This Demonstration finds the steady states using both the mass and energy balance equations and the arc-length continuation technique [1].

The mass balance equations for the species and give:

,

and ,

where is the residence time and and are the reaction rate constants given by the Arrhenius law.

The energy balance can be written as ,

where ,

and .

Here, and are the heats of reactions, is the molar flow rate, is the heat capacity, is the density, the subscript indicates inlet conditions, is the overall heat transfer coefficient, is the area of the cooling jacket, is the temperature of cooling, and is the reactor's volume.

The steady states are shown by the blue dots and are given if you choose the "solution list" tab. In addition, the four turning points are shown using green dots in a separate plot.

Finally, you can vary the parameter and see that up to five steady states can be obtained.