0.01+t]
Out[]=
{9}
In[]:=
(*solversinDo*)​​​​unknown=Flatten[Table[
T
i
[t],{i,1,NN-1}]]​​unknown2=MatrixForm[unknown]​​eqns2=MatrixForm[eqns]​​Solve[eqns2,unknown2]​​
Out[]=
{
T
1
[t],
T
2
[t],
T
3
[t],
T
4
[t],
T
5
[t],
T
6
[t],
T
7
[t],
T
8
[t],
T
9
[t]}
Out[]//MatrixForm=
T
1
[t]
T
2
[t]
T
3
[t]
T
4
[t]
T
5
[t]
T
6
[t]
T
7
[t]
T
8
[t]
T
9
[t]
Out[]//MatrixForm=
T
1
[t]0.000138889+
T
2
[t]
2327.5
T
2
[t]0.0111111+1967.5
T
2
[-0.01+t]+360.
T
3
[t]
2687.5
T
3
[t]0.0111111+360.
T
2
[t]+1967.5
T
3
[-0.01+t]+360.
T
4
[t]
2687.5
T
4
[t]0.0111111+360.
T
3
[t]+1967.5
T
4
[-0.01+t]+360.
T
5
[t]
2687.5
T
5
[t]0.0111111+360.
T
4
[t]+1967.5
T
5
[-0.01+t]+360.
T
6
[t]
2687.5
T
6
[t]0.0111111+360.
T
5
[t]+1967.5
T
6
[-0.01+t]+360.
T
7
[t]
2687.5
T
7
[t]0.0111111+360.
T
6
[t]+1967.5
T
7
[-0.01+t]+360.
T
8
[t]
2687.5
T
8
[t]0.0111111+360.
T
7
[t]+1967.5
T
8
[-0.01+t]+360.
T
9
[t]
2687.5
T
9
[t]9000.01+360.
T
8
[t]+1967.5
T
9
[-0.01+t]
Solve
:(1) is not a quantified system of equations and inequalities.
Out[]=
Solve
T
1
[t]0.000138889+
T
2
[t]
2327.5
T
2
[t]0.0111111+1967.5
T
2
[-0.01+t]+360.
T
3
[t]
2687.5
T
3
[t]0.0111111+360.
T
2
[t]+1967.5
T
3
[-0.01+t]+360.
T
4
[t]
2687.5
T
4
[t]0.0111111+360.
T
3
[t]+1967.5
T
4
[-0.01+t]+360.
T
5
[t]
2687.5
T
5
[t]0.0111111+360.
T
4
[t]+1967.5
T
5
[-0.01+t]+360.
T
6
[t]
2687.5
T
6
[t]0.0111111+360.
T
5
[t]+1967.5
T
6
[-0.01+t]+360.
T
7
[t]
2687.5
T
7
[t]0.0111111+360.
T
6
[t]+1967.5
T
7
[-0.01+t]+360.
T
8
[t]
2687.5
T
8
[t]0.0111111+360.
T
7
[t]+1967.5
T
8
[-0.01+t]+360.
T
9
[t]
2687.5
T
9
[t]9000.01+360.
T
8
[t]+1967.5
T
9
[-0.01+t]
,
T
1
[t]
T
2
[t]
T
3
[t]
T
4
[t]
T
5
[t]
T
6
[t]
T
7
[t]
T
8
[t]
T
9
[t]

(*m=0;​​Do[​​m=m+1;​​t=m*Δt;​​unknown=Flatten[Table[
T
i
[t],{i,1,NN-1}]];​​solution=unknown/.Solve[eqns,unknown][[1]];​​Table[
T
i
[t]=solution[[i-1]],{i,1,NN-1}];,nt]​​Print[unknown]​​Print[solution]​​​​​​​​​​
(*solution1=Table[
T
i
[t],{i,1,NN},{t,Δt,tt,Δt}];​​MatrixForm[Transpose[solution1]]*)
​
​​