Example 3.11 Spherical Catalyst Pellet
Concentration distribution inside a spherical catalyst pellet is governed by the following equation:
(3.68)
This equation is solved below using Maple's 'dsolve' command:
| > |
eq:=diff(c(x),x$2)+2/x*diff(c(x),x)-phi^2*c(x); |
 |
(1) |
 |
(2) |
| > |
sol:=dsolve({eq,BCs},c(x)); |
 |
(3) |
Maple is not able to solve this problem directly. We can solve this problem without specifying the boundary conditions:
| > |
sol:=dsolve({eq},c(x)); |
 |
(4) |
The solution obtained can be assigned as:
 |
(5) |
Now if ya has to be finite at x = 0, _C2 should be zero.
 |
(6) |
 |
(7) |
Next, the boundary condition at x = 1 is used to solve for _C1.
 |
(8) |
 |
(9) |
 |
(10) |
A three dimensional plot can be made as:
| > |
plot3d(Ca,x=0..1,phi=0..10,axes=boxed,orientation=[120,60],title="Figure Exp.3.1.15.",labels=[x,phi,"Ca"]); |