Reaction time—non-isothermal operation

Finding the time required for a particular conversion involves the solution of two simultaneous equations, i.e. 1.24 or 1.25 for the material balance and 1.27 for the heat balance. Generally, a solution in analytical form is unobtainable and numerical methods or analogue simulation must be used. Taking, for example, a first-order reaction with constant volume  

A typical requirement is that the temperature shall not rise above Tmx in order to avoid byproducts or hazardous operation. The forms of the solutions obtained are sketched in Fig. 1.12. 

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