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Year 2017, Volume: 5 Issue: 1, 51 - 58, 01.01.2017

Abstract

References

  • D. Ganji, M. Hosseini, and J. Shayegh, "Some nonlinear heat transfer equations solved by three approximate methods," International Communications in Heat and Mass Transfer, vol. 34, pp. 1003-1016, 2007.
  • M. Sheikholeslami, D.D. Ganji, Heat transfer of Cu-water nanofluid flow between parallel plates, Powder Technology 235 (2013) 873-879.
  • He J. H., Homotopy perturbation technique, Compute. Methods Appl Mech. Eng, 178, 1999, 257-262.
  • M.G. Sfahani, S.S. Ganji, A. Barari, H. Mirgolbabaei, G. Domairry. Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity. Earthquake Engineering and Engineering Vibration 9 (3), 367-374.
  • D.D. Ganji, M. Rafei, A. Sadighi, Z.Z. Ganji, A comparative comparison of He’s method with perturbation and numerical methods for nonlinear vibrations equations, Int. J. Nonlinear Dyn. Eng. Sci. 1 (1) (2009) 1-20.
  • M. Gorji, D.D. Ganji, S. Soleimani, New application of He’s homotopy perturbation method, Int. J. Nonlinear Sci. Numer. Simul. 8 (3) (2007) 319-328.
  • M. Sheikholeslami, R. Ellahi, H. R. Ashorynejad, G. Domairry, and T. Hayat, Effects of Heat Transfer in Flow of Nanofluids Over a Permeable Stretching Wall in a Porous Medium, Journal of Computational and Theoretical Nanoscience, Vol. 11, 1–11, 2014.
  • He J. H., Variational iteration method for autonomous ordinary differential systems, Appl. Math. Compute, 114, 2000, 115–123.
  • S. Ghafoori, M. Motevalli, M. G. Nejad, F. Shakeri, D. D. Ganji, and M. Jalaal, Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM,” Current Applied Physics, vol. 11, no. 4, pp. 965-971, 2011.
  • M. Sheikholeslami, R. Ellahi, H. R. Ashorynejad, G. Domairry, and T. Hayat, Effects of Heat Transfer in Flow of Nanofluids Over a Permeable Stretching Wall in a Porous Medium, Journal of Computational and Theoretical Nanoscience, Vol. 11, 1–11, 2014.
  • M. Sheikholeslami, H. R. Ashorynejad, G. Domairry and I. Hashim, Flow and Heat Transfer of Cu-Water Nanofluid between a Stretching Sheet and a Porous Surface in a Rotating System, Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2012, Article ID 421320, 19 pages, http://dx.doi.org/10.1155/2012/421320.
  • M. Sheikholeslami, M.M. Rashidi, Dhafer M. Al Saad,F. Firouzi,Houman B. Rokni, G. Domairry, Steady nanofluid flow between parallel plates considering Thermophoresis and Brownian effects, Journal of King Saud University - Science, (2015),http://dx.doi.org/10.1016/j.jksus.2015.06.003
  • Adomian G. Solving Frontier Problems of Physics, the Decomposition Method. Boston: Kluwer Academic Publishers, 1994.
  • M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Investigation of squeezing unsteady nanofluid flow using ADM, Powder Technology 239 (2013) 259-265.
  • S.T. Ledari, H. Mirgolbabaee, D.D. Ganji, Heat transfer analysis of a fin with temperature dependent thermal conductivity and heat transfer coefficient, New Trends in Mathematical Sciences, No. 2, Pages 55-69, 2015.
  • H. Mirgolbabaee, S.T. Ledari, D.D. Ganji, New approach method for solving Duffing-type nonlinear oscillator, Alexandria Engineering Journal, Volume 55, Issue 2, June 2016, Pages 1695-1702, ISSN 1110-0168, http://dx.doi.org/10.1016/j.aej.2016.03.007.
  • H. Mirgolbabaee, S.T. Ledari, D.D. Ganji, An assessment of a semi analytical AG method for solving nonlinear oscillators, New Trends in Mathematical Sciences, No. 1, Paper 283-299, 2016, http://dx.doi.org/10.1016/j.aej.2016.03.007.
  • S.T.Ledari, H. Mirgolbabaee, D.D.Ganji. An assessment of a semi analytical AG method for solving two-dimension nonlinear viscous flow, International Journal of Nonlinear Analysis and Applications, 6(2): 47-64 (2015).
  • A. Yaziz, G. Hamad, Int. J. Mech. Eng. Educ. 5 (1977) 167.

