Figure 6.28:

Conversion and temperature vs. time for \tau =30min.

Code for Figure 6.28

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 k_m T_m E c_Af theta C_ps T_f DeltaH_R U T_a Kc T_fs T_set
%
% limit cycle parameters
%
% units are kmol, min, kJ, K, m^3
%
k_m      = 0.004;
T_m      = 298;
E        = 15000;
c_Af     = 2;
C_p      = 4;
rho      = 1000;
C_ps     = C_p*rho;
T_f      = 298;
T_a      = T_f;
DeltaH_R = -2.2e5;
U        = 340;
theta    = 30;
T_set    = 321.53;
c_set    = 0.48995;
T_fs     = T_f;
Kc       = 0;
gamma    = E/T_f;
B        = -DeltaH_R*c_Af*gamma/(C_ps*T_f);
beta     = U/C_ps*theta;
Da       = k_m*exp(-E*(1/T_f-1/T_m))*theta;
x2c      = (T_a-T_f)/T_f*gamma;


x0=[c_Af; T_f];
tfinal = 10*theta;
ntimes = 500;
tout   = linspace(0, tfinal, ntimes);
opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, x] = ode15s (@rhs, tout, x0, opts);
u = (x(:,2) - T_set)*Kc + T_fs;
conv = (c_Af - x(:,1)) / c_Af;
table = [tout' x conv u];
save -ascii dyn_osc_hopf1.dat table;

if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
subplot(2,1,1);
plot (table(:,1), table(:,4));
% TITLE dyn_osc_hopf1

subplot(2,1,2);
plot (table(:,1), table(:,3));
% TITLE dyn_osc_hopf1
end % PLOTTING

rhs.m


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function retval = rhs(t,x)
global k_m T_m E c_Af theta C_ps T_f DeltaH_R U T_a Kc T_fs T_set
c_A   = x(1);
T     = x(2);
k     = k_m*exp(-E*(1/T - 1/T_m));
T_f   = T_fs + Kc*(T-T_set);
retval = zeros (2, 1);
retval(1) = (c_Af - c_A)/theta - k*c_A;
retval(2) = U/C_ps*(T_a - T) + (T_f - T)/theta - k*c_A*DeltaH_R/C_ps;