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Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM

Abstract

In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using two powerful analytical methods, Homotopy Perturbation Method (HPM) and a simple and innovative approach which we have named it Akbari-Ganji’s Method(AGM). Comparisons have been made between HPM, AGM and Numerical Method and the acquired results show that these methods have high accuracy for different values of α, Hartmann numbers, and Reynolds numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.

It is necessary to represent some of the advantages of choosing the new method, AGM, for solving nonlinear differential equations as follows: AGM is a very suitable computational process and is applicable for solving various nonlinear differential equations. Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration, the solution of the problem can be obtained very simply and easily. It is notable that this solution procedure, AGM, can help students with intermediate mathematical knowledge to solve a broad range of complicated nonlinear differential equations.

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Correspondence to D. D. Ganji.

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Rostami, A.K., Akbari, M.R., Ganji, D.D. et al. Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM. cent.eur.j.eng 4, 357–370 (2014). https://doi.org/10.2478/s13531-013-0175-9

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  • DOI: https://doi.org/10.2478/s13531-013-0175-9

Keywords

  • Magnetohydrodynamic
  • Jeffery-Hamel flow
  • Akbari-Ganji’s Method (AGM)
  • Homotopy Perturbation Method (HPM)
  • nanofluid