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The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem

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  • Ahmed A. Khidir

Abstract

In this study, the effects of magnetic field on the Jeffery–Hamel problem is studied using a powerful numerical method called the spectral Adomian decomposition method (SADM). The traditional Navier–Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. Comparisons with the numerical solutions are made to demonstrate the validity and high accuracy of the present approach. The velocity profile of the inner part of the divergent channel is studied for various values of magnetic field parameter and angle of channel. It was found that an increase in the magnetic field parameter leads to increase in the velocity profile. The results indicated that this technique is more efficient and converges faster than the standard Adomian decomposition method.

Suggested Citation

  • Ahmed A. Khidir, 2023. "The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:2181127
    DOI: 10.1155/2023/2181127
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    References listed on IDEAS

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    1. Mohamed E. A. Alnair & Ahmed A. Khidir, 2022. "Approximation Technique for Solving Linear Volterra Integro‐Differential Equations with Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
    2. Mohamed E. A. Alnair & Ahmed A. Khidir & Yufeng Xu, 2022. "Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2022, pages 1-14, April.
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