MHD Squeezing Flow of a Micropolar Fluid Between Parallel Disks

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
T. Hayat ◽  
M. Nawaz ◽  
Awatif A. Hendi ◽  
S. Asghar
Keyword(s):  
Micropolar Fluid ◽  
Weak Interactions ◽  
Skin Friction Coefficient ◽  
Similarity Solutions ◽  
Squeezing Flow ◽  
Analysis Method ◽  
Parallel Disks ◽  
Stress Coefficient ◽  
Homotopy Analysis ◽  
Incompressible Micropolar Fluid

The squeezing flow of an incompressible micropolar fluid between two parallel infinite disks is investigated in the presence of a magnetic flied. An analysis of strong and weak interactions has been carried out. Similarity solutions are derived by homotopy analysis method. The variation of dimensionless velocities are sketched in order to see the influence of pertinent parameters. Skin friction coefficient and wall couple stress coefficient have been tabulated. In addition, the derived results are compared with the homotopy perturbation solution in a viscous fluid.

THERMO-DIFFUSION AND DIFFUSO-THERMO EFFECTS ON MHD SQUEEZING FLOW BETWEEN PARALLEL DISKS

2017 ◽  
Vol 24 (02) ◽  
pp. 1750022 ◽  
Author(s):  
SHEIKH IRFANULLAH KHAN ◽  
SYED TAUSEEF MOHYUD-DIN ◽  
BANDAR BIN-MOHSIN
Keyword(s):  
Skin Friction Coefficient ◽  
Squeezing Flow ◽  
Validity And Reliability ◽  
Soret And Dufour Effects ◽  
Parallel Disks ◽  
Homotopy Analysis ◽  
Number Formula ◽  
Soret Number ◽  
Dufour Number ◽  
Order Four

In this article, Magnetohydrodynamic (MHD) squeezing flow between two parallel disks is considered. The upper disk is taken to be solid and the lower one is permeable. Soret and Dufour effects are measured to explore the thermal-diffusion and diffusion-thermo effects. Governing PDEs are converted into system of ODEs with the support of suitable similarity transforms. Homotopy analysis method (HAM) has been employed to obtain the expressions for velocity, temperature and concentration profiles. Effects of different emerging parameters such as squeezing number [Formula: see text], Hartman number [Formula: see text], Prandtl number Pr, Eckert number Ec, dimensionless length [Formula: see text] and Schmidt number Sc on the flow are also discussed with the help of graphs for velocity, temperature and concentration. The local Nusselt and Sherwood numbers along with convergence of the series solutions are presented with the help of graphs. From the results obtained, we observed that the physical quantities like skin friction coefficient increases with increasing value of Hartmann number [Formula: see text] in the blowing case [Formula: see text] whereas a fall is observed in the suction case [Formula: see text]. However, the rate of heat transfer at upper wall increases with increasing values of Dufour number Du and Soret number Sr for both the suction [Formula: see text] and blowing flow [Formula: see text], whereas, for the larger values of Dufour number Du and smaller values of Soret number Sr, a rapid fall is observed in Sherwood number Sh for both the suction [Formula: see text] and blowing [Formula: see text] cases. A numerical solution is obtained by employing Runge–Kutta method of order four (RK-4) to check the validity and reliability of the developed algorithm. A well agreement is found between both the solutions.

Soret and Dufour Effects on the Stagnation-Point Flow of a Micropolar Fluid Toward a Stretching Sheet

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
T. Hayat ◽  
M. Mustafa ◽  
S. Obaidat
Keyword(s):  
Mass Transfer ◽  
Stagnation Point ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Analysis Method ◽  
Soret And Dufour Effects ◽  
Homotopy Analysis ◽  
Incompressible Micropolar Fluid

This communication reports the heat and mass transfer analysis in the stagnation-point flow toward a stretching sheet. An incompressible micropolar fluid takes into account the diffusion-thermo- (Dufour) and thermal-diffusion (Soret) effects. The arising nonlinear differential system is solved by homotopy analysis method. Convergence of the obtained homotopy solutions is clearly justified. Special emphasis has been given to various physical parameters through graphs and tables. It is noticed that fields are influenced appreciably with the variation of embedding parameters. A comparison of the present results with the existing numerical solution is discussed in a limiting sense.

Flow of a Hydromagnetic Viscous Fluid between Parallel Disks with Slip

2015 ◽  
Vol 31 (6) ◽  
pp. 713-726 ◽  
Author(s):  
N. Khan ◽  
M. Sajid ◽  
T. Mahmood
Keyword(s):  
Reynolds Number ◽  
Series Solution ◽  
Fluid Velocity ◽  
Similarity Solutions ◽  
Analysis Method ◽  
Symmetric Flow ◽  
Parallel Disks ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Parameter Values

ABSTRACTThe present paper is devoted to the investigation of steady MHD axi-symmetric flow between two infinite stretching disks with slip effects. Our attention lies in obtaining the similarity solutions of the governing partial differential equations. The transformed boundary value problem is solved analytically for a series solution using homotopy analysis method. The convergence of the obtained solution is established and fluid velocity and pressure are analyzed for various set of parameter values. The obtained results are valid for both moderate and large values of Reynolds number.

scholarly journals Homotopy Analysis Solution for Magnetohydrodynamic Squeezing Flow in Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Inayat Ullah ◽  
M. T. Rahim ◽  
Hamid Khan ◽  
Mubashir Qayyum
Keyword(s):  
Porous Medium ◽  
Control Parameter ◽  
Analytical Techniques ◽  
Squeezing Flow ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
Flow Through ◽  
Convergence Control Parameter ◽  
Good Agreement

The aim of the present work is to analyze the magnetohydrodynamic (MHD) squeezing flow through porous medium using homotopy analysis method (HAM). Fourth-order boundary value problem is modeled through stream functionψ(r,z)and transformationψ(r,z)=r2f(z). Absolute residuals are used to check the efficiency and consistency of HAM. Other analytical techniques are compared with the present work. It is shown that results of good agreement can be obtained by choosing a suitable value of convergence control parameterhin the valid regionRh. The influence of different parameters on the flow is argued theoretically as well as graphically.

