Flow of Magnetohydrodynamic Micropolar Fluid Induced by Radially Stretching Sheets

2011 ◽  
Vol 66 (1-2) ◽  
pp. 53-60 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Nawaz ◽  
Awatif A. Hendi
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Skin Friction ◽  
Nonlinear Problem ◽  
Homotopy Analysis Method ◽  
Micropolar Fluid ◽  
Analysis Method ◽  
Fluid Parameter ◽  
Homotopy Analysis ◽  
Radial Stretching

We investigate the flow of a micropolar fluid between radial stretching sheets. The magnetohydrodynamic (MHD) nonlinear problem is treated using the homotopy analysis method (HAM) and the velocity profiles are predicted for the pertinent parameters. The values of skin friction and couple shear stress coefficients are obtained for various values of Reynolds number, Hartman number, and micropolar fluid parameter.

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.

The flow of a micropolar fluid through a porous channel with expanding or contracting walls

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Xinhui Si ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Ying Chao
Keyword(s):  
Dynamic Characteristics ◽  
Homotopy Analysis Method ◽  
Micropolar Fluid ◽  
Expansion Ratio ◽  
Velocity Fields ◽  
Porous Channel ◽  
Analysis Method ◽  
Governing Equations ◽  
Homotopy Analysis ◽  
Expanding Or Contracting Walls

AbstractThe flow of a micropolar fluid in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for the velocity fields and microrotation fields. Graphs are sketched for the effects of some values of parameters, especially the expansion ratio, on the velocity and microrotation fields and associated dynamic characteristics are analyzed in detail.

The analysis of the flow of a micropolar fluid between two orthogonally moving porous disks with counter rotating directions

Open Physics ◽  
2013 ◽  
Vol 11 (5) ◽  
Author(s):  
Yina Sun ◽  
Xinhui Si ◽  
Liancun Zheng ◽  
Yanan Shen ◽  
Xinxin Zhang
Keyword(s):  
Reynolds Number ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Flow Behavior ◽  
Angular Speed ◽  
Expansion Ratio ◽  
Physical Parameters ◽  
Analysis Method ◽  
Rotating Disks ◽  
Homotopy Analysis

AbstractThe present work investigates the unsteady, imcompressible flow of a micropolar fluid between two orthogonally moving porous coaxial disks. The lower and upper disks are rotating with the same angular speed in counter directions. The flows are driven by the contraction and the rotation of the disks. An extension of the Von Kármán type similarity transformation is proposed and is applied to reduce the governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. These differential equations with appropriate boundary conditions are responsible for the flow behavior between large but finite coaxial rotating disks. The analytical solutions are obtained by employing the homotopy analysis method. The effects of some various physical parameters like the expansion ratio, the rotational Reynolds number, the permeability Reynolds number, and micropolar parameters on the velocity fields are observed in graphs and discussed in detail.

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.

Analytic Approximations for a Strongly Nonlinear Problem of Combined Convective and Radiative Cooling of a Spherical Body

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
A. El-Nahhas
Keyword(s):  
Boundary Condition ◽  
Nonlinear Problem ◽  
Homotopy Analysis Method ◽  
Spherical Body ◽  
Radiative Cooling ◽  
Strong Nonlinearity ◽  
Analysis Method ◽  
Strongly Nonlinear ◽  
Analytic Approximations ◽  
Homotopy Analysis

In this paper, a nonlinear problem for combined convective and radiative cooling of a spherical body is considered. This problem represents a strong nonlinearity in both the governing equation and the boundary condition. Analytic approximations for the solution of this problem are obtained using the homotopy analysis method and via a polynomial exponential basis. Also, the effect of the radiation-conduction parameter Nrc and the Biot number Bi for the temperature on the surface of the spherical body is investigated and discussed.

scholarly journals Fundamental flow problems considering non-Newtonian hyperbolic tangent fluid with Navier slip: Homotopy analysis method

2020 ◽  
Vol 14 (2) ◽  
Author(s):  
Lalrinpuia Tlau
Keyword(s):  
Skin Friction ◽  
Homotopy Analysis Method ◽  
Fluid Velocity ◽  
Weissenberg Number ◽  
Analysis Method ◽  
Hyperbolic Tangent ◽  
Navier Slip ◽  
Flow Problems ◽  
Flow Parameters ◽  
Homotopy Analysis

The presented research article deals with the classical fundamental flows (Poiseuille and Couette) of an incompressible hyperbolic tangent fluid while considering the Navier slip at the walls. The governing equations are solved using the homotopy analysis method. The velocity expressions are obtained for each problem and the effect of the flow parameters are discussed while being supplemented by graphical displays. Increasing the slip parameter reduces the fluid velocity for both problems, respectively. An increase in the Weissenberg number shows that skin friction at the lower wall reduces. This shows that a dominant elastic force is crucial in reducing the skin friction.

Analytic Approximations for Cooling Turbine Disks

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
A. El-Nahhas
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Perturbation Method ◽  
Homotopy Analysis Method ◽  
Temperature Profiles ◽  
Analysis Method ◽  
Analytic Approximations ◽  
Viscosity Parameter ◽  
Homotopy Analysis ◽  
Turbine Disks

In this paper, we use the homotopy analysis method as a tool to obtain analytic approximations to the nonlinear problem of the cooling of turbine disks with a non-Newtonian viscoelastic fluid. The application of this method is executed via a polynomial exponential basis. The effects on velocity and temperature profiles with variations of the cross viscosity parameter, the Reynolds number, and the Prandtl number are discussed. A comparison with corresponding results of the perturbation method is illustrated and also, as a result of application of the homotopy analysis method, an analytic evaluation for the Nusselt number compared to the perturbation method is achieved.

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