Mass, Momentum and Energy Flux in Nonlinear Water Wave Based on HAM Solution

2016 ◽  
Author(s):  
Zhiliang Lin
Keyword(s):  
Energy Transport ◽  
Nonlinear Partial Differential Equation ◽  
Analysis Method ◽  
Free Surface Elevation ◽  
Ham Solution ◽  
Fitting Procedure ◽  
Pressure Fields ◽  
Homotopy Analysis ◽  
Finite Water Depth ◽  
Discrete Integration

In this paper, the Homotopy Analysis Method (HAM) is applied to solve the fully nonlinear partial differential equation for the steady propagating periodic gravity wave of finite water depth. The series solution of the wave elevation and the velocity potential function are obtained. And then the velocity and pressure fields are plotted and discussed carefully. In order to overcome the drawback of the integral calculations with complex free surface elevation, the discrete integration and fitting procedure based on high-order Fourier series is developed. Based on the accurate HAM solution and fitting technique, the mass, momentum and energy conservation equations are validated. At last, the corresponding mean fluxes are calculated and the velocities of the mass transport and energy transport are supplied accurately.

Studying Dynamic Pull-In Behavior of Microbeams by Means of the Homotopy Analysis Method

2008 ◽  
Author(s):  
Mahdi Moghimi Zand ◽  
S. Ahmad Tajalli ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Nonlinear Partial Differential Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Strong Nonlinearity ◽  
Analysis Method ◽  
Solution Methods ◽  
Homotopy Analysis ◽  
Fringing Field ◽  
Fringing Field Effect

In this study, the homotopy analysis method (HAM) is used to study dynamic pull-in instability in microbeams considering different sources of nonlinearity. Electrostatic actuation, fringing field effect and midplane stretching causes strong nonlinearity in microbeams. In order to investigate dynamic pull-in behavior, using Galerkin’s decomposition method, the nonlinear partial differential equation of motion is reduced to a single nonlinear ordinary differential equation. The obtained equation is solved analytically in time domain using HAM. The problem is studied by two separate manners: direct use of HAM and indirect use of HAM in conjunction with He’s Modified Lindstedt-Poincare´ Method. To demonstrate the effectiveness of the solution methods, results are compared with those in literature. The comparison between obtained results and those available in literature shows good agreement.

scholarly journals A Note on Solutions of the SIR Models of Epidemics Using HAM

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
M. Sajid ◽  
Z. Abbas ◽  
N. Ali ◽  
T. Javed
Keyword(s):  
Excellent Agreement ◽  
Homotopy Analysis Method ◽  
Numerical Results ◽  
Analysis Method ◽  
New Approach ◽  
Entire Domain ◽  
Ham Solution ◽  
Homotopy Analysis

Recently, Awawdeh et al. (2009) discussed the solutions of SIR epidemics model using homotopy analysis method. This comment points out some crucial flaws in (Awawdeh et al. 2009). Particularly, results presented in Figure 1 of the (Awawdeh et al. 2009) do not represent the 20 term solution of the considered problem as stated. The present paper also provides a new approach for solving SIR epidemics model using homotopy analysis method. The new approach is based on dividing the entire domain into subintervals. In each subinterval the three-term HAM solution is sufficient for obtaining accurate and convergent results. The comparison of the obtained solution using new approach is made with the numerical results and found in excellent agreement.

scholarly journals Optimal homotopy analysis solution of fingero-imbibition phenomenon in homogeneous porous medium with magnetic fluid effect

10.29007/kq3n ◽  
2018 ◽  
Author(s):  
Dipakkumar Prajapati ◽  
Narendrasinh Desai
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Magnetic Fluid ◽  
Nonlinear Partial Differential Equation ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Double Phase ◽  
Homotopy Analysis ◽  
Homogeneous Porous Medium

The present paper discusses the fingero-imbibition phenomenon in a double phase dis- placement process through homogeneous porous medium with the involvement of a layer of magnetic fluid in the injected phase. This phenomenon has much importance in petroleum technology. The nonlinear partial differential equation governing this phenomenon with appropriate boundary conditions is solved by an optimal homotopy analysis method. The convergence of the solution is decided by minimizing discrete squared residual.

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

scholarly journals Unsteady thermal Maxwell power law nanofluid flow subject to forced thermal Marangoni Convection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Jawad ◽  
Anwar Saeed ◽  
Taza Gul ◽  
Zahir Shah ◽  
Poom Kumam
Keyword(s):  
Relaxation Time ◽  
Power Law ◽  
Marangoni Convection ◽  
Power Law Model ◽  
Analysis Method ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Welan Gum ◽  
Homotopy Analysis ◽  
Power Law Nanofluid

AbstractIn the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

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