| Citation: |
Necdet Bildik, Sinan Deniz. OPTIMAL ITERATIVE PERTURBATION TECHNIQUE FOR SOLVING JEFFERY–HAMEL FLOW WITH HIGH MAGNETIC FIELD AND NANOPARTICLE[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2476-2490. doi: 10.11948/20190378
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OPTIMAL ITERATIVE PERTURBATION TECHNIQUE FOR SOLVING JEFFERY–HAMEL FLOW WITH HIGH MAGNETIC FIELD AND NANOPARTICLE
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Abstract
In this research paper, a different semi-analytical analysis of modified magnetohydrodynamic Jeffery–Hamel flow is conducted via the newly developed technique. We use the optimal iterative perturbation method with multiple parameters to see the effects of the magnetic field and nanoparticle on the Jeffery–Hamel flow. Comparing our new approximate solutions with some earlier works proved the excellent accuracy of the newly proposed technique. Convergence analysis of the proposed method is also discussed and error estimation is given to anticipate the accuracy of higher-order approximate solutions. -
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References
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Necdet Bildik, Sinan Deniz. OPTIMAL ITERATIVE PERTURBATION TECHNIQUE FOR SOLVING JEFFERY–HAMEL FLOW WITH HIGH MAGNETIC FIELD AND NANOPARTICLE[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2476-2490. doi: 10.11948/20190378
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Figure 1. Configuration of the Jeffery–Hamel flow: The rigid walls are considered to be divergent if
$ \alpha>0 $ and convergent if$ \alpha<0 $ . - Figure 2. Errors for fifth order OIPM solutions
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Figure 3. Numerical results and the second order approximation for
$ \alpha=\dfrac{\pi}{20} $ ,$ Ha=0 $ ,$ \phi=0.01 $ ,$ Re=100 $ . -
Figure 4. Numerical results and the second order approximation for
$ \alpha=\dfrac{\pi}{20} $ ,$ Ha=0 $ ,$ \phi=0.02 $ $ Re=110 $ . -
Figure 5. Numerical results and the third order approximation for
$ Re=130 $ ,$ \phi=0.015 $ and$ \alpha=\dfrac{\pi}{20} $ ,$ Ha=100 $ -
Figure 6. Numerical results and the third order approximation for
$ Re=130 $ ,$ \phi=0.015 $ and$ \alpha=\dfrac{\pi}{20} $ ,$ Ha=1000 $ -
Figure 7. Numerical results and the second order approximation for
$ Re=110 $ ,$ \phi=0.01 $ ,$ Ha=0 $ ,$ \alpha=\dfrac{\pi}{20} $ . -
Figure 8. Numerical results and the second order approximation for
$ Re=100 $ ,$ Ha=1000 $ ,$ \phi=0.05 $ ,$ \alpha=-\dfrac{\pi}{36} $ -
Figure 9. Numerical results and the second order approximation for
$ Re=100 $ ,$ Ha=1000 $ ,$ \phi=0.02 $ ,$ \alpha=-\dfrac{\pi}{120} $