Mathematical Modelling and Kinetics of Microchannel Reactor

Kirthiga Murali; Chitra Devi Mohan; Meena Athimoolam; Rajendran Lakshmanan

doi:doi:10.11648/j.acm.20160506.12

| Peer-Reviewed

Mathematical Modelling and Kinetics of Microchannel Reactor

Kirthiga Murali, Chitra Devi Mohan, Meena Athimoolam, Rajendran Lakshmanan

Published in Applied and Computational Mathematics (Volume 5, Issue 6)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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), 2024. Published by Science Publishing Group

Keywords

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

References

[1]	Khan, Y., M, Marin., R, Karinen., J. Lehtonen., J. Kanervo., 2015.1-Butanol dehydration in microchannel reactor: Kinetics and reactor modeling. Chemical Engineering Science, 137: 740–751.
[2]	Spatenka, S., V, Fila., B, Bernauer., J, Fulem., G, Germani., Y, Schuurman., 2005. Modeling and simulation of microchannel catalytic WGS reactor for an automotive fuel processor. Chem. Ind. Chem. Eng. Q., 11 (3): 143–151.
[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.
[5]	Schmidt, S. A., N, Kumar., A, Reinsdorf., K, Eränen., J, Wärnå., D. Y Murzin., T, Salmi., 2013. Methyl chloride synthesis over Al₂O₃ catalyst coated micro strucured reactor thermo dynamics. kinetics and mass transfer, Chem. Eng. Sci., 95: 232–245.
[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.
[24]	Berteau, P., M, Ruwet., B, Delmon., 1985. Reaction path ways in 1-butanol dehydration on γ-alumina, Bull. Des Sociétés Chim. Belges, 94 (11–12): 859–868.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
SP  - 234
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  -

Copy | Download

Author Information

Kirthiga Murali

Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India
Chitra Devi Mohan

Department of Mathematics, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India
Meena Athimoolam

Department of Mathematics, Saraswathi Narayanan College, Perungudi, Tamil Nadu, India
Rajendran Lakshmanan

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
SP  - 234
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  -

Copy | Download