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On the MHD squeeze flow between two parallel disks with suction or injection via HAM and HPM

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Frontiers of Mechanical Engineering 2014年第3期9卷 270-280页

作者： D. D. GANJI M. ABBASI J. RAHIMI M. GHOLAMI I. RAHIMIPETROUDI Department of Mechanical Engineering Babol University of Technology Babol Iran Department of Mechanical Engineering Sari Branch Islamic AzadUniversity Sari Iran Department of Electrical and Computer Engineering Babol Universityof Technology Babol Iran Department of Mechanical Engineering College of Mechanic TehranScience and Research Branch Islamic Azad University Darnavand Iran

An analysis has been performed to study the problem of magneto-hydrodynamic （MHD） squeeze flow of an electrically conducting fluid between two infinite, parallel disks. The analytical methods called homotopy analysis method （HAM） and homotopy Perturbation method （HPM） have been used to solve nonlinear differential equations. It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as Boundary Value Problem （BVP） in solving this problem. Also, the velocity fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the velocity field. Furthermore, the results reveal that HAM and HPM are very effective and convenient.

关键词： homotopy analysis method homotopy Perturbation method incompressible flow magneto-hydrodynamic flow parallel disks

Numerical investigation of the flow of a micropolar fuid through a porous channel with expanding or contracting walls

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Propulsion and Power Research 2014年第3期3卷 133-142页

作者： M.T.Darvishi F.Khani F.G.Awad A.A.Khidir P.Sibanda Deparment of Mathematics Razi UniversityKermanshah 67149Iran School of Mathematical Sciences University of KwaZulu-NatalPrivate Bag X01ScottsvillePietermaritzburg 3209South Africa

In this paper,we study the flow of a micropolar fluid in a porous channel with expanding or contracting ***,we use spectral collocation method on the governing equations to obtain an initial approximation for the solution of *** using the obtained initial approximation,we apply the homotopy analysis method to obtain a recursive fomula for the solution.

关键词： homotopy analysis method Spectral collocation method Series solution Micropolar fluid

Heat transfer analysis for a free boundary problem arising in n-diffusion equation

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Propulsion and Power Research 2016年第4期5卷 261-266页

作者： Ulrich Olivier Dangui-Mbani Jize Sui Chunying Ming Liancun Zheng Goong Chen School of Mathematics and Physics University of Science and Technology BeijingBeijing 100083China School of Mechanical Engineering University of Science and Technology BeijingBeijing 100083China Department of Mathematics and Institute for Quantum Science and Engineermg Texas A&M UniversityCollege StationTX 77843USA Science Program Texas A&M University at QatarEducation CityDohaQatar

This paper presents research on a free boundary value problem arising in a nonlinear n-diffiision equation by using a homotopy analysis method(HAM).Approximate analytical solutions are obtained for special nonlinear diffusion functional coefficient(variable thermal conduction)k(s)=s{i}for i=1,3,5 and convection functional coefficient h(s)=s{j}for j=1,4 and power law parameter of n=0.2,0.5,1.0,*** and efficiency of the approximate solutions are verified by numerical ones showing good *** effects of the power law exponent,the nonlinear diffusion or convection functional coefficients,and the free boundary'parameter on the flux transport characteristics are presented graphically and analyzed in *** mathematical techniques employed in this paper have the significance in studying some other problems of engineering.

关键词： n-Diffusion equation Free boundary homotopy analysis method Non-linear problem Approximate solution

MHD flow of Boungiorno model nanofluid over a vertical plate with internal heat generation/absorption

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Propulsion and Power Research 2016年第3期5卷 211-222页

作者： B.Ganga S.Mohamed Yusuff Ansari N.Vishnu Ganesh A.K.Abdul Hakeem Department of Mathematics Providence College for WomenCoonoor 643104India Department of Mathematics Jamal Mohamed CollegeTrichy 620020India Department of Mathematics Sri Ramakrishna Mission Vidyalaya College of Arts&ScienceCoimbatore 641020India

A mathematical analysis has been carried out to investigate the effect of internal heat generation/absorption on steady two-dimensional radiative magnetohydrodynamics(MHD)boundary-layer flow of a viscous,incompressible nanofluid over a vertical plate.A system of governing nonlinear PDEs is converted into a set of nonlinear ODEs by suitable similarity transformations and then solved analytically using HAM and numerically by the fourth order Runge–Kutta integration scheme with shooting *** effects of different controlling parameters on the dimensionless velocity,temperature and nanoparticle volume fraction profiles are discussed *** reduced Nusslet number and the local Sherwood number are *** is found that the nanosolid volume fraction profile decreases in the presence of heat generation and increases in the case of heat absorption and a reverse trend is observed in velocity *** excellent agreement is observed between present analytical and numerical ***,comparisons have been made with bench mark solutions for a special case and obtained a very good agreement.

关键词： Heat generation/absorption homotopy analysis method Magnetohydrodynamics(MHD) Nanofluid Vertical plate

Numerical investigation on MHD Jeffery-Hamel nanofluid flow with different nanoparticles using fuzzy extension of generalized dual parametric homotopy algorithm

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Journal of Central South University 2024年第6期31卷 1915-1930页

作者： LALCHAND Verma RAMAKANTA Meher Department of Mathematics Sardar Vallabhbhai National Institute of TechnologySurat-395007GujratIndia

This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy *** nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and *** to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the *** short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel ***,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.

关键词： fuzzy number Jeffery-Hamel(J-H)flow nanofluid homotopy analysis method

homotopy analysis Solution to Radial Diffusivity Equation of Slightly Compressible Fluid

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Applied Mathematics 2016年第9期7卷 993-1004页

作者： Olugbenga Adebanjo Falode Victor Sunday Chukwunagolu Department of Petroleum Engineering University of Ibadan Ibadan Nigeria

The salient significance of the solution of radial diffusivity equation to well testing analysis done in oil and gas industry cannot be over-emphasized. Varieties of solutions have been proposed to the radial diffusivity equation, of which the Van Everdingen-Hurst constant terminal rate solution is the most widely accepted and the others are approximate solution having their respective limitations. The main objective of this project, being its first application to oil and gas industry, is to use a new mathematical technique, the homotopy analysis method (HAM) to solve the radial diffusivity equation for slightly compressible fluid. In Using HAM, the Boltzmann transformation method was used to transform the radial PDE to ODE, then a homotopy series was then constructed for the new equation with the linear boundary condition from the original radial diffusivity equation of slightly compressible fluid and the final equation then solved using computation software Maple. The result gotten reveals that the homotopy analysis method gives good results compared to the Van Everdingen and Hurst Solution (Exact solution) and thus proves to be very effective, simple, and accurate when compared to other form of solutions. Hence from the results gotten, homotopy analysis method can therefore be applied in solving other non-linear equations in the petroleum engineering field since it is simple and accurate.

关键词： homotopy analysis method Boltzmann Transformation Exact Solution Diffusivity Equation

homotopy analysis of MHD Free Convective Micropolar Fluid Flow along a Vertical Surface Embedded in Non-Darcian Thermally-Stratified Medium

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Open Journal of Fluid Dynamics 2016年第3期6卷 198-221页

作者： Olubode Kolade Koriko Tosin Oreyeni Adeola John Omowaye Isaac Lare Animasaun Department of Mathematical Sciences Federal University of Technology Akure Nigeria

The dynamics of steady, two-dimensional magnetohydrodynamics (MHD) free convective flow of micropolar fluid along a vertical porous surface embedded in a thermally stratified medium is investigated. The ratio of pressure drop caused by liquid-solid interactions to that of pressure drop caused by viscous resistance are equal;hence, the non-Darcy effect is properly accounted for in the momentum equation. The temperature at the wall and at the free stream which best accounts for thermal stratification are adopted. Similarity transformations are used to convert the nonlinear partial differential equation to a system of coupled non-linear ordinary differential equation and also to parameterize the governing equations. The approximate analytical solution of the corresponding BVP are obtained using homotopy analysis method (HAM). The effects of stratification parameter, thermal radiation and other pertinent parameters on velocity, angular velocity and temperature profiles are shown graphically. It is observed that increase in the stratification parameter leads to decrease in both velocity and temperature distribution and also makes the microrotation distribution to increase near the plate and decrease away from the plate. The influence of both thermal stratification and exponential space dependent internal heat source on velocity, micro-rotation and temperature profiles are presented. The comparison of the solutions obtained using analytical techniques (HAM) and MATLAB package (bvp4c) is shown and a good agreement is observed.

关键词： Porous Medium Thermal Stratification homotopy analysis method Free Convection Micropolar

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Burgers方程的最优同伦渐近方法研究

高等学校计算数学学报 2019年第1期41卷 45-53页

作者：单丽冯思佳辽宁工程技术大学理学院

1引言Burgers方程是由Bateman在1915年提出的.求解该方程对于空气动力学、湍流、热传导、交通流、半导体模拟以及地下水污染等领域具有重要意义.求解Burgers方程的数值方法很多,例如有限差分法、LDG有限元方法、拟小波配点法、直线法等.

关键词： Burgers equation Optimal homotopy Asymptotic method homotopy analysis method

Loop Soliton Solutions of a Short Wave Model for a Degasperis-Procesi Equation

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Journal of Marine Science and Application 2011年第2期10卷 220-225页

作者：邹丽宗智王振张朔 School of Aeronautics and Astronautics Dalian University of Technology The State Key Laboratory of Structure analysis for Industrial Equipment School of Naval Architecture and Ocean Engineering Dalian University of Technology Department of Applied Mathematics Dalian University of Technology

An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.

关键词： homotopy analysis method one-loop soliton explicit analytic solution nonlinearity Degasperis-Procesi equation