Figure A.5:

Dimensionless concentration versus dimensionless radial position for different numbers of collocation points.

Code for Figure A.5

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.

Phi  = 10;
n    = 1;
p.Phi = Phi;
p.n = n;

nint = 100;
xint = linspace(0, 3, nint)';


colvec = [5; 10; 30; 50];
ncol   = length(colvec);
ccol   = zeros(ncol, ncol);
csave  = zeros(nint, ncol);
cerr   = zeros(nint, ncol);
can    = 3./xint.*sinh(Phi*xint)/sinh(3*Phi);
can(1) = 3*Phi/sinh(3*Phi);
etaan = 1./Phi*(1./tanh(3*Phi)-1/(3*Phi));
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;
  W = polinterp(R,xint);
  %
  % 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);
  cint = W*c;
  csave(:,i) = cint;
  cerr(:,i)  = abs((cint - can))./can;
  %
  % compute the effectiveness factor
  %
  eta  = (n+1)/2*A(npts,:)*c/Phi^2;
  etaerr(i) = abs(eta - etaan)/etaan;
  results = [R c];
%  save ('-ascii', sprintf ('pelletcolloc_%d.dat', i), 'results');
end
table = [xint csave cerr];
save -ascii pelletcolloc.dat table;

if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
%plot the pellet profiles for different collocation numbers
plot(xint, csave(:,1:ncol))
% TITLE
end % PLOTTING

polinterp.m

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function W = polinterp(xcol,xint)
  ncol = length(xcol);
  nint = length(xint);
  W = zeros(nint, ncol);
  for i = 1: ncol
    d = 1.0;
    for j = 1: ncol
      if (j ~= i )
	d = d*(xcol(i) - xcol(j));
      end
    end
    for k = 1: nint
      xx = xint(k);
      n = 1.0;
      for j = 1: ncol
	if (j ~= i)
	  n = n*(xx- xcol(j));
	end
      end
      W(k,i) = n/d;
    end
  end

pellet.m

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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);