The equations that describe the CSTR consist of a temperature equation coupled to the equations for the concentrations of the chemical species considered in the mechanism. In the limiting case that the reactor operates adiabatically, i.e. there is no heat loss between the sides of the reactor and the reaction mixture, the number of equations can be reduced by one.
This is a useful simplication if the total number of equations is small, e.g. 2 or 3. For instance, the most widely studied mechanism is the first-order non-isothermal reaction where a reactive species A decays to a product B. In this case we have a temperature equation and one concentration equation. Thus we have two equations, but in the adiabatic limit we only have one. Thus periodic behaviour does not occur for this model in the adiabatic reactor.
The main reason to assumpe adiabatic behaviour is the resulting simplification of the model. However [Russo & Bequette, 1995] have shown that increasing the reactor size causes a reduction in the ratio of heat transfer area to reactor volume. Therefore as the reactor size is increased the effective heat transfer coefficient decreases. As a result adiabatic operation may be approached when scaling up laboratory sized reactors for industrial operation. Furthermore, combustion in a CSTR can be viewed as an zero-dimensional model for a premixed flame. The assumption of no heat loss therefore equates to a study of an adiabatic flame. It is believed that the treatment of peak premixed flame temperatures as adiabatic is a reasonable approximation [Ewing et al, 1984]. Thus the adiabatic CSTR is therefore of independent interest.