Figure A.6:

Relative error in the effectiveness factor versus number of collocation points.

Code for Figure A.6

Text of the GNU GPL.

main.m


 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as
% published by the Free Software Foundation; either version 2, or (at
% your option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
% General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; see the file COPYING.  If not, write to
% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
% MA 02111-1307, USA.

Phi  = 10;
n    = 1;
p.Phi = Phi;
p.n = n;
nint = 100;
xint = linspace(0, 3, nint)';


colvec = [5; 10; 15; 20; 25; 30];
ncol   = length(colvec);
etaan = 1./Phi*(1./tanh(3*Phi)-1/(3*Phi));
etaerror = zeros (ncol, 1);
for i = 1: ncol
  npts = colvec(i);
  % collocation
  [R A B Q] = colloc(npts-2, 'left', 'right');
  R = R*3;
  A = A/3;
  B = B/9;
  Q = Q*3;
  p.R = R;
  p.A = A;
  p.B = B;

  % solve the problem
  c0=0.5*linspace(0,1,npts)';
  tol = 1e-10;
  opts = optimset ('TolFun', tol);
  [c,fval,info] = fsolve(@(x) pellet(x,p), c0, opts);
  %
  % compute the effectiveness factor
  %
  eta  = (n+1)/2*A(npts,:)*c/Phi^2;
  etaerror(i) = abs(eta - etaan)/etaan;
end
table  = [colvec etaerror];
save -ascii etaerr.dat table;
if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
semilogy (table(:,1), table(:,2), '-o');
% TITLE
end % PLOTTING

pellet.m


1
2
3
4
function retval = pellet(c, p)
  retval = p.B*c + 2*p.A*c./p.R - 2/(p.n+1)*p.Phi^2*(c.^p.n);
  retval(1)    = p.A(1,:)*c;
  retval(end) = 1 - c(end);