On the Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) for a nonlinearly stretching sheet flow of Eyring-Powell fluids

Jafarimoghaddam, Amin

doi:10.1016/j.jestch.2018.11.001

Cited by 28 publications

(21 citation statements)

References 48 publications

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“…As it has been shown in the paper by Jafarimoghaddam regarding a stretching sheet flow of Eyring‐Powell fluids, similarity solution exists if only a specific nonlinear stretching scheme is considered. Therefore, many of the previous studies in this field stand as nonsimilar/local‐similar flow of Eyring‐Powell fluids; in particular, requiring local‐similarity/ nonsimilarity techniques.…”

Section: Introductionmentioning

confidence: 89%

“…We consider two‐dimensional boundary layer equations for an incompressible flow of Eyring‐Powell fluids due to a stretching sheet in the presence of a transverse magnetic field. Following Jafarimoghaddam:

\begin{matrix} left \\ \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0 \\ u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = (υ + \frac{1}{ρ β d}) \frac{\partial^{2} u}{\partial y^{2}} - \frac{1}{2 ρ β d^{3}} {(\frac{\partial u}{\partial y})}^{2} \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B {(x)}^{2}}{ρ} u \\ u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α \frac{\partial^{2} T}{\partial y^{2}} - \frac{1}{ρ C_{p}} \frac{\partial q_{r}}{\partial y} \end{matrix}

…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Following the papers by Jafarimoghaddam, it is easy to indicate that similarity transformation exists if only

n = \frac{1}{3}

whilst, other cases should be treated as nonsimilar flows.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Jafarimoghaddam has recently solved the similar Eyring‐Powell fluids over a nonlinearly stretching sheet by the means of homotopy. Indeed, the similarity case is that previously discussed in the paper by Jafarimoghaddam . Other cases remain inherently nonsimilar.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

MHD flow of eyring‐powell fluids: HPM and a novel topological technique

Jafarimoghaddam¹

2019

Heat Trans. Asian Res.

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Stretching sheet flow of magnetohydrodynamic (MHD)Eyring-Powell fluids is studied. The nonlinear ordinary differential equation associated with the similarity case is considered. The focus of the present work is to solve the governing equations using homotopy perturbation method (HPM) and a novel topological technique, which is to be shortly introduced in here. The results from the above techniques are compared with Runge-Kutta 4th order. Eventually, it is rigorously confirmed that the new proposed technique is more feasible, powerful, and iterative compared with HPM. The technique is indeed simple and promising that may find its place in analytic nonlinear analysis in the very close future. K E Y W O R D Sa novel topological technique for differential equations, homotopy perturbation method, MHD flow of Eyring-Powell fluids, nonlinearly stretching sheet

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Section: Introductionmentioning

confidence: 89%

\begin{matrix} left \\ \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0 \\ u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = (υ + \frac{1}{ρ β d}) \frac{\partial^{2} u}{\partial y^{2}} - \frac{1}{2 ρ β d^{3}} {(\frac{\partial u}{\partial y})}^{2} \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B {(x)}^{2}}{ρ} u \\ u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α \frac{\partial^{2} T}{\partial y^{2}} - \frac{1}{ρ C_{p}} \frac{\partial q_{r}}{\partial y} \end{matrix}

…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Following the papers by Jafarimoghaddam, it is easy to indicate that similarity transformation exists if only

n = \frac{1}{3}

whilst, other cases should be treated as nonsimilar flows.…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

MHD flow of eyring‐powell fluids: HPM and a novel topological technique

Jafarimoghaddam¹

2019

Heat Trans. Asian Res.

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“…There have been many attempts in the literature to discuss the varied fluid problems utilizing the homotopy analysis method [42][43][44][45][46][47][48][49].…”

mentioning

confidence: 99%

Impact of Second-Order Slip and Double Stratification Coatings on 3D MHD Williamson Nanofluid Flow with Cattaneo–Christov Heat Flux

et al. 2019

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The present research examines the impact of second-order slip with thermal and solutal stratification coatings on three-dimensional (3D) Williamson nanofluid flow past a bidirectional stretched surface and envisages it analytically. The novelty of the analysis is strengthened by Cattaneo-Christov (CC) heat flux accompanying varying thermal conductivity. The appropriate set of transformations is implemented to get a differential equation system with high nonlinearity.The structure is addressed via the homotopy analysis technique. The authenticity of the presented model is verified by creating a comparison with the limited published results and finding harmony between the two. The impacts of miscellaneous arising parameters are deliberated through graphical structures. Some useful tabulated values of arising parameters versus physical quantities are also discussed here. It is observed that velocity components exhibit an opposite trend with respect to the stretching ratio parameter. Moreover, the Brownian motion parameter shows the opposite behavior versus temperature and concentration distributions.

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Perturbed‐analytic direct transcription for optimal control (PADOC)

Jafarimoghaddam

Soler

2023

Optim Control Appl Methods

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The herein coined PADOC (perturbed-analytic direct transcription for optimal control) stands for a new transcription method for direct trajectory optimization. We construct PADOC on a novel segmented decomposition method that provides series solutions for nonlinear problems. To transcribe the infinite dimensional problem into a finite one, PADOC comes along with a new solution approach, namely, the herein coined average nonlinear programming (aNLP). The aNLP theorem suggests generating a staircase optimal solution (low resolution) and turning it into a distributed optimal solution (high resolution) by exploiting the Hamiltonian of the problem. The analytic architecture provides PADOC with an analytic connection of a truncated order between the discrete nodes of the solution. This renders stability, accuracy within an analytic resolution, robustness, and a cut-down in the number of the decision variables in the frame of NLP. We also prove that the multipliers associated with the Karush-Kuhn-Tucker optimality conditions in the frame of NLP (as transcribed by PADOC) correspond to a backward analytic solution for the costate equations. We finally show distinct features of PADOC through some examples.

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On the Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) for a nonlinearly stretching sheet flow of Eyring-Powell fluids

Cited by 28 publications

References 48 publications

MHD flow of eyring‐powell fluids: HPM and a novel topological technique

MHD flow of eyring‐powell fluids: HPM and a novel topological technique

Impact of Second-Order Slip and Double Stratification Coatings on 3D MHD Williamson Nanofluid Flow with Cattaneo–Christov Heat Flux

Perturbed‐analytic direct transcription for optimal control (PADOC)

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