Analyzing the nonlinear heat transfer equation by AGM

Year 2017, Volume: 5 Issue: 1, 51 - 58, 01.01.2017

Abstract

In this paper, a novel nonlinear differential equation in the field of heat transfer has been investigated and solved completely by a new method that we called it Akbari-Ganjiâ Method (AGM). Regarding to the previously published papers, investigating this kind of equations is a very hard project to do and the obtained solution is not accurate and reliable. This issue will be appeared after comparing the obtained solution by Numerical Method or the Exact Solution. Based on the comparison which has been made between the achieved solutions by AGM and Numerical Method (Runge-Kutte 4th), it is possible to indicate that AGM can be successfully applied to various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with other approaches can be considered as follows: Boundary conditions are required in accordance with order of the differential equation, this approach can create additional new boundary conditions in regard to the own differential equation and its derivatives. Therefore, it is logical to mention which AGM is operational for miscellaneous nonlinear differential equations in comparison with the other methods.

References

  • D. Ganji, M. Hosseini, and J. Shayegh, "Some nonlinear heat transfer equations solved by three approximate methods," International Communications in Heat and Mass Transfer, vol. 34, pp. 1003-1016, 2007.
  • M. Sheikholeslami, D.D. Ganji, Heat transfer of Cu-water nanofluid flow between parallel plates, Powder Technology 235 (2013) 873-879.
  • He J. H., Homotopy perturbation technique, Compute. Methods Appl Mech. Eng, 178, 1999, 257-262.
  • M.G. Sfahani, S.S. Ganji, A. Barari, H. Mirgolbabaei, G. Domairry. Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity. Earthquake Engineering and Engineering Vibration 9 (3), 367-374.
  • D.D. Ganji, M. Rafei, A. Sadighi, Z.Z. Ganji, A comparative comparison of He’s method with perturbation and numerical methods for nonlinear vibrations equations, Int. J. Nonlinear Dyn. Eng. Sci. 1 (1) (2009) 1-20.
  • M. Gorji, D.D. Ganji, S. Soleimani, New application of He’s homotopy perturbation method, Int. J. Nonlinear Sci. Numer. Simul. 8 (3) (2007) 319-328.
  • M. Sheikholeslami, R. Ellahi, H. R. Ashorynejad, G. Domairry, and T. Hayat, Effects of Heat Transfer in Flow of Nanofluids Over a Permeable Stretching Wall in a Porous Medium, Journal of Computational and Theoretical Nanoscience, Vol. 11, 1–11, 2014.
  • He J. H., Variational iteration method for autonomous ordinary differential systems, Appl. Math. Compute, 114, 2000, 115–123.
  • S. Ghafoori, M. Motevalli, M. G. Nejad, F. Shakeri, D. D. Ganji, and M. Jalaal, Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM,” Current Applied Physics, vol. 11, no. 4, pp. 965-971, 2011.
  • M. Sheikholeslami, R. Ellahi, H. R. Ashorynejad, G. Domairry, and T. Hayat, Effects of Heat Transfer in Flow of Nanofluids Over a Permeable Stretching Wall in a Porous Medium, Journal of Computational and Theoretical Nanoscience, Vol. 11, 1–11, 2014.
  • M. Sheikholeslami, H. R. Ashorynejad, G. Domairry and I. Hashim, Flow and Heat Transfer of Cu-Water Nanofluid between a Stretching Sheet and a Porous Surface in a Rotating System, Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2012, Article ID 421320, 19 pages, http://dx.doi.org/10.1155/2012/421320.
  • M. Sheikholeslami, M.M. Rashidi, Dhafer M. Al Saad,F. Firouzi,Houman B. Rokni, G. Domairry, Steady nanofluid flow between parallel plates considering Thermophoresis and Brownian effects, Journal of King Saud University - Science, (2015),http://dx.doi.org/10.1016/j.jksus.2015.06.003
  • Adomian G. Solving Frontier Problems of Physics, the Decomposition Method. Boston: Kluwer Academic Publishers, 1994.
  • M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Investigation of squeezing unsteady nanofluid flow using ADM, Powder Technology 239 (2013) 259-265.
  • S.T. Ledari, H. Mirgolbabaee, D.D. Ganji, Heat transfer analysis of a fin with temperature dependent thermal conductivity and heat transfer coefficient, New Trends in Mathematical Sciences, No. 2, Pages 55-69, 2015.
  • H. Mirgolbabaee, S.T. Ledari, D.D. Ganji, New approach method for solving Duffing-type nonlinear oscillator, Alexandria Engineering Journal, Volume 55, Issue 2, June 2016, Pages 1695-1702, ISSN 1110-0168, http://dx.doi.org/10.1016/j.aej.2016.03.007.
  • H. Mirgolbabaee, S.T. Ledari, D.D. Ganji, An assessment of a semi analytical AG method for solving nonlinear oscillators, New Trends in Mathematical Sciences, No. 1, Paper 283-299, 2016, http://dx.doi.org/10.1016/j.aej.2016.03.007.
  • S.T.Ledari, H. Mirgolbabaee, D.D.Ganji. An assessment of a semi analytical AG method for solving two-dimension nonlinear viscous flow, International Journal of Nonlinear Analysis and Applications, 6(2): 47-64 (2015).
  • A. Yaziz, G. Hamad, Int. J. Mech. Eng. Educ. 5 (1977) 167.
There are 19 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hadi Mirgolbabaee This is me

