Solution of Boundary Layer Problems with Heat Transfer by Optimal Homotopy Asymptotic Method

Application of Optimal Homotopy Asymptotic Method (OHAM), a new analytic approximate technique for treatment of Falkner-Skan equations with heat transfer, has been applied in this work. To see the efficiency of the method, we consider Falkner-Skan equations with heat transfer. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature as finite difference (N. S. Asaithambi, 1997) and shooting method (Cebeci and Keller, 1971). The obtained solutions show that OHAM is effective, simpler, easier, and explicit.

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Solution of the Differential-Difference Equations by Optimal Homotopy Asymptotic Method

Abstract and Applied Analysis ◽

10.1155/2014/520467 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

H. Ullah ◽

S. Islam ◽

M. Idrees ◽

M. Fiza

Keyword(s):

Difference Equations ◽

Asymptotic Method ◽

Volterra Equation ◽

Approximate Solutions ◽

Optimal Homotopy Asymptotic Method ◽

Convergence Of Approximate Solutions ◽

Efficiency And Reliability

We applied a new analytic approximate technique, optimal homotopy asymptotic method (OHAM), for treatment of differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Volterra equation in different form. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier, and explicit.

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The Optimal Homotopy Asymptotic Method for Solving Two Strongly Fractional-Order Nonlinear Benchmark Oscillatory Problems

Mathematics ◽

10.3390/math9182218 ◽

2021 ◽

Vol 9 (18) ◽

pp. 2218

Author(s):

Mohd Taib Shatnawi ◽

Adel Ouannas ◽

Ghenaiet Bahia ◽

Iqbal M. Batiha ◽

Giuseppe Grassi

Keyword(s):

Fractional Order ◽

Asymptotic Method ◽

Approximate Solutions ◽

Analytic Solutions ◽

Auxiliary Function ◽

Approximate Methods ◽

Homotopy Analysis ◽

Optimal Homotopy Asymptotic Method ◽

Relativistic Oscillator ◽

Convergence Of Approximate Solutions

This paper proceeds from the perspective that most strongly nonlinear oscillators of fractional-order do not enjoy exact analytical solutions. Undoubtedly, this is a good enough reason to employ one of the major recent approximate methods, namely an Optimal Homotopy Asymptotic Method (OHAM), to offer approximate analytic solutions for two strongly fractional-order nonlinear benchmark oscillatory problems, namely: the fractional-order Duffing-relativistic oscillator and the fractional-order stretched elastic wire oscillator (with a mass attached to its midpoint). In this work, a further modification has been proposed for such method and then carried out through establishing an optimal auxiliary linear operator, an auxiliary function, and an auxiliary control parameter. In view of the two aforesaid applications, it has been demonstrated that the OHAM is a reliable approach for controlling the convergence of approximate solutions and, hence, it is an effective tool for dealing with such problems. This assertion is completely confirmed by performing several graphical comparisons between the OHAM and the Homotopy Analysis Method (HAM).

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Approximate Solutions to a Cantilever Beam Using Optimal Homotopy Asymptotic Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.430.22 ◽

2013 ◽

Vol 430 ◽

pp. 22-26 ◽

Cited By ~ 1

Author(s):

Vasile Marinca ◽

Nicolae Herisanu ◽

Traian Marinca

Keyword(s):

Small Parameter ◽

Cantilever Beam ◽

Asymptotic Method ◽

Approximate Solutions ◽

Lumped Mass ◽

Engineering Problems ◽

Approximate Frequency ◽

Optimal Homotopy Asymptotic Method ◽

Analytical Expressions

The response of a cantilever beam with a lumped mass attached to its free end subject to harmonical excitation at the base is investigated by means of the Optimal Homotopy Asymptotic Method (OHAM). Approximate accurate analytical expressions for the solutions and for approximate frequency are determined. This method does not require any small parameter in the equation. The obtained results prove that our method is very accurate, effective and simple for investigation of such engineering problems.

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Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

Open Physics ◽

10.1515/phys-2017-0072 ◽

2017 ◽

Vol 15 (1) ◽

pp. 620-626 ◽

Cited By ~ 1

Author(s):

Vasile Marinca ◽

Remus-Daniel Ene ◽

Liviu Bereteu

Keyword(s):

Asymptotic Method ◽

Approximate Solutions ◽

Bingham Fluid ◽

Rapid Convergence ◽

Bingham Model ◽

Mr Dampers ◽

Approximate Analytical Solutions ◽

Small Parameters ◽

Optimal Homotopy Asymptotic Method ◽

Fluid Dampers

AbstractDynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

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Implicit Finite Difference Solution of MHD Boundary Layer Heat Transfer over a Moving plate

