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


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% 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.

global Phi A Aint Bint Rint n

Phi  = 10;
n    = 1;
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);
  %
  % global collocation
  %
  [R A B Q] = colloc(npts-2, 'left', 'right');
  R = R*3;
  A = A/3;
  B = B/9;
  Q = Q*3;
  Aint = A(2:npts-1,:);
  Bint = B(2:npts-1,:);
  Rint = R(2:npts-1);
  %
  % solve the problem
  %
  c0=0.5*linspace(0,1,npts)';
  tol = 1e-10;
  opts = optimset ('TolFun', tol);
  [c,fval,info] = fsolve('pellet',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


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function retval = pellet(c)
  global Phi A Aint Bint Rint n
  npts = length(c);
  cint = c(2:npts-1);
  retval(1)    = A(1,:)*c;
  retval(2:npts-1,1) = Bint*c + 2*Aint*c./Rint - 2/(n+1)*Phi^2*(cint.^n);
  retval(npts) = 1 - c(npts);