Soheil Tahernejad Ledari This is me

Davood Domiri Ganji This is me

Esmail Karimi Valujai This is me

Publication Date January 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Mirgolbabaee, H., Ledari, S. T., Ganji, D. D., Valujai, E. K. (2017). Analyzing the nonlinear heat transfer equation by AGM. New Trends in Mathematical Sciences, 5(1), 51-58.
AMA Mirgolbabaee H, Ledari ST, Ganji DD, Valujai EK. Analyzing the nonlinear heat transfer equation by AGM. New Trends in Mathematical Sciences. January 2017;5(1):51-58.
Chicago Mirgolbabaee, Hadi, Soheil Tahernejad Ledari, Davood Domiri Ganji, and Esmail Karimi Valujai. “Analyzing the Nonlinear Heat Transfer Equation by AGM”. New Trends in Mathematical Sciences 5, no. 1 (January 2017): 51-58.
EndNote Mirgolbabaee H, Ledari ST, Ganji DD, Valujai EK (January 1, 2017) Analyzing the nonlinear heat transfer equation by AGM. New Trends in Mathematical Sciences 5 1 51–58.
IEEE H. Mirgolbabaee, S. T. Ledari, D. D. Ganji, and E. K. Valujai, “Analyzing the nonlinear heat transfer equation by AGM”, New Trends in Mathematical Sciences, vol. 5, no. 1, pp. 51–58, 2017.
ISNAD Mirgolbabaee, Hadi et al. “Analyzing the Nonlinear Heat Transfer Equation by AGM”. New Trends in Mathematical Sciences 5/1 (January 2017), 51-58.
JAMA Mirgolbabaee H, Ledari ST, Ganji DD, Valujai EK. Analyzing the nonlinear heat transfer equation by AGM. New Trends in Mathematical Sciences. 2017;5:51–58.
MLA Mirgolbabaee, Hadi et al. “Analyzing the Nonlinear Heat Transfer Equation by AGM”. New Trends in Mathematical Sciences, vol. 5, no. 1, 2017, pp. 51-58.
Vancouver Mirgolbabaee H, Ledari ST, Ganji DD, Valujai EK. Analyzing the nonlinear heat transfer equation by AGM. New Trends in Mathematical Sciences. 2017;5(1):51-8.