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Nonadiabatic Tubular Reactor with Negligible Mass Dispersion

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Consider a nonadiabatic tubular reactor with negligible mass dispersion (i.e. ) where a first-order exothermic reaction takes place [1, 2]. This system is governed by the following two dimensionless parabolic partial differential equations and boundary conditions BC1 and BC2:

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,

,

BC1: : ,

BC2: : , .

Here is concentration and is temperature, is the activation energy, is the heat Thiele modulus, is the mass Thiele modulus, is the heat evolution parameter, is the dimensionless cooling temperature, is the dimensionless cooling parameter, is the Damköhler number, and is the Lewis number.

As can be seen from snapshot 1, periodic solutions are obtained for and . In the figure, and are plotted versus in blue and green, respectively. Also, you can see from snapshot 1 that a limit cycle is obtained for the above values of and .

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Contributed by: Housam Binous, Abdullah A. Shaikh, and Ahmed Bellagi (February 2016)
(King Fahd University of Petroleum and Minerals, KSA; ENIM, University of Monastir, Tunisia)
Open content licensed under CC BY-NC-SA

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References

[1] S. Subramanian and V. Balakotaiah, "Classification of Steady-State and Dynamic Behavior of Distributed Reactor Models," Chemical Engineering Science, 51(3), 1996 pp. 401–421. doi:10.1016/0009-2509(95)00261-8.

[2] M. Kubíček, and M. Marek, Computational Methods in Bifurcation Theory and Dissipative Structures, Springer Series in Computational Physics, New York: Springer-Verlag, 1983.

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