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An Effective Numerical Technique for Boundary Value Problems Arising from an Adiabatic Tubular Chemical Reactor Theory

Year 2022, Volume: 11 Issue: 3, 857 - 860, 30.09.2022
https://doi.org/10.17798/bitlisfen.1128254

Abstract

Mathematical models for an adiabatic tubular chemical reactor which forms an irreversible exothermic reaction are investigated by an efficient numerical technique, Fibonacci Collocation method in this study. The reaction's steady-state temperature is calculated for several values of three parameters, namely, Peclet and Damkohler numbers and the dimensionless adiabatic temperature increment. When the generated outcomes are compared with the other numerical approaches, it has been sighted that the presented method produces reliable results for this type of problems.

References

  • R. F. Heinemann and A. B. Poore, “The effect of activation energy on tubular reactor multiplicity,” Chemical Engineering Science, vol. 37, no. 1, pp. 128–131, 1982. A. B. Poore, “A tubular chemical reactor model, in A Collection of Nonlinear Model Problems “ Contributed to the Proceedings of the AMS-SIAM pp. 28–31, 1989.
  • R. F. Heinemann and A. B. Poore, “Multiplicity, stability, and oscillatory dynamics of the tubular reactor,” Chemical Engineering Science, vol. 36, no. 8, pp. 1411–1419, 1981.
  • E. Abdolmaleki and H. Saberi Najafi, “An efficient algorithmic method to solve Hammerstein integral equations and application to a functional differential equation,” Advances in Mechanical Engineering, vol. 9, no. 6, pp. 1-8, 2017.
  • A. Saadatmandi, M. Razzaghi, and M. Dehghan, “Sinc-galerkin solution for nonlinear two-point boundary value problems with applications to chemical reactor theory,” Mathematical and Computer Modelling, vol. 42, no. 11-12, pp. 1237–1244, 2005.
  • N. M. Madbouly, D. F. McGhee, and G. F. Roach, “Adomian's method for Hammerstein integral equations arising from chemical reactor theory,” Applied Mathematics and Computation, vol. 117, no. 2-3, pp. 241–249, 2001.
  • A. Saadatmandi and M. R. Azizi, “Chebyshev finite difference method for a two-point boundary value problems with applications to chemical reactor theory,” Iranian Journal of Mathematical Chemistry, vol. 3, pp. 1-7, 2012.
  • M. Zarebnia and R. Parvaz, “B-spline collocation method for numerical solution of the nonlinear two-point boundary value problems with applications to chemical reactor theory,” International Journal of Mathematical Engineering and Science, vol. 3, pp. 6-10, 2014.
  • J. Rashidinia and M. Nabati, “Sinc-galerkin and sinc-collocation methods in the solution of nonlinear two-point boundary value problems,” Computational and Applied Mathematics, vol. 32, no. 2, pp. 315–330, 2013.
  • H. Q. Kafri, S. A. Khuri, and A. Sayfy, “A fixed-point iteration approach for solving a BVP arising in chemical reactor theory,” Chemical Engineering Communications, vol. 204, no. 2, pp. 198–204, 2016.
  • M. R. Ali and D. Baleanu, “New wavelet method for solving boundary value problems arising from an adiabatic tubular chemical reactor theory,” International Journal of Biomathematics, vol. 13, no. 07, p. 2050059, 2020.
  • A. Kurt, S. Yalçınbaş, and M. Sezer, “Fibonacci collocation method for solving linear differential - difference equations,” Mathematical and Computational Applications, vol. 18, no. 3, pp. 448–458, 2013.
  • A. Kurt, S. Yalcinbas, M. Sezer, Fibonacci collocation method for solving high-order linear Fredholm integro-differentialdifference equations, Int. J. Math. Math. Sci. 2013 (2013).
  • F. Mirzaee and S. F. Hoseini, “Solving systems of linear Fredholm Integro-differential equations with Fibonacci polynomials,” Ain Shams Engineering Journal, vol. 5, no. 1, pp. 271–283, 2014.
  • M. Cakmak and S. Alkan, “A numerical method for solving a class of systems of nonlinear pantograph differential equations,” Alexandria Engineering Journal, vol. 61, no. 4, pp. 2651–2661, 2022.
  • S. Falcón and Á. Plaza, “The K-fibonacci sequence and the pascal 2-triangle,” Chaos, Solitons & Fractals, vol. 33, no. 1, pp. 38–49, 2007.
  • S. Falcón and Á. Plaza, “On K-fibonacci sequences and polynomials and their derivatives,” Chaos, Solitons & Fractals, vol. 39, no. 3, pp. 1005–1019, 2009.
Year 2022, Volume: 11 Issue: 3, 857 - 860, 30.09.2022
https://doi.org/10.17798/bitlisfen.1128254

