Exact flow of a third grade fluid past a porous plate using homotopy analysis method

Ayub, M.; Rasheed, Amer; Hayat, Tasawar

doi:10.1016/s0020-7225(03)00207-6

Cited by 181 publications

(90 citation statements)

References 20 publications

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“…In the past, HAM has been successfully used to solve many problems in science and engineering [8][9][10][11][12][13][14][15], and also in epidemic models such as SIR [16] and SIS models [17].…”

Section: Introductionmentioning

confidence: 99%

Solving a model for the evolution of smoking habit in Spain with homotopy analysis method

Guerrero

Santonja

Micó

2013

Nonlinear Analysis: Real World Applications

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. a b s t r a c tWe obtain an approximated analytical solution for a dynamic model for the prevalence of the smoking habit in a constant population but with equal and different from zero birth and death rates. This model has been successfully used to explain the evolution of the smoking habit in Spain. By means of the Homotopy Analysis Method, we obtain an analytic expression in powers of time t which reproduces the correct solution for a certain range of time. To enlarge the domain of convergence we have applied the so-called optimal convergence-control parameter technique and the homotopy-Padé technique. We present and discuss graphical results for our solutions.

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Section: Introductionmentioning

confidence: 99%

Solving a model for the evolution of smoking habit in Spain with homotopy analysis method

Guerrero

Santonja

Micó

2013

Nonlinear Analysis: Real World Applications

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“…This method used to find the solutions of algebraic equations, ordinary differential equations, integro-differential equations and so on. Unlike the perturbation methods, homotopy analysis method is independent from small / large physical parameters and also it is not important whether the small / large physical parameters of the problem contains or not for the implementation of the method [17], [18].…”

Section: Description Of the Homotopy Analysis Methodsmentioning

confidence: 99%

Implementation to the Different Differential Equations of Homotopy Analysis, Differential Transformed and Adomian Decomposition Method

Bıldık¹

2013

IJMO

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Abstract-In this study, the concept of Homotopy analysis method (HAM) is briefly introduced. Furthermore some non-linear problems are handled and the solutions of these problems are given using by HAM, DTM, ADM methods and the convergence of the solution is shown to the exact solution. Additionally, the three methods are compared and it is observed that the HAM is more-less efficient and effective than the ADM and DTM in according to the exact solution. In the end, some of the numerical solutions of two examples are presented and the results are shown in graphs and figures.Index Terms-Homotopy analysis method, differential transform method, adomian decomposition method, auxiliary linear operator, embedding parameter, deformation equation.

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“…Due to this fact, rheological parameter involved in the constitutive equations of such fluids adds complexity in the arising systems. Regardless of all these complexities, several researchers [4][5][6][7][8] studied the flow of non-Newtonian fluids in different geometrical configurations. However, the microscopic properties like micro-rotation and rotation-inertia of micropolar fluids be different from the other non-Newtonian fluids.…”

Section: Introductionmentioning

confidence: 99%

Squeezing Flow of Micropolar Nanofluid between Parallel Disks

Khan¹,

Mohyud‐Din²,

Yang³

2016

Journal of Magnetics

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In the present study, squeezing flow of micropolar nanofluid between parallel infinite disks in the presence of magnetic field perpendicular to plane of the disks is taken into account. The constitutive equations that govern the flow configuration are converted into nonlinear ordinary differential with the help of suitable similarity transforms. HAM package BVPh2.0 has been employed to solve the nonlinear system of ordinary differential equations. Effects of different emerging parameters like micropolar parameter K, squeezed Reynolds number R, Hartmann number M, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le for dimensionless velocities, temperature distribution and concentration profile are also discussed graphically. In the presence of strong and weak interaction (i.e. n = 0 and n = 0.5), numerical values of skin friction coefficient, wall stress coefficient, local Nusselt number and local Sherwood number are presented in tabulated form. To check the validity and reliability of the developed algorithm BVPh2.0 a numerical investigation is also a part of this study.

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Exact flow of a third grade fluid past a porous plate using homotopy analysis method

Cited by 181 publications

References 20 publications

Solving a model for the evolution of smoking habit in Spain with homotopy analysis method

Solving a model for the evolution of smoking habit in Spain with homotopy analysis method

Implementation to the Different Differential Equations of Homotopy Analysis, Differential Transformed and Adomian Decomposition Method

Squeezing Flow of Micropolar Nanofluid between Parallel Disks

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