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Consider a CSTR with the first order consecutive exothermic reaction according to the scheme 
and with a perfectly mixed cooling jacket. Using the usual simplifications, the model of the CSTR is described by four nonlinear differential equations [6][7].
(Babu & Angira, 2001a)
(Back, Fogel, & Michalewicz, 1997)
(Nauman, n.d.)
(Dieu, Ngoc, & Schegner, 2012)with initial conditions
and
Here,
t is the time,
c are concentrations,
T are temperatures,
V are volumes, ρ are densities,
cp are specific heat capacities,
Q are volumetric flow rates,
Ah is the heat exchange surface area and
U is the heat transfer coefficient. The subscripts are denoted (
.)
r for the reactant mixture, (
.)
c for the coolant, (
.)
i for feed (inlet) values and the superscript (
.)
s for steady-state values. The reaction rates and the reaction heat are expressed as
(Dasgupta & Michalewicz, 1997)
(Dostál, Bobál & Blaha, 2001)Where
k0 are pre-exponential factors,
E are activation energies and
h are reaction entalpies. The values of all parameters, feed values and steady-state values are given in Table 1 [7].