Skip to main content
SpringerLink
Log in

Differential transformation method for Newtonian and Non-Newtonian fluids flow analysis: comparison with HPM and numerical solution

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

An Erratum to this article was published on 01 June 2016

Abstract

In this study, a simple and high accurate series-based method called differential transformation method (DTM) is used for solving the coupled nonlinear differential equations in fluids’ mechanic problems. The concept of the DTM is briefly introduced, and its application for two different cases, natural convection of a non-Newtonian fluid between two vertical plates and Newtonian fluid flow between two horizontal plates, has been studied. DTM results are compared with those obtained by another series-based analytical technique namely homotopy perturbation method (HPM) and a numerical solution (Fourth-order Runge–Kutta) to show the accuracy of the proposed method. Results reveal that DTM is very effective and convenient and can achieve more suitable results compared to HPM in some areas of equations in engineering and science problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. He JH (1999) Homotopy perturbation technique. Comput Methods Appl Mech Eng 178:257–262

    Article  MathSciNet  MATH  Google Scholar 

  2. He JH (2003) Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 135:73–79

    MathSciNet  MATH  Google Scholar 

  3. He JH (2012) Asymptotic methods for solitary solutions and compactons, Abstract and Applied Analysis, 916793

  4. He JH (2005) Homotopy perturbation method for bifurcation of nonlinear problems. Int J Nonlinear Sci Numer Simul 6:207–208

    MathSciNet  Google Scholar 

  5. Roozi A, Alibeiki E, Hosseini SS, Shafiof SM, Ebrahimi M (2011) Homotopy perturbation method for special nonlinear partial differential equations. J King Saud Uni Sci 23:99–103

    Article  Google Scholar 

  6. Ganji DD, Sadighi A (2007) Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. J Comput App Math 207:24–34

    Article  MathSciNet  MATH  Google Scholar 

  7. Sadighi A, Ganji DD (2008) Analytic treatment of linear and nonlinear Schrödinger equations: a study with homotopy-perturbation and Adomian decomposition methods equations. Phys Lett A 372:465–469

    Article  MathSciNet  MATH  Google Scholar 

  8. Sadighi A, Ganji DD (2007) Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods. Phys Lett A 367:83–87

    Article  MathSciNet  MATH  Google Scholar 

  9. Ziabakhsh Z, Domairry G (2009) Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using homotopy analysis method. Commun Nonlinear Sci Numer Simulat 14:1868–1880

    Article  Google Scholar 

  10. Zhou JK (1986) Differential transformation method and its application for electrical circuits. Hauzhang University Press, Wuhan

    Google Scholar 

  11. Ghafoori S, Motevalli M, Nejad MG, Shakeri F, Ganji DD, Jalaal M (2011) Efficiency of differential transformation method for nonlinear oscillation: comparison with HPM and VIM. Current Appl Phys 11:965–971

    Article  Google Scholar 

  12. Yahyazadeh H, Ganji DD, Yahyazadeh A, Taghi M (2012) Khalili, P. Jalili, M. Jouya, evaluation of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field by the differential transformation method. Therm Sci 16(5):1281–1287

    Article  Google Scholar 

  13. Biazar J, Eslami M (2010) Differential transform method for quadratic riccati differential equation. Int J Nonlinear Sci 9(4):444–447

    MathSciNet  MATH  Google Scholar 

  14. Gokdogan A, Merdan M, Yildirim A (2012) The modified algorithm for the differential transform method to solution of Genesio systems. Commun Nonlinear Sci Numer Simulat 17:45–51

    Article  MathSciNet  Google Scholar 

  15. Ayaz F (2003) On the two-dimensional differential transform method. Appl Math Comput 143:361–374

    MathSciNet  MATH  Google Scholar 

  16. Ni Q, Zhang ZL, Wang L (2011) Application of the differential transformation method to vibration analysis of pipes conveying fluid. Appl Math Comput 217:7028–7038

    MathSciNet  MATH  Google Scholar 

  17. Ganji DD, Hashemi Kachapi SH (2011) Progress in nonlinear science: analysis of nonlinear equations in fluids. Asian Academic Publisher Limited, HongKong

