2412 The following differential equation describes the stead

24.12 The following differential equation describes the steady-state concentration of a substance that reacts with first-order kinetics in an axially dispersed plug-flow reactor (Fig. P24.12): dx2 dx where D the dispersion coefficient (m /hr), c concen tration (mol/L), x distance (m), U the velocity (m/hr), 637 reactor.

Solution

% Centred Difference method

%The length is divided in to 10 segments starting from x=0 (denoted 1) to

%x=100 (denoted as 11)

D=5000;

U=100;

k=2;

L=100;

Cin=100;

step=10;

x=[0:step:100];

for i=1:length(x)

for j=1:length(x)

if j==i-1

A(i,j)=1+(U*step)/(2*D);

elseif j==i

A(i,j)=-(2+(k*step^2)/D);

elseif j==i+1

A(i,j)=1-(U*step)/(2*D);

else

A(i,j)=0;

end

end

A(1,1)=-62/25;

A(1,2)=2;

A(11,10)=2;

x(i+1)=x(i)+step;

end

b=[-44;0;0;0;0;0;0;0;0;0;0];

C=A\\b;

C