Thermal behavior of a tubular flow reactor

In a tubular reactor system, the temperature rises along the reactor length for an exothermic reaction unless effective cooling is maintained. For multiple steady states to appear, it is necessary that a 

If an appropriate thermal feedback mechanism is not provided, the reaction occurs at the lower stationary state where the reaction rate may be negligible. The reaction could be extinguished, if the temperature of the feed entering the reactor drops below some critical value due to fouling of the heat exchange surface. 

An important effect in the design of a tubular flow reactor is the development of a radial temperature gradient in a highly exothermic reaction with wall cooling. The temperatures near the tube axis are 

Consider a first order adiabatic reaction in a CFSTR with the following characteristics  

The rate constant k is expressed as k = exp(15.32 - 7,550/T), sec Determine the operating points for both the mass and heat balance equations. 

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