diffreact_spherecat.m

《实用化工计算机模拟：MATLAB在化学工程中的应用 》这本书光盘里的程序~

function DiffReact_SphereCat
% Diffusion with Simultaneous Reaction in a Sphere
%
%   Author: HUANG Huajiang
%   Copyright 2003 UNILAB Research Center, 
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2003/05/13 $

clear all
clc
global CAs R De kppa
CAs = 0.2;
R = 0.5;
De = 0.1;
kppa = 6.4;         % kppa: k''

a = 0;
b = R;

% solution is obtained using an initial guess of y1(x)=1, y2(x)=0 
solinit = bvpinit(linspace(a,b,50),[0 CAs 0]);
sol = bvp4c(@ODEs,@BCfun,solinit);      % 求解ODE-BVP问题
y = deval(sol,[a b])
fprintf('催化剂的有效因子为η = %.3f',y(end,2))

% ------------------------------------------------------------------
function dydr = ODEs(r,y)
global CAs R De kppa
NArr = y(1);
CA = y(2);
eta = y(3);
dNArrdr = -kppa*CA*r^2;
if r == 0
    NA = 0.0;
else
    NA = NArr/r^2;
end
dCAdr = NA/(-De);
detadr = 3*CA*r^2/(CAs*R^3);
dydr = [dNArrdr; dCAdr; detadr];

% ------------------------------------------------------------------
function bc = BCfun(ya,yb)
global CAs
bc = [ya(1); yb(2)-CAs; ya(3)];