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Mathematical Modelling and Kinetics of Microchannel Reactor

Received: 19 December 2016     Accepted: 5 January 2017     Published: 23 January 2017
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Abstract

The coupled nonlinear system of differential equations in 1-butanol dehydration under atmospheric and isothermal conditions are solved analytically for the microchannel reactor. Approximate analytical expressions of concentrations of 1-butanol, 1-butene, water and dibutyl ether are presented by using homotopy analysis method. The homotopy analysis method eliminated the classical perturbation method problem, because of the existence a small parameter in the equation. The analytical results are compared with the numerical solution and experimental results, satisfactory agreement is noted.

Published in Applied and Computational Mathematics (Volume 5, Issue 6)
DOI 10.11648/j.acm.20160506.12
Page(s) 234-246
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Mathematical Modelling, Homotopy Analysis Method, 1-Butanol Dehydration, Microchannel Reactor, Channel Electrode, Non Linear Equation

References
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[3] Walter, S., S, Malmberg., B, Schmidt., M. A. Liauw., 2005. Mass transfer limitations in micro channel reactors. Catal. Today, 110: 15–25.
[4] Görke, O., P, Pfeifer., K, Schubert., 2009. Kinetic study of ethanol reforming in a microreactor. Appl. Catal. A: Gen., 360: 232–241.
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[6] Baker, G. A and P, Graves-Morris., in Rota, G. C.(Ed.), 1981. Encyclopaedia of Mathematics, Vol. 13, Pade Approximants, Part II, Addison-Wesley, Reading, MA, Chapter 1.
[7] Rajendran, L., 2000. Padé approximation for ECE and DISP processes at channel electrodes. Electrochemistry Communication, 2: 186-189.
[8] Loghambal, S and L, Rajendran., 2010. Analysis of Amperometric Enzyme electrodes in the homogeneous mediated mechanism using Variational iteration method. Int. J. Electrochem. Sci., 5: 327-343.
[9] Liao, S., 2004. On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 147: 499–513.
[10] Meena, A and Rajendran, L., 2010. Analysis of pH-Based Potentiometric Biosensor using Homotopy perturbation method. Chemical Engineering & Technology, 33: 1-10.
[11] Yusufoglu, E., 2009. An improvement to homotopy perturbation method for solving system of linear equations. Computers and Mathematics with Applications, 58: 2231-2235.
[12] Rajendran, L and S, Anitha., 2013. Reply to-Comments on analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method, by Ji-Huan He, Lu-Feng Mo [Electrochim. Acta (2013)]. Electrochimica Acta, 102: 474– 476.
[13] Sen, A. K., 1988. An application of the Adomian decomposition method to the transient behavior of a model biochemical reaction, Journal of Mathematical analysis and applications, 131: 232–245.
[14] El-Sayed, S. M., 2002. The modified decomposition method for solving nonlinear algebraic equations. Applied Mathematics and Computation, 132: 589–597.
[15] Liao, S. J., 1992. The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems, Ph. D. Thesis, Shanghai Jiao Tong University.
[16] Liao, S. J., 1997. An approximate solution technique which does not depend upon small parameters (part 2): an application in fluid mechanics. Int. J. Nonlinear. Mech., 32 (5): 815–822.
[17] Liao, S. J., 2003. Beyond Perturbation: Introduction to the Homotopy Analysis Method. CRC Press, Boca Raton: Chapman & Hall.
[18] Jafari, H., M, Saeidy., J. V. Ahidi., 2009. The homotopy analysis method for solving fuzzy system of linear equations. Int. J. Fuzzy. Syst., 11 (4): 308–313.
[19] Jafari, H., M, Saeidy., M. A. Firoozjaee, 2009. The Homotopy Analysis Method for Solving Higher Dimensional Initial Boundary Value Problems of Variable Coefficients. Numerical Methods for Partial Differential Equations, 26 (5): 1021-1032.
[20] Manimozhi, P and L, Rajendran., 2013. Analytical expression of substrate and enzyme concentration in the Henri-Michaelis-Menten model using Homotopy analysis method. International Journal of Mathematical Archive, 4 (10): 204-214.
[21] Ananthaswamy, V., S. P. Ganesan., L, Rajendran., 2013. Approximate analytical solution of non-linear reaction-diffusion equation in microwave heating model in a slab: Homotopy analysis method. International Journal of Mathematical Archive, 4 (7): 178-189.
[22] Ananthaswamy, V., S, Kala., L, Rajendran., 2014. Approximate analytical solution of non-linear initial value problem for an autocatalysis in a continuous stirred tank reactor: Homotopy analysis method. Int. Journal of Mathematical Archive, 5 (4): 1-12.
[23] Subha M., V, Ananthaswamy., L, Rajendran., 2014. A comment on Liao’s Homotopy analysis method. International Journal of Applied Sciences and Engineering Research, 3 (1): 177-186.
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  • APA Style

