Transient Heat Flow
Calfem - example
2D Heat Flow
Conductivity = 1*10-4 W/m oC
Capacity = 0.25 J/K Kg
0oC
qn=0
3m
7m
0oC
Initial temp. 20oC
20oC
qn=0
12m
5m
Vertices = [ % Define the vertex coordinates
0 0
12 0
17 0
17 7
10
12 7
12 10
0 10
8
0 7 ];
Segments = [ % Define the line segments
6
1 2
2 3
4
3 4
4 5
5 6
2
6 7
7 8
0
8 1
2 5
8 5];
0
2
4
6
8
10
12
Surfaces=[
1 9 10 8
% Define the surfaces
2 3 4 9
10 5 6 7];
Seed = [ 9 4 7 4 3 9 3 7 7 9]*2; % Define the number of elements on each segment
Segp=[Seed];
nen=3;
% Three node elements
dofsPerNode=1;
mp=[ dofsPerNode, nen];
geomdraw2(Vertices,Segments,Surfaces,Segp,mp) % Draw the geometry
% Generate the element mesh
[Coord Edof Dof meshdb ]=strmeshgen(Vertices,Segments,Surfaces,Segp,mp);
[Ex,Ey]=coordxtr(Edof,Coord,Dof,nen);
Element mesh
14
16
t=1;
rho=1;
c=0.25;
ep=[t, rho ,c];
D=1E-4*[1 0;0 1];
nel=size(Edof,1);
ndof=max(Dof));
K=sparse(ndof,ndof);
C=sparse(ndof,ndof);
f=sparse(ndof,1);
for i=1:nel
[Ke,Ce]=flw2tt(Ex(i,:),Ey(i,:),ep,D);
K=sparse_assem(Edof(i,:),K,Ke);
C=sparse_assem(Edof(i,:),C,Ce);
End
bc1=extrseg ([3]',meshdb,1);
bc2=extrseg ([6 7 8]',meshdb,1);
bc=[bc1, ones(length(bc1),1)*20; bc2, ones(length(bc2),1)*0];
Using step1.m
a0=ones(ndof,1)*0;
% The initial temperature 0 degrees
ti=[3600:3600:3600*96];
% Define a time-step vector
ip=[3600 3600*96 0.5 [96 278 ti Dof']]; % Define: ∆t, total time, Crank-Nicholson,
[no. of values to store, ndof, times ti, dofs]
[Tsnap,D,V]=step1(K,C,a0,ip,f,bc)
% Solve problem in time
Temperature distribution
2 hours
96 hours
Flux distribution
2 hours
96 hours