Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

Marinca, Vasile; Ene, Remus-Daniel

doi:10.1515/phys-2017-0006

Cited by 10 publications

(16 citation statements)

References 24 publications

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“…Method [15] for some values of the physical parameters, i.e. Rey = 50, (α = π/24, Ha = 250), (α = π/24, Ha = 500), (α = π/24, Ha = 1000), (α = π/36, Ha = 250), (α = π/36, Ha = 500) and (α = π/36, Ha = 1000), respectively.…”

Section: Comparison Of the Exact Solution And Analytical Solutionmentioning

confidence: 99%

“…Finally, we compare the phase curves given by Eq. (5) of the dynamics (2) with the corresponding approximate analytic solutions from [15] for the physical values presented in Table 1.…”

Section: Comparison Of the Exact Solution And Analytical Solutionmentioning

confidence: 99%

“…Observation: Iff (η) is the approximate analytic solution obtained via Optimal Homotopy Perturbation Method [15], then the corresponding residual functions are:…”

Section: Comparison Of the Exact Solution And Analytical Solutionmentioning

confidence: 99%

“…and C = const. As a consequence, we can sketch a comparison with the analytic solutions proposed in [15].…”

Section: Introductionmentioning

confidence: 99%

“…In the last section a comparison of the exact solution provided by the Hamilton-Poisson realization and the analytic solution given in [15] is proposed.…”

Section: Introductionmentioning

confidence: 99%

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Some new remarks on MHD Jeffery-Hamel fluid flow problem

Ene

Pop

2017

Open Physics

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Section: Comparison Of the Exact Solution And Analytical Solutionmentioning

confidence: 99%

“…Finally, we compare the phase curves given by Eq. (5) of the dynamics (2) with the corresponding approximate analytic solutions from [15] for the physical values presented in Table 1.…”

Section: Comparison Of the Exact Solution And Analytical Solutionmentioning

confidence: 99%

“…Observation: Iff (η) is the approximate analytic solution obtained via Optimal Homotopy Perturbation Method [15], then the corresponding residual functions are:…”

Section: Comparison Of the Exact Solution And Analytical Solutionmentioning

confidence: 99%

“…and C = const. As a consequence, we can sketch a comparison with the analytic solutions proposed in [15].…”

Section: Introductionmentioning

confidence: 99%

“…In the last section a comparison of the exact solution provided by the Hamilton-Poisson realization and the analytic solution given in [15] is proposed.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Some new remarks on MHD Jeffery-Hamel fluid flow problem

Ene

Pop

2017

Open Physics

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On the solution of MHD Jeffery–Hamel problem involving flow between two nonparallel plates with a blood flow application

El‐Shenawy,

El‐Gamel,

Abd El‐Hady

2024

Heat Trans

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The Jeffery–Hamel flow phenomenon appears in a variety of real‐world applications involving the flow of two nonparallel plates. BY using a similarity transformation derived from the equation of continuity, partial differential equations determining flow characteristics are translated into nonlinear ordinary differential equations. The problem involves the flow of a specific type of fluid, namely, an incompressible and electrically conducting fluid, between two nonparallel plates. The flow is assumed to be steady, two‐dimensional, and subject to certain boundary conditions. Specifically, the plates are impermeable, and the fluid adheres to a no‐slip condition, resulting in zero fluid velocity at the plates' surfaces. Moreover, the problem incorporates the effects of magnetic fields and pressure fluctuations, making it highly applicable to scenarios, such as blood flow through arteries in the human body, which can be modeled as a special case of the magnetohydrodynamic (MHD) Jeffery–Hamel problem referred to as the (MHD) blood pressure equation. This work compares two numerical approaches for solving the MHDs Jeffery–Hamel problem: B‐spline and Bernstein polynomial collocation. The given approaches are used to discretize and transform the equation into a system of algebraic equations. Matrix algebra techniques are then used to solve the resultant system. A complete error analysis and convergence rates for different grid sizes are derived for both methods and are used to compare the accuracy and efficiency of the two approaches. Both approaches produce correct solutions, according to the numerical findings, although the Bernstein polynomial collocation method is more efficient and accurate than the B‐spline collocation.

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Analytical Investigation of MHD Jeffery–Hamel flow problem with heat transfer by differential transform method

Meher

Patel

2019

SN Appl. Sci.

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The aim of this research paper is to study and analyse the effects of Reynolds number, Hartmann number and thermal profile on velocity profiles of magneto hydro dynamics Jeffery-Hamel fluid flow between two non-parallel plates with angles 2θ and electromagnetic induction (E 0). An approximate analytical solution of the problem that is formulated using the Navier-Stokes and continuity equations has obtained in the form of a convergent series using differential transform method. The nature and the variation of the velocity profiles of Jeffery-Hamel flow with heat transfer are discussed herewith considering different thermal profiles with distinct positive values of Ha and Re in both convergent and divergent channels. The authenticity and the usefulness of this method have demonstrated by comparing with the available results of optimal homotopy perturbation method and the numerical method. Keywords Differential transform method • Heat transfer • Jeffery-Hamel flow • System of differential equations List of symbols P Pressure k Conductivity of the thermal ρ Density T Temperature Re Reynolds number E 0 Electromagnetic induction v Kinematic viscosity M Magnetic field θ Half-angle between the two plates Ha Hartmann number

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Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

Cited by 10 publications

References 24 publications

Some new remarks on MHD Jeffery-Hamel fluid flow problem

Some new remarks on MHD Jeffery-Hamel fluid flow problem

On the solution of MHD Jeffery–Hamel problem involving flow between two nonparallel plates with a blood flow application

Analytical Investigation of MHD Jeffery–Hamel flow problem with heat transfer by differential transform method

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