Abstract

References

  • R. F. Heinemann and A. B. Poore, “The effect of activation energy on tubular reactor multiplicity,” Chemical Engineering Science, vol. 37, no. 1, pp. 128–131, 1982. A. B. Poore, “A tubular chemical reactor model, in A Collection of Nonlinear Model Problems “ Contributed to the Proceedings of the AMS-SIAM pp. 28–31, 1989.
  • R. F. Heinemann and A. B. Poore, “Multiplicity, stability, and oscillatory dynamics of the tubular reactor,” Chemical Engineering Science, vol. 36, no. 8, pp. 1411–1419, 1981.
  • E. Abdolmaleki and H. Saberi Najafi, “An efficient algorithmic method to solve Hammerstein integral equations and application to a functional differential equation,” Advances in Mechanical Engineering, vol. 9, no. 6, pp. 1-8, 2017.
  • A. Saadatmandi, M. Razzaghi, and M. Dehghan, “Sinc-galerkin solution for nonlinear two-point boundary value problems with applications to chemical reactor theory,” Mathematical and Computer Modelling, vol. 42, no. 11-12, pp. 1237–1244, 2005.
  • N. M. Madbouly, D. F. McGhee, and G. F. Roach, “Adomian's method for Hammerstein integral equations arising from chemical reactor theory,” Applied Mathematics and Computation, vol. 117, no. 2-3, pp. 241–249, 2001.
  • A. Saadatmandi and M. R. Azizi, “Chebyshev finite difference method for a two-point boundary value problems with applications to chemical reactor theory,” Iranian Journal of Mathematical Chemistry, vol. 3, pp. 1-7, 2012.
  • M. Zarebnia and R. Parvaz, “B-spline collocation method for numerical solution of the nonlinear two-point boundary value problems with applications to chemical reactor theory,” International Journal of Mathematical Engineering and Science, vol. 3, pp. 6-10, 2014.
  • J. Rashidinia and M. Nabati, “Sinc-galerkin and sinc-collocation methods in the solution of nonlinear two-point boundary value problems,” Computational and Applied Mathematics, vol. 32, no. 2, pp. 315–330, 2013.
  • H. Q. Kafri, S. A. Khuri, and A. Sayfy, “A fixed-point iteration approach for solving a BVP arising in chemical reactor theory,” Chemical Engineering Communications, vol. 204, no. 2, pp. 198–204, 2016.
  • M. R. Ali and D. Baleanu, “New wavelet method for solving boundary value problems arising from an adiabatic tubular chemical reactor theory,” International Journal of Biomathematics, vol. 13, no. 07, p. 2050059, 2020.
  • A. Kurt, S. Yalçınbaş, and M. Sezer, “Fibonacci collocation method for solving linear differential - difference equations,” Mathematical and Computational Applications, vol. 18, no. 3, pp. 448–458, 2013.
  • A. Kurt, S. Yalcinbas, M. Sezer, Fibonacci collocation method for solving high-order linear Fredholm integro-differentialdifference equations, Int. J. Math. Math. Sci. 2013 (2013).
  • F. Mirzaee and S. F. Hoseini, “Solving systems of linear Fredholm Integro-differential equations with Fibonacci polynomials,” Ain Shams Engineering Journal, vol. 5, no. 1, pp. 271–283, 2014.
  • M. Cakmak and S. Alkan, “A numerical method for solving a class of systems of nonlinear pantograph differential equations,” Alexandria Engineering Journal, vol. 61, no. 4, pp. 2651–2661, 2022.
  • S. Falcón and Á. Plaza, “The K-fibonacci sequence and the pascal 2-triangle,” Chaos, Solitons & Fractals, vol. 33, no. 1, pp. 38–49, 2007.
  • S. Falcón and Á. Plaza, “On K-fibonacci sequences and polynomials and their derivatives,” Chaos, Solitons & Fractals, vol. 39, no. 3, pp. 1005–1019, 2009.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Araştırma Makalesi
Authors

Soner Aydınlık 0000-0003-0321-4920

Publication Date September 30, 2022
Submission Date June 9, 2022
Acceptance Date September 22, 2022
Published in Issue Year 2022 Volume: 11 Issue: 3

Cite

IEEE S. Aydınlık, “An Effective Numerical Technique for Boundary Value Problems Arising from an Adiabatic Tubular Chemical Reactor Theory”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 3, pp. 857–860, 2022, doi: 10.17798/bitlisfen.1128254.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS