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Peristaltic flow of Sisko fluid in a uniform inclined tube

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Acta Mechanica Sinica 2010年第5期26卷 675-683页

作者： Sohail Nadeem Noreen Sher Akbar Department of Mathematics Quaid-i-Azam University 45320

We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non- Newtonian fluid is investigated under the considerations of long wavelength and low Reynolds number approximation. The analytic solution is obtained using （i） the regular perturbation method （ii） the homotopy analysis method （HAM）. The comparison of both the solutions is presented graphically. The results for the pressure rise, frictional force and pressure gradient have been calculated numerically and the results are studied for various values of the physical parameters of interest, such as α （angle of inclination）, b^＊（Sisko fluid parameter）, Ф （amplitude ratio） and n （power law index）. Trapping phenomena is discussed at the end of the article.

关键词： Peristaltic flow Sisko fluid Perturbation method homotopy analysis method

A short comment on the effect of a shear layer on nonlinear water waves

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Science China(Physics,Mechanics & Astronomy) 2011年第1期54卷 67-73页

作者： CANG Jie CHENG Jun GRIMSHAW Roge School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai 200240 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China Department of Mathematical Sciences Loughborough University Loughborough LE11 3TU UK

In this paper we study nonlinear periodic deep water waves propagating on a background shear current,which decays exponentially with *** extend the study of Cheng,Cang and Liao(2009) by introducing a second parameter which measures the depth of the shear current.A high-order convergent analytical series solution is obtained by the homotopy analysis method(HAM).A detailed analysis of the impact of the depth parameter is *** find that increasing this parameter so that the shear current is thinner reduces the wave phase speed,smoothes the wave crest,sharpens the trough,and enlarges the maximum wave height for the case of propagating waves on an opposing current;while it produces the opposite effect on an aiding current.

关键词： nonlinear water waves wave-current interaction homotopy analysis method

What＇s　the　Common　Ground　of　Al　Numerical　and　Analytical　Techniques　for　Nonlinear　Problems？

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Communications in Nonlinear Science and Numerical Simulation 1996年第4期1卷 28-32页

作者： Shi-Jun LIAO (Dept. of Naval Arch. & Ocean Engineering, Shanghai Jiao Tong Univ.,Shanghai 200030, P. R. China) E-mail: SJLIAO@hkucc.hku.hk Dept. of Naval Arch. & Ocean Engineering Shanghai Jiao Tong Univ. Shanghai 200030 P.R. China

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关键词： common ground of nonlinear techniques iterative techniques perturbation techniques homotopy analysis method

Thermal analysis of annular fins with temperature-dependent thermal properties

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Applied Mathematics and Mechanics(English Edition) 2013年第11期34卷 1349-1360页

作者： I. G. AKSOY Department of Mechanical Engineering Inonu University

The thermal analysis of the annular rectangular profile fins with variable thermal properties is investigated by using the homotopy analysis method （HAM）. The thermal conductivity and heat transfer coefficient are assumed to vary with a linear and power-law function of temperature, respectively. The effects of the thermal-geometric fin parameter and the thermal conductivity parameter variations on the temperature distribution and fin efficiency are investigated for different heat transfer modes. Results from the HAM are compared with numerical results of the finite difference method （FDM）. It can be seen that the variation of dimensionless parameters has a significant effect on the temperature distribution and fin efficiency.

关键词： annular fin variable thermal property homotopy analysis method

Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

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Communications in Theoretical Physics 2015年第1期63卷 51-56页

作者：刘爱洁郑连存马连喜张欣欣 School of Mathematics and Physics University of Science and Technology Beijing Department of Physics Blinn College

In this paper, the analytical solutions of Schrodinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker-P1anck equation known as the Klein-Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr6dinger equation. The anaiytical results obtained from the two different methods agree with each other well The double well potentiai is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.

关键词： Brown motion homotopy analysis method Schrodinger equation double well potential

Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

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Frontiers of physics 2013年第3期8卷 319-327页

作者：石玉仁王雪玲王光辉刘丛波周志刚杨红娟 College of Physics and Electronic Engineering Northwest Normal University Lanzhou 730070 China

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear SchrSdinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.

关键词： spin-1 Bose-Einstein condensate Gross-Pitaevskii equation homotopy analysis method analytical solution

Analytical approximate solutions of AdS black holes in Einstein-Weyl-scalar gravity

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Chinese Physics C 2023年第12期47卷 139-150页

作者：张明李盛源邹德成张晁铭 Faculty of Science Xi’an Aeronautical UniversityXi’an 710077 China School of Physics Northwest UniversityXi’an710069China Center for Gravitation and Cosmology College of Physical Science and TechnologyYangzhou UniversityYangzhou 225009China College of Physics and Communication Electronics Jiangxi Normal UniversityNanchang 330022China

We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional *** the minimal geometric deformation(MGD)approach,we split the highly nonlinear coupled field equations into two subsystems that describe the background geometry and scalar field source,*** considering the Schwarzschild-AdS metric as background geometry,we derive analytical approximate solutions of the scalar field and deformation metric functions using the homotopy analysis method(HAM),providing their analytical approximations to fourth ***,we discuss the accuracy of the analytical approximations,showing they are sufficiently accurate throughout the exterior spacetime.

关键词： black hole scalar field analytical approximate solutions homotopy analysis method minimal geometric deformation

Analytic Solution for Steady Slip Flow between Parallel Plates with Micro-Scale Spacing

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Chinese Physics Letters 2008年第1期25卷 180-183页

作者：张田田贾力王志成 Department of Power Engineering School of Mechanical and Electronic Control Engineering Beijing Jiaotong University Beijing 100044

The Navier-Stokes equations for slip flow between two very closely spaced parallel plates are transformed to an ordinary differential equation based on the pressure gradient along the flow direction using a new similarity transformation. A powerful easy-to-use homotopy analysis method was used to obtain an analytical solution. The convergence theorem for the homotopy analysis method is presented. The solutions show that the second-order homotopy analysis method solution is accurate enough for the current problem.

关键词： homotopy analysis method APPROXIMATE SOLUTION TECHNIQUE HEAT-TRANSFER SMALL PARAMETERS MICROCHANNELS FLUID

homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

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Applied Mathematics and Mechanics(English Edition) 2011年第7期32卷 859-874页

作者：司新毅司新辉郑连存张欣欣 College of Water Conservancy and Hydropower Engineering Hohai University School of Mathematics and Physics University of Science and Technology Beijing School of Mechanical Engineering University of Science and Technology Beijing

The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method （HAM） is used＇to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu＇s model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations axe transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α（t） from the initial state α0 to the final state al. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

关键词： homotopy analysis method micropolar fluid expanding or contractingwall porous channel different permeability