IOSR Journal of Mathematics ◽

10.9790/5728-0931621 ◽

2013 ◽

Vol 9 (3) ◽

pp. 16-21 ◽

Cited By ~ 1

Author(s):

Satish V Desale

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Finite Difference ◽

Moving Plate ◽

Mhd Boundary Layer ◽

Finite Difference Solution ◽

Implicit Finite Difference ◽

Difference Solution

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Approximate Solutions of Thermal Boundary-layer Problems in a Semi-infinite Flat Plate by using He's Homotopy Perturbation Method

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns.2008.9.4.415 ◽

2008 ◽

Vol 9 (4) ◽

Cited By ~ 20

Author(s):

Z.Z. Ganji ◽

D.D. Ganji

Keyword(s):

Boundary Layer ◽

Perturbation Method ◽

Flat Plate ◽

Thermal Boundary Layer ◽

Homotopy Perturbation Method ◽

Approximate Solutions ◽

Homotopy Perturbation ◽

Boundary Layer Problems

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Analytical approximate solutions to the Thomas-Fermi equation

Open Physics ◽

10.2478/s11534-014-0472-9 ◽

2014 ◽

Vol 12 (7) ◽

Cited By ~ 3

Author(s):

Vasile Marinca ◽

Remus-Daniel Ene

Keyword(s):

Excellent Agreement ◽

Asymptotic Method ◽

Numerical Solutions ◽

Approximate Solutions ◽

Rapid Convergence ◽

Thomas Fermi ◽

Small Parameters ◽

Optimal Homotopy Asymptotic Method

AbstractThe purpose of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to solve the nonlinear differential Thomas-Fermi equation. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. An excellent agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

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Mathematical study of fractional-order biological population model using optimal homotopy asymptotic method

International Journal of Biomathematics ◽

10.1142/s1793524516500819 ◽

2016 ◽

Vol 09 (06) ◽

pp. 1650081 ◽

Cited By ~ 11

Author(s):

S. Sarwar ◽

M. A. Zahid ◽

S. Iqbal

Keyword(s):

Fractional Order ◽

Asymptotic Method ◽

Population Model ◽

Approximate Solutions ◽

High Accuracy ◽

Population Models ◽

Mathematical Study ◽

Third Order ◽

Biological Population ◽

Optimal Homotopy Asymptotic Method

In this paper, we study the fractional-order biological population models (FBPMs) with Malthusian, Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method (OHAM) for partial differential equations (PDEs) is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional-order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.

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Analytic Approximate Solution for Falkner-Skan Equation

The Scientific World JOURNAL ◽

10.1155/2014/617453 ◽

2014 ◽

Vol 2014 ◽

pp. 1-22 ◽

Cited By ~ 4

Author(s):

Vasile Marinca ◽

Remus-Daniel Ene ◽

Bogdan Marinca

Keyword(s):

Differential Equation ◽

Boundary Layer ◽

Numerical Solutions ◽

Approximate Solutions ◽

Rapid Convergence ◽

Boundary Layer Problem ◽

Small Parameters ◽

Optimal Homotopy Asymptotic Method ◽

Good Agreement ◽

Layer Problem

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

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Analytical Investigation of Nusselt Number and Skin Friction of Fluid Flow Over a Stretching Sheet Using Optimal Homotopy Asymptotic Method

Advanced Science Engineering and Medicine ◽

10.1166/asem.2020.2570 ◽

2020 ◽

Vol 12 (5) ◽

pp. 657-661

Author(s):

Zohreh Aliannejadi

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Boundary Layer ◽

Nusselt Number ◽

Fluid Flow ◽

Differential Equations ◽

Skin Friction ◽

Flow And Heat Transfer ◽

Optimal Homotopy Asymptotic Method ◽

The Magnetic Field

In many cases such as production of metal sheets, the behavior of fluid flow and heat transfer in the neighborhood of a hot plate is very important. The CFD simulation of fluid flow is a widespread study that reveals detail information about the fluid flow in the calculated domain. In this study, the flow and heat transfer of a specific fluid in the above area of a stretching plate is examined analytically to find the variation of skin friction and Nusselt number. For this purpose, the similarity transformations can be employed to achieve the ordinary differential equations from the governing partial differential equations. The optimal homotopy asymptotic method (OHAM) is used to solve the ordinary differential equations which is applicable in solving of nonlinear equations. The effects of magnetic field on the analytical results from solving the equations are evaluated in detail. It is found that the thickness of the flow boundary layer decreases and the thickness of the thermal boundary layer increases by increasing in the magnetic field. Moreover, the Nusselt number is lower and skin friction is higher for the higher values of the magnetic field.

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