Series solution for flow of a second-grade fluid in a divergent–convergent channel

2010 ◽  
Vol 88 (12) ◽  
pp. 911-917 ◽  
Author(s):  
T. Hayat ◽  
M. Nawaz ◽  
S. Asghar ◽  
Awatif A. Hendi
Keyword(s):  
Series Solution ◽  
Problem Formulation ◽  
Skin Friction Coefficient ◽  
Second Grade ◽  
Physical Parameters ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Convergent Channel ◽  
Homotopy Analysis ◽  
Grade Fluid

This study explores the flow of a second-grade fluid in divergent–convergent channel. The problem formulation is first developed, and then the corresponding nonlinear problem is solved by homotopy analysis method (HAM). The effects of different physical parameters on the velocity profile are shown. The numerical values of the skin friction coefficient for different values of parameters are tabulated.

scholarly journals Slip effects on squeezing flow of nanofluid between two parallel disks

2016 ◽  
Vol 21 (1) ◽  
pp. 5-20 ◽  
Author(s):  
K. Das ◽  
S. Jana ◽  
N. Acharya
Keyword(s):  
Differential Equations ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Skin Friction Coefficient ◽  
Integration Scheme ◽  
Squeezing Flow ◽  
Linear Ordinary Differential Equations ◽  
Slip Conditions ◽  
Electrically Conducting ◽  
Parallel Disks

Abstract In this study, the influence of temperature and wall slip conditions on the unsteady flow of a viscous, incompressible and electrically conducting nanofluid squeezed between two parallel disks in the presence of an applied magnetic field is investigated numerically. Using the similarity transformation, the governing coupled partial differential equations are transformed into similarity non-linear ordinary differential equations which are solved numerically using the Nachtsheim and Swigert shooting iteration technique together with the sixth order Runge-Kutta integration scheme. The effects of various emerging parameters on the flow characteristics are determined and discussed in detail. To check the reliability of the method, the numerical results for the skin friction coefficient and Nusselt number in the absence of slip conditions are compared with the results reported by the predecessors and an excellent agreement is observed between the two sets of results.

scholarly journals Series Solutions of Boundary Layer Flow of a Micropolar Fluid Near the Stagnation Point Towards a Shrinking Sheet

2009 ◽  
Vol 64 (9-10) ◽  
pp. 575-582 ◽  
Author(s):  
Sohail Nadeem ◽  
Saeid Abbasbandy ◽  
Majid Hussain
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Local Skin ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Local Skin Friction ◽  
Layer Flow

An analysis has been carried out to obtain the series solution of boundary layer flow of a micropolar fluid towards a shrinking sheet. The governing equations of micropolar fluid are simplified using suitable similarity transformations and then solved by homotopy analysis method (HAM). The convergence of the HAM solutions has been obtained by using homotopy-pade approximation. The effects of various parameters such as porosity parameter R, the ratio λ and the microinertia K on the velocity and microinertia profiles as well as local skin friction coefficient are presented graphically and in tabulated form.

Effect of Heat Transfer on Magnetohydrodynamic Axisymmetric Flow Between Two Stretching Sheets

2010 ◽  
Vol 65 (11) ◽  
pp. 961-968 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Nawaz
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Skin Friction Coefficient ◽  
Navier Stokes ◽  
Tabular Form ◽  
Analysis Method ◽  
Navier Stokes Equations ◽  
Homotopy Analysis

This investigation describes the effects of heat transfer on magnetohydrodynamic (MHD) axisymmetric flow of a viscous fluid between two radially stretching sheets. Navier-Stokes equations are transformed into the ordinary differential equations by utilizing similarity variables. Solution computations are presented by using the homotopy analysis method. The convergence of obtained solutions is checked. Skin friction coefficient and Nusselt number are given in tabular form. The dimensionless velocities and temperature are also analyzed for the pertinent parameters entering into the problem.

scholarly journals Stagnation-Point Flow and Heat Transfer over a Nonlinearly Stretching/Shrinking Sheet in a Micropolar Fluid

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Khairy Zaimi ◽  
Anuar Ishak
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Micropolar Fluid ◽  
Material Parameter ◽  
Limited Range ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Incompressible Micropolar Fluid

This paper considers the problem of a steady two-dimensional stagnation-point flow and heat transfer of an incompressible micropolar fluid over a nonlinearly stretching/shrinking sheet. A similarity transformation is employed to convert the partial differential equations into nonlinear ordinary ones which are then solved numerically using a shooting method. Numerical results obtained are presented graphically, showing the effects of the micropolar or material parameter and the stretching/shrinking parameter on the flow field and heat transfer characteristics. The dual solutions are found to exist in a limited range of the stretching/shrinking parameter for the shrinking case, while unique solutions are possible for all positive values of the stretching/shrinking parameter (stretching case). It is also observed that the skin friction coefficient and the magnitude of the local Nusselt number increase as the material parameter increases.

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