    Kirthiga Murali, Chitra Devi Mohan, Meena Athimoolam, Rajendran Lakshmanan. (2017). Mathematical Modelling and Kinetics of Microchannel Reactor. Applied and Computational Mathematics, 5(6), 234-246. https://doi.org/10.11648/j.acm.20160506.12

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    ACS Style

    Kirthiga Murali; Chitra Devi Mohan; Meena Athimoolam; Rajendran Lakshmanan. Mathematical Modelling and Kinetics of Microchannel Reactor. Appl. Comput. Math. 2017, 5(6), 234-246. doi: 10.11648/j.acm.20160506.12

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    AMA Style

    Kirthiga Murali, Chitra Devi Mohan, Meena Athimoolam, Rajendran Lakshmanan. Mathematical Modelling and Kinetics of Microchannel Reactor. Appl Comput Math. 2017;5(6):234-246. doi: 10.11648/j.acm.20160506.12

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  • @article{10.11648/j.acm.20160506.12,
      author = {Kirthiga Murali and Chitra Devi Mohan and Meena Athimoolam and Rajendran Lakshmanan},
      title = {Mathematical Modelling and Kinetics of Microchannel Reactor},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {6},
      pages = {234-246},
      doi = {10.11648/j.acm.20160506.12},
      url = {https://doi.org/10.11648/j.acm.20160506.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160506.12},
      abstract = {The coupled nonlinear system of differential equations in 1-butanol dehydration under atmospheric and isothermal conditions are solved analytically for the microchannel reactor. Approximate analytical expressions of concentrations of 1-butanol, 1-butene, water and dibutyl ether are presented by using homotopy analysis method. The homotopy analysis method eliminated the classical perturbation method problem, because of the existence a small parameter in the equation. The analytical results are compared with the numerical solution and experimental results, satisfactory agreement is noted.},
     year = {2017}
    }
    

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    T1  - Mathematical Modelling and Kinetics of Microchannel Reactor
    AU  - Kirthiga Murali
    AU  - Chitra Devi Mohan
    AU  - Meena Athimoolam
    AU  - Rajendran Lakshmanan
    Y1  - 2017/01/23
    PY  - 2017
    N1  - https://doi.org/10.11648/j.acm.20160506.12
    DO  - 10.11648/j.acm.20160506.12
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    EP  - 246
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20160506.12
    AB  - The coupled nonlinear system of differential equations in 1-butanol dehydration under atmospheric and isothermal conditions are solved analytically for the microchannel reactor. Approximate analytical expressions of concentrations of 1-butanol, 1-butene, water and dibutyl ether are presented by using homotopy analysis method. The homotopy analysis method eliminated the classical perturbation method problem, because of the existence a small parameter in the equation. The analytical results are compared with the numerical solution and experimental results, satisfactory agreement is noted.
    VL  - 5
    IS  - 6
    ER  - 

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Author Information
  • Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India

  • Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India

  • Department of Mathematics, Saraswathi Narayanan College, Perungudi, Tamil Nadu, India

  • Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India

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