Catalytic Reaction in a Flat Particle

Variables and parameters:

y: dimensionless concentration

x: dimensionless coordinate ( $0\leq x\leq 1$)

$\vartheta$: Thiele modulus (bifurcation parameter: $\lambda :=\vartheta^2$)

$\gamma$: dimensionless energy of activation

$\beta$: dimensionless parameter of heat evolution, $\beta=0.4$

ODE boundary-value problem

\begin{displaymath}\displaystyle{d^2 y \over d x^2}
= \vartheta^2 y^m
\exp\left[ {\gamma \beta (1 - y ) \over 1 + \beta (1 - y)}\right ]

\begin{displaymath}\displaystyle{dy(0) \over dx} = 0,\ \ \ y (1) = 1.\end{displaymath}

We choose the first-order reaction (m=1).


Figure 1
Branching diagrams y1(0) versus $\lambda$ for six values of the second parameter $\gamma$: $\gamma=20$ (left profile), $\gamma=18$, 14, 12, and $\gamma=10$ (right profile).

Figure 2
$(\lambda,\gamma)$-parameter chart with two turning point curves.

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