Details

The equations in this problem are the following:

mass balance (concentration)

; (1)

boundary conditions

, (2)

; (3)

initial condition

; (4)

=, (5)

with boundary conditions

, (6)

, (7)

and initial condition

. (8)

We can define

, , , ;

then for a dimensionless concentration,

, (9)

with the boundary conditions

, (10)

and , (11)

and initial condition

. (12)

For dimensionless temperature,

=, (13)

with boundary conditions

, (14)

, (15)

and initial condition

. (16)

Equations (9) to (16) are solved using the Mathematica command NDSolve for different parameters. It is possible to solve this problem using a collocation method.