Stationary states and flow diagrams with exponential approximation

Stationary states and flow diagrams with exponential approximation 

Equations (7.16a) and (7.16b) correspond to our single first-order exothermic reaction occurring in 9 CSTR fed by reactants at the oven temperature, with the exponential approximation made to the Arrhenius temperature dependence of the reaction rate constant. Stationary-state solutions cor-repond to values of the dimensionless concentration a and temperature rise 9 for which da/dr and dO/dt are simultaneously equal to zero, i.e. 

Dividing eqn(7.18) throughout by the dimensionless adiabatic temperature rise 0ad and then adding these two conditions gives the stationary-state 

The left-hand side of this equation is the extent of reaction the quotient 0ss/0ad on the right-hand side is the fractional temperature rise compared with the maximum possible (adiabatic temperature rise). 

At the extreme of perfect adiabatic operation (x - 0 so tn becomes infinite and no heat is lost through the reactor walls), then eqn (7.19) reduces to 

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