scholarly journals Off-Centered Stagnation Point Flow of a Couple Stress Fluid towards a Rotating Disk

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Fatima Riaz
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Similarity Transformation ◽  
Rotating Disk ◽  
Analytical Approximation ◽  
Couple Stress Fluid ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Special Case

An investigation has been made to study the off-centered stagnation flow of a couple stress fluid over a rotating disk. The model developed for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most promising analytical approach, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The effects of couple stress and nondimensional parameters have been observed on the flows of couple stress fluid. Also comparison has been made with the Newtonian fluid as the special case of considered problem.

Analytic Approximate Solutions and Numerical Results for Stagnation Point Flow of Jeffrey Fluid Towards an Off-Centered Rotating Disk

2014 ◽  
Vol 31 (2) ◽  
pp. 201-215 ◽  
Author(s):  
N. A. Khan ◽  
S. Khan ◽  
F. Riaz
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Approximate Solutions ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Special Case ◽  
Non Linear Equations

AbstractThe present paper studies the three-dimensional, off centered stagnation flow of a Jeffrey fluid over a rotating disk. The governing non-linear equations and their associated boundary conditions are transformed into coupled ordinary differential equations by utilizing an appropriate similarity transformation. Homotopy analysis method is utilized to evaluate the analytical solution in the form of infinite series. Also, the convergence region of the obtained solution is determined and plotted. The effects of pertaining parameters on radial, azimuthal and induced velocities of the fluid flow are presented graphically and discussed. Moreover comparisons have also been made with the previous results as a special case.

scholarly journals Swirling flow of couple stress fluid due to a rotating disk

2019 ◽  
Vol 8 (1) ◽  
pp. 261-269 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Nadeem Alam Khan ◽  
Saif Ullah ◽  
Farah Naz
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Swirling Flow ◽  
Nonlinear Differential Equations ◽  
Rotating Disk ◽  
Tangential Component ◽  
Couple Stress Fluid ◽  
Governing System ◽  
Fluid Parameter ◽  
Homotopy Analysis

AbstractThe main objective of the present investigation is to examine the couple stress fluid flow occurring as a result of rotation of a disk. On implementing a suitable transformation, the governing system of partial differential equations (PDEs) is converted into nonlinear differential equations of a single independent variable. These equations are solved analytically by virtue of the Homotopy Analysis Method (HAM) which gives solutions in the form of a series. The solution of most of the governing problems is determined in terms of the absolute exponential and decaying functions by means of this powerful technique. To support analytic results, some graphs are plotted for determining the convergence of the solution. Also the graphical interpretation of velocity profiles corresponding to the effects of pertinent parameters are shown and discussed in detail. The numerical results are calculated for evaluation of the influence of fluid parameter. It can also be anticipated that the radial and axial velocity components show decreasing behavior due to rise in the values of couple stress parameter which conflict the behavior of the tangential component of velocity.

scholarly journals Analytical solution of MHD free convective flow of couple stress fluid in an annulus with Hall and ion-slip effects

2011 ◽  
Vol 16 (4) ◽  
pp. 477-487 ◽  
Author(s):  
Darbhashayanam Srinivasacharya ◽  
Kolla Kaladhar
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Circular Cylinders ◽  
Couple Stress Fluid ◽  
Electrically Conducting ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Ion Slip

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and  temperature are discussed and shown graphically.

scholarly journals Serious Solutions for Unsteady Axisymmetric Flow over a Rotating Stretchable Disk with Deceleration

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 96 ◽  
Author(s):  
Sadiq
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Axisymmetric Flow ◽  
Analysis Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Rotating Stretchable Disk ◽  
Comparison Table

In this article, the author has examined the unsteady flow over a rotating stretchable disk with deceleration. The highly nonlinear partial differential equations of viscous fluid are simplified by existing similarity transformation. Reduced nonlinear ordinary differential equations are solved by homotopy analysis method (HAM). The convergence of HAM solutions is also obtained. A comparison table between analytical solutions and numerical solutions is also presented. Finally, the results for useful parameters, i.e., disk stretching parameters and unsteadiness parameters, are found.