    MATH  Google Scholar 

  18. Hatami M, Ganji DD (2014) Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods. Case Studies in Thermal Engineering 2:14–22

    Article  Google Scholar 

  19. Rajagopal KR, Na TY (1985) Natural convection flow of a non-Newtonian fluid between two vertical flat plates. Acta Mech 54:39–46

    Article  MATH  Google Scholar 

  20. Bervillier C (2012) Status of the differential transformation method. Appl Math Comput 218:10158–10170

    MathSciNet  MATH  Google Scholar 

  21. Hatami M, Ganji DD (2013) Heat transfer and flow analysis for SA-TiO2 non-Newtonian nanofluid passing through the porous media between two coaxial cylinders. J Mol Liq 188:155–161

    Article  Google Scholar 

  22. Hatami M, Hatami J, Ganji DD (2014) Computer simulation of MHD blood conveying gold nanoparticles as a third grade non-Newtonian nanofluid in a hollow porous vessel. Comput Methods Programs Biomed 113(2):632–641

    Article  Google Scholar 

  23. Domairry G, Hatami M (2014) Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM-Padé Method. J Mol Liquids 193:37–44

    Article  Google Scholar 

  24. Hatami M, Ganji DD (2014) Thermal and flow analysis of microchannel heat sink (MCHS) cooled by Cu–water nanofluid using porous media approach and least square method. Energy Convers Manag 78:347–358

    Article  Google Scholar 

  25. Hatami M, Nouri R, Ganji DD (2013) Forced convection analysis for MHD Al2O3–water nanofluid flow over a horizontal plate. J Mol Liq 187:294–301

    Article  Google Scholar 

  26. Sheikholeslami M, Hatami M, Ganji DD (2013) Analytical investigation of MHD nanofluid flow in a semi-porous channel. Powder Technol 246:327–336

    Article  Google Scholar 

  27. Sheikholeslami M, Hatami M, Ganji DD (2013) Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field. J Mol Liquids 190:112–120

    Article  Google Scholar 

  28. Hatami M, Sheikholeslami M, Ganji DD (2014) Laminar flow and heat transfer of nanofluid between contracting and rotating disks by least square method. Powder Technol 253:769–779

    Article  Google Scholar 

  29. Hatami M, Ganji DD (2013) Thermal performance of circular convective-radiative porous fins with different section shapes and materials. Energy Convers Manag 76:185–193

    Article  Google Scholar 

  30. Hatami M, Hasanpour A, Ganji DD (2013) Heat transfer study through porous fins (Si3N4 and AL) with temperature-dependent heat generation. Energy Convers Manag 74:9–16

    Article  Google Scholar 

  31. Hatami M, Ganji DD (2013) Investigation of refrigeration efficiency for fully wet circular porous fins with variable sections by combined heat and mass transfer analysis. Int J Refrig. doi:10.1016/j.ijrefrig.2013.11.002

    Google Scholar 

  32. Hatami M, Domairry G (2014) Transient vertically motion of a soluble particle in a Newtonian fluid media. Powder Technol 253:481–485

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Esfarayen University of Technology, Esfarayen, North Khorasan, Iran

    M. Hatami

  2. Garmsar Health & Care Center, Semnan University of Medical Sciences, Semnan, Garmsar, Semnan, Iran

    J. Hatami

  3. Mechanical Engineering Department, Mazandaran Institute of Technology, Babol, Iran

    M. Jafaryar

  4. Mechanical Engineering Faculty, Babol University of Technology, Babol, Iran

    G. Domairry

Authors
  1. M. Hatami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Hatami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Jafaryar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Domairry
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. Hatami or J. Hatami.

Additional information

Technical Editor: Francisco Ricardo Cunha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hatami, M., Hatami, J., Jafaryar, M. et al. Differential transformation method for Newtonian and Non-Newtonian fluids flow analysis: comparison with HPM and numerical solution. J Braz. Soc. Mech. Sci. Eng. 38, 589–599 (2016). https://doi.org/10.1007/s40430-014-0275-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-014-0275-3

Keywords

Search

Navigation