EFFECTS OF SLIP ON FLOW BETWEEN TWO STRETCHABLE DISKS USING OPTIMAL HOMOTOPY ANALYSIS METHOD

2011 ◽  
Vol 1 ◽  
pp. 50-67
Author(s):  
Sufian Munawar ◽  
Keyword(s):  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Solution Technique ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Similarity Transformations ◽  
Governing System ◽  
Homotopy Analysis ◽  
One Step ◽  
Two Parameters

This work presents the analytic solution of flow of a viscous fluid between two stretching disks with slip boundaries. Suitable similarity transformations are used to normalize the governing system. Optimal homotopy analysis method has been used as a solution technique by considering one parameter; two parameters; three parameters and one step optimal HAM approaches

scholarly journals The Optimal q-Homotopy Analysis Method (Oq-HAM)

2013 ◽  
Vol 11 (8) ◽  
pp. 2859-2866 ◽  
Author(s):  
Shaheed N Huseen ◽  
Said R.Grace ◽  
Magdy A. El-Tawil
Keyword(s):  
Homotopy Analysis Method ◽  
Control Parameter ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
One Step ◽  
The One ◽  
Convergence Control Parameter

In this paper, an optimal q-homotopy analysis method (Oq-HAM) is proposed. We present some examples to show the reliability and efficiency of the method. It is compared with the one-step optimal homotopy analysis method. The results reveal that the Oq-HAM has more accuracy to determine the convergence-control parameter than the one-step optimal HAM.

scholarly journals The One Step Optimal Homotopy Analysis Method to Circular Porous Slider

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammad Ghoreishi ◽  
Ahmad Izani B. Md. Ismail ◽  
Abdur Rashid
Keyword(s):  
Reynolds Number ◽  
Approximate Solution ◽  
Homotopy Analysis Method ◽  
Momentum Equation ◽  
Analysis Method ◽  
Lateral Velocity ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
One Step ◽  
The One

An incompressible Newtonian fluid is forced through the porous of a circular slider which is moving laterally on a horizontal plan. In this paper, we introduce and apply the one step Optimal Homotopy Analysis Method (one step OHAM) to the problem of the circular porous slider where a fluid is injected through the porous bottom. The effects of mass injection and lateral velocity on the heat generated by viscous dissipation are investigated by solving the governing boundary layer equations using one step optimal homotopy technique. The approximate solution for the coupled nonlinear ordinary differential equations resulting from the momentum equation is obtained and discussed for different values of the Reynolds number of the velocity field. The solution obtained is also displayed graphically for various values of the Reynolds number and it is shown that the one step OHAM is capable of finding the approximate solution of circular porous slider.

Optimal Homotopic Exploration of features of Cattaneo-Christov model in Second Grade Nanofluid flow via Darcy-Forchheimer medium subject to Viscous Dissipation and Thermal Radiation

2021 ◽  
Vol 24 ◽  
Author(s):  
Ghulam Rasool ◽  
Anum Shafiq ◽  
Yu-Ming Chu ◽  
Muhammad Shoaib Bhutta ◽  
Amjad Ali
Keyword(s):  
Temperature Distribution ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Homotopy Analysis Method ◽  
Stream Velocity ◽  
Analysis Method ◽  
Nanofluid Flow ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis

Introduction: In this article Optimal Homotopy analysis method (oHAM) is used for exploration of the features of Cattaneo-Christov model in viscous and chemically reactive nanofluid flow through a porous medium with stretching velocity at the solid/sheet surface and free stream velocity at the free surface. Methods: The two important aspects, Brownian motion and Thermophoresis are considered. Thermal radiation is also included in present model. Based on the heat and mass flux, the Cattaneo-Christov model is implemented on the Temperature and Concentration distributions. The governing Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs) using similarity transformations. The results are achieved using the optimal homotopy analysis method (oHAM). The optimal convergence and residual errors have been calculated to preserve the validity of the model. Results: The results are plotted graphically to see the variations in three main profiles i.e. momentum, temperature and concentration profile. Conclusion: The outcomes indicate that skin friction enhances due to implementation of Darcy medium. It is also noted that the relaxation time parameter results in enhancement of the temperature distribution. Thermal radiation enhances the temperature distribution and so is the case with skin friction.

Application of Optimal Homotopy Analysis Method for Solitary Wave Solutions of Kuramoto-Sivashinsky Equation

2011 ◽  
Vol 66 (1-2) ◽  
pp. 117-122
Author(s):  
Qi Wang
Keyword(s):  
Solitary Wave ◽  
Homotopy Analysis Method ◽  
Solitary Wave Solutions ◽  
Analysis Method ◽  
Convergence Region ◽  
Optimal Method ◽  
Optimal Homotopy Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis ◽  
Sivashinsky Equation

In this paper, the optimal homotopy analysis method is applied to find the solitary wave solutions of the Kuramoto-Sivashinsky equation. With three auxiliary convergence-control parameters, whose possible optimal values can be obtained by minimizing the averaged residual error, the method used here provides us with a simple way to adjust and control the convergence region of the solution. Compared with the usual homotopy analysis method, the optimal method can be used to get much faster convergent series solutions.

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