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

2008 ◽  
Vol 9 (4) ◽  
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

Orthogonal Flow Impinging on a Wall with Suction or Blowing

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Najeeb Alam Khan ◽  
Asmat Ara ◽  
Syed Anwer Ali ◽  
Muhammad Jamil
Keyword(s):  
Incompressible Fluid ◽  
Perturbation Method ◽  
Flat Plate ◽  
Skin Friction ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Viscous Incompressible Fluid ◽  
Approximate Solutions ◽  
Homotopy Perturbation ◽  
Porous Flat Plate

The goal of this work is the approximate solutions of a viscous incompressible fluid impinging orthogonally on a porous flat plate. The equation governing the flow of an incompressible fluid is investigated using the homotopy perturbation method (HPM) with the aid of Padé-approximants. The approximate solutions can be successfully applied to provide the value of the skin-friction. The reliability and efficiency of the approximate solutions were verified using numerical solutions in the literature.

AN APPLICATION OF ALGORITHMS OF ADAMS AND GEAR METHODS ON BOUNDARY LAYER CONVECTIVE HEAT TRANSFER WITH PRESSURE GRADIENT USING HOMOTOPY PERTURBATION METHOD (HPM) OVER A FLAT PLATE

2018 ◽  
Vol 80 (3) ◽  
Author(s):  
Amber Nehan Kashif ◽  
Zainal Abdul Aziz ◽  
Faisal Salah ◽  
K. K. Viswanathan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Perturbation Method ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Layer Flow

Boundary layer flow of convective heat transfer with pressure gradient over a flat plate is solved with an application of algorithms of Adams Method (AM) and Gear Method (GM) using Homotopy Perturbation Method (HPM). The distributions of temperature and velocity in the boundary layer are examined, particularly on the influences due to Prandtl number (Pr) and pressure gradient (m). Consequently, the equations of momentum and energy are resolved concurrently. These HPM outcomes have been compared with the previous published work in the literature; and these are found to be in good agreement with the results obtained from numerical methods.

scholarly journals Second Approximate Solution of Duffing Equation with Strong Nonlinearity by Homotopy Perturbation Method

1970 ◽  
Vol 30 ◽  
pp. 59-75
Author(s):  
M Alhaz Uddin ◽  
M Abdus Sattar
Keyword(s):  
Approximate Solution ◽  
Nonlinear Systems ◽  
Perturbation Method ◽  
Differential System ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Second Order ◽  
Strong Nonlinearity ◽  
Analytical Technique ◽  
Homotopy Perturbation

 In this paper, the second order approximate solution of a general second order nonlinear ordinary differential system, modeling damped oscillatory process is considered. The new analytical technique based on the work of He’s homotopy perturbation method is developed to find the periodic solution of a second order ordinary nonlinear differential system with damping effects. Usually the second or higher order approximate solutions are able to give better results than the first order approximate solutions. The results show that the analytical approximate solutions obtained by homotopy perturbation method are uniformly valid on the whole solutions domain and they are suitable not only for strongly nonlinear systems, but also for weakly nonlinear systems. Another advantage of this new analytical technique is that it also works for strongly damped, weakly damped and undamped systems. Figures are provided to show the comparison between the analytical and the numerical solutions. Keywords: Homotopy perturbation method; damped oscillation; nonlinear equation; strong nonlinearity. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 59-75  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8504

Application of He’s Homotopy Perturbation Method for Solving Fractional Fokker-Planck Equations

2009 ◽  
Vol 64 (12) ◽  
pp. 788-794 ◽  
Author(s):  
Mohamed M. Mousa ◽  
Aidarkhan Kaltayev
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Planck Equation ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Homotopy Perturbation ◽  
External Force Field ◽  
Promising Tool ◽  
Transport Problems ◽  
Fokker Planck

Abstract The fractional Fokker-Planck equation (FFPE) has been used in many physical transport problems which take place under the influence of an external force field and other important applications in various areas of engineering and physics. In this paper, by means of the homotopy perturbation method (HPM), exact and approximate solutions are obtained for two classes of the FFPE initial value problems. The method gives an analytic solution in the form of a convergent series with easily computed components. The obtained results show that the HPM is easy to implement, accurate and reliable for solving FFPEs. The method introduces a promising tool for solving other types of differential equation with fractional order derivatives

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