# Stationary States in a Nonisothermal Continuous Stirred-Tank Reactor

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This Demonstration analyzes the single-step reaction in a nonisothermal continuous well-stirred tank reactor (CSTR) where is the heat of reaction. The rate of reaction is first order in the concentration of species , so that , and the rate constant has an Arrhenius temperature dependence: . Heat is removed from the reactor using a cooling coil that has an overall heat transfer coefficient and surface area . The Demonstration shows the complex steady states (expressed as plots of temperature versus , and conversion fraction versus ) that can occur in the reactor as the residence time and the heat transfer parameter are varied. The possibilities include a unique steady state and multiple steady states, as well as the birth and death of an isola (or island), which is a region in the solution space described by a closed loop.

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Contributed by: Brian G. Higgins and Housam Binous (February 2012)

Open content licensed under CC BY-NC-SA

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## Details

The dynamics of the nonadiabatic CSTR are described by the following mass and energy balances [1]:

,

,

subject to the initial conditions , .

[1] P. G. Gray and S. K. Scott, *Chemical Oscillations and Instabilities: Non-linear Chemical Kinetics*, Oxford: Claredon Press, 1994.

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