Fig. 9.5-1 from BSL
This problem is intended to model a chemical reaction in a fixed-bed flow reactor. The section from z=0 to z=L is packed with catalytic pellets. We want to find how the temperature varies in the reactor. We make the assumption that the reactor is well insulated so temperature does not vary radially. We also assume plug flow. The fluid enters with a velocity, v1, and temperature, T1.
The graph above is for the values of N between -2 and 2. It is identical to the graph shown in the book. The graph below contains plots for N values of 4 and 10. For this range of N, Maple has some difficulty as it generates negative numbers. Also the temperature fluctuates greatly in the catalytic region of the reactor. Large values of N imply that the reaction is proceeding very quickly and generating a lot of heat. For this case our starting equation, 9.5-1, is invalid and the reactor will not operate in steady state because the velocity of the flow is not large enough to counteract the amount of heat generated.
