scholarly journals Evaluation of electro-osmotic flow in a nanochannel via semi-analytical method

2012 ◽  
Vol 16 (5) ◽  
pp. 1297-1302 ◽  
Author(s):  
Payam Jalili ◽  
Domairry Ganji ◽  
Bahram Jalili ◽  
Domiri Ganji
Keyword(s):  
Shear Stress ◽  
Analytical Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Electrical Potential ◽  
Osmotic Flow ◽  
Homotopy Perturbation ◽  
Stress Profiles ◽  
Electro Osmotic Flow ◽  
Cation Distributions

In this paper, equations due to anion and cation distributions, electrical potential and shear stress profiles in a nanochannel are formed for 1-D electro-osmotic flow, and solved by homotopy perturbation method. Results are compared with numerical solutions.

Application of Homotopy Perturbation Method for Harmonically Forced Duffing Systems

2011 ◽  
Vol 110-116 ◽  
pp. 2277-2283 ◽  
Author(s):  
Xiang Meng Zhang ◽  
Ben Li Wang ◽  
Xian Ren Kong ◽  
A Yang Xiao
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Primary Resonance ◽  
Effective Technique ◽  
Duffing System ◽  
First Order ◽  
Homotopy Perturbation ◽  
Analytical Approximations ◽  
Case Based

In this paper, He’s homotopy perturbation method (HPM) is applied to solve harmonically forced Duffing systems. Non-resonance of an undamped Duffing system and the primary resonance of a damped Duffing system are studied. In the former case, the first-order analytical approximations to the system’s natural frequency and periodic solution are derived by HPM, which agree well with the numerical solutions. In the latter case, based on HPM, the first-order approximate solution and the frequency-amplitude curves of the system are acquired. The results reveal that HPM is an effective technique to the forced Duffing systems.

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

Optimal control homotopy perturbation method for cancer model

2019 ◽  
Vol 12 (03) ◽  
pp. 1950027 ◽  
Author(s):  
Malihe Najafi ◽  
Hadi Basirzadeh
Keyword(s):  
Mathematical Modeling ◽  
Optimal Control ◽  
Perturbation Method ◽  
Cancer Immunotherapy ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Cancer Model ◽  
Homotopy Perturbation

In this paper, we introduced the optimal control homotopy perturbation method (OCHPM) by using the homotopy perturbation method (HPM). Every one, by using of the proposed method, can obtain numerical solutions of mathematical modeling for cancer-immunotherapy. In this paper, in order to prove the preciseness and efficiency of the OCHPM method, we compared the obtained numerical solutions with HPM. The results obtained showed that the OCHPM method is powerful to generate the numerical solutions for some therapeutic models.

Thermal Effect on Microchannel Electro-osmotic Flow With Consideration of Thermodiffusion

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Yi Zhou ◽  
Yongqi Xie ◽  
Chun Yang ◽  
Yee Cheong Lam
Keyword(s):  
Charge Density ◽  
Thermal Effect ◽  
Temperature Difference ◽  
Electrical Potential ◽  
Ionic Concentration ◽  
Free Charge ◽  
Regular Perturbation ◽  
Osmotic Flow ◽  
Ionic Distribution ◽  
Electro Osmotic Flow

Electro-osmotic flow (EOF) is widely used in microfluidic systems. Here, we report an analysis of the thermal effect on EOF under an imposed temperature difference. Our model not only considers the temperature-dependent thermophysical and electrical properties but also includes ion thermodiffusion. The inclusion of ion thermodiffusion affects ionic distribution, local electrical potential, as well as free charge density, and thus has effect on EOF. In particular, we formulate an analytical model for the thermal effect on a steady, fully developed EOF in slit microchannel. Using the regular perturbation method, we solve the model analytically to allow for decoupling several physical mechanisms contributing to the thermal effect on EOF. The parametric studies show that the presence of imposed temperature difference/gradient causes a deviation of the ionic concentration, electrical potential, and electro-osmotic velocity profiles from their isothermal counterparts, thereby giving rise to faster EOF. It is the thermodiffusion induced free charge density that plays a key role in the thermodiffusion induced electro-osmotic velocity.

scholarly journals An approximate analytical technique for solving second order strongly nonlinear generalized duffing equation with small damping

2015 ◽  
Vol 39 (1) ◽  
pp. 103-114
Author(s):  
M Alhaz Uddin ◽  
M Wali Ullah ◽  
Rehana Sultana Bipasha
Keyword(s):  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Second Order ◽  
Extended Form ◽  
Analytical Technique ◽  
Strongly Nonlinear ◽  
Homotopy Perturbation ◽  
Kbm Method ◽  
Method Accuracy ◽  
Academy Of Sciences

In this paper, He’s homotopy perturbation method has been extended for obtaining the analytical approximate solution of second order strongly nonlinear generalized duffing oscillators with damping based on the extended form of the Krylov-Bogoliubov-Mitropolskii (KBM) method. Accuracy and validity of the solutions obtained by the presented method are compared with the corresponding numerical solutions obtained by the well-known fourth order Rangue-Kutta method. The method has been illustrated by examples.Journal of Bangladesh Academy of Sciences, Vol. 39, No. 1, 103-114, 2015

scholarly journals A New Spectral-Homotopy Perturbation Method and Its Application to Jeffery-Hamel Nanofluid Flow with High Magnetic Field

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Magnetic Field ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Nonlinear Boundary Value Problems ◽  
Nanofluid Flow ◽  
New Approach ◽  
Homotopy Perturbation ◽  
Chebyshev Pseudospectral

We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method, and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the Jeffery-Hamel flow considering the effects of magnetic field and nanoparticle. Comparisons are made between the proposed technique, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the present approach. The results demonstrate that the new modification is more efficient and converges faster than the standard homotopy perturbation method.

scholarly journals Analytical Method in Solving Flow of Viscoelastic Fluid in a Porous Converging Channel

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
M. Esmaeilpour ◽  
Naeem Roshan ◽  
Negar Roshan ◽  
D. D. Ganji
Keyword(s):  
Analytical Method ◽  
Homotopy Perturbation Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Homotopy Perturbation ◽  
Converging Channel ◽  
Grade Fluid

An analytical method, called homotopy perturbation method (HPM), is used to compute an approximation to the solution of the nonlinear differential equation governing the problem of two-dimensional and steady flow of a second-grade fluid in a converging channel. The table and figures are presented for influencing various parameters on the velocity field. The results compare well with those obtained by the numerical method. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.

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