**Adiabatic Plug Flow Reactor with Recycle**

An adiabatic plug flow reactor (PFR) with recycle is used to carry out a first-order reaction. The fresh feed inlet temperature T_{i} and concentration are known, but the inlet temperature T_{0} and the inlet concentration to the PFR are not. Since T_{0} and the inlet concentration are initial conditions needed to solve the differential equations for the mass and energy balances for the PFR, an iterative solution is needed. The value of T_{0} can be calculated only when the differential equations are solved for T_{final}. Thus, the value of T_{0} is guessed using the slider (and the feed concentration to the reactor calculated using the adiabatic relation between temperature and concentration), and the exit temperature T_{final} from the PFR is then obtained from the solution of the differential equations. The estimated value of T_{0} is adjusted until the calculated value of T_{i} (arrow in figure on left) equals the known T_{i} (the green circle); multiple solutions are possible under some conditions. High recycle ratios approach continuous-stirred tank reactor (CSTR) behavior. A plot of temperature as a function of distance down the PFR is generated. The inlet temperature to the system T_{i} and the recycle ratio can be varied.
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