scholarly journals Series Solution of the System of Fuzzy Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. S. Hashemi ◽  
J. Malekinagad ◽  
H. R. Marasi
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Solution Series ◽  
Homotopy Analysis ◽  
Contour Plots ◽  
And Control

The homotopy analysis method (HAM) is proposed to obtain a semianalytical solution of the system of fuzzy differential equations (SFDE). The HAM contains the auxiliary parameterħ, which provides us with a simple way to adjust and control the convergence region of solution series. Concept ofħ-meshes and contour plots firstly are introduced in this paper which are the generations of traditionalh-curves. Convergency of this method for the SFDE has been considered and some examples are given to illustrate the efficiency and power of HAM.

scholarly journals Investigation of combined heat and mass transfer between vertical parallel plates in a two-layer flow of couple stress nanofluid

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Najeeb Alam Khan ◽  
Faqiha Sultan ◽  
Fatima Riaz ◽  
Muhammad Jamil
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Homotopy Analysis Method ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Parallel Plates ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis

Abstract This study is an investigation of fully-developed laminar flow in a two-layer vertical channel; one part filled with couple stress nanofluid and the other part with clear couple stress fluid. The flow is examined for combined heat and mass transfer using uniform wall temperature and concentration boundary conditions. Optimal homotopy analysis method (OHAM) is used to solve the nonlinear coupled ordinary differential equations (ODEs) governing the flow in each region. This method is based on the homotopy analysis method (HAM)which is an effective method to analytically approximate the solution of highly nonlinear problems. The influence of pertinent parameters is observed on velocity, temperature, and concentration distributions, specifically, the effect of Brownian parameter on couple stress fluid is mentioned.

scholarly journals Flow of an Erying-Powell fluid over a stretching sheet in presence of chemical reaction

2016 ◽  
Vol 20 (6) ◽  
pp. 1903-1912 ◽  
Author(s):  
Ilyas Khan ◽  
Muhammad Qasim ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Similarity Transformation ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Analysis Method ◽  
Stretching Surface ◽  
Shooting Technique ◽  
Homotopy Analysis

In this paper we study the flow of an incompressible Erying-Powell fluid bounded by a linear stretching surface. The mass transfer analysis in the presence of destructive /generative chemical reactions is also analyzed. A similarity transformation is used to transform the governing partial differential equations into ordinary differential equations. Computations for dimensionless velocity and concentration fields are performed by an efficient approach namely the homotopy analysis method (HAM) and numerical solution is obtained by shooting technique along with Runge-Kutta-Fehlberg integration scheme. Graphical results are prepared to illustrate the details of flow and mass transfer characteristics and their dependence upon the physical parameters. The values for gradient of mass transfer are also evaluated and analyzed. A comparison of the present solutions with published results in the literature is performed and the results are found to be in excellent agreement.

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.

The Approximate Analytical Solution of the MHD Flow of a Power-Law Fluid

2013 ◽  
Vol 431 ◽  
pp. 198-201
Author(s):  
Jing Zhu ◽  
Lian Cun Zheng
Keyword(s):  
Differential Equations ◽  
Power Law ◽  
Velocity Ratio ◽  
Mhd Flow ◽  
Convergent Series ◽  
Analysis Method ◽  
Governing System ◽  
Homotopy Analysis ◽  
Incompressible Mhd ◽  
Good Agreement

This paper presents a theoretical analysis for the incompressible MHD stagnation-point flows of a Non-Newtonian Fluid over stretching sheets.The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. By using the homotopy analysis method, a convergent series solution is obtained. The reliability and efficiency of series solutions are illustrated by good agreement with numerical results in the literature.Besides, the effects of the power-law indexthe magnetic field parameter and velocity ratio parameter on the flow are investigated.

Sign in / Sign up

Export Citation Format

Share Document