Example 3.2.11 Axial Conduction and Diffusion in a Tabular Reactor

Axial diffusion and conduction in an adiabatic tabular reactor can be described by:[6]

(3.2.31)

(0) = θ(0)1 (3.2.32)

and

(1)=0 (3.2.33)

This coupled boundary value problem is solved in Maple below for the following value of parameters Pe = 10, B0 = 10, E = 18

> |

> | with(plots):

> | Eq[1]:=1/Pe*diff(y(x),x$2)-diff(y(x),x)=4*y(x)*exp(E*(1-1/theta(x)));

| (1)

> | Eq[2]:=1/Bo*diff(theta(x),x$2)-diff(theta(x),x)=-4*beta*y(x)*exp(E*(1-1/theta(x)));

| (2)

> | BCs:=[1/Pe*D(y)(0)-y(0)+1,D(y)(1),1/Bo*D(theta)(0)-theta(0)+1,D(theta)(1)];

| (3)

> | pars:={Pe=10,Bo=10,E=18,beta=0.05};

| (4)

> | for i to 2 do eq[i]:=subs(pars,Eq[i]);od;

| (5)

> | eqs:=(eq[1],eq[2]);

| (6)

> | vars:=(y(x),theta(x));

| (7)

> | bcs:=op(subs(pars,BCs));

| (8)

> | sol:=dsolve({eqs,bcs},{vars},type=numeric);

| (9)

> | sol(0);

| (10)

> | sol(1);

| (11)

> | odeplot(sol,[x,y(x)],0..1,thickness=4,title="Figure Exp. 3.2.21.",axes=boxed);

> | odeplot(sol,[x,theta(x)],0..1,thickness=4,color=green,title="Figure Exp. 3.2.22.",axes=boxed);

> |