Hiemenz flow of a micropolar viscoelastic fluid in hydromagnetics

2005 ◽  
Vol 83 (10) ◽  
pp. 1007-1017 ◽  
Author(s):  
S MM El-Kabeir
Keyword(s):  
Numerical Solutions ◽  
Transverse Magnetic ◽  
Shooting Technique ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Viscoelastic Parameters ◽  
Governing System ◽  
Hiemenz Flow ◽  
Range Of Values ◽  
Numerical Integration Procedure

Boundary-layer equations are solved for the hydromagnetic problem of two-dimensional Hiemenz flow, for a micropolar, viscoelastic, incompressible, viscous, electrically conducting fluid, impinging perpendicularly onto a plane in the presence of a transverse magnetic field. The governing system of equations is first transformed into a dimensionless form. The resulting equations then are solved by using the Runge–Kutta numerical integration procedure in conjunction with shooting technique. Numerical solutions are presented for the governing momentum and angular-momentum equations. The proposed approximate solution, although simple, is nevertheless sufficiently accurate for the entire investigated range of values of the Hartman number. The effect of micropolar and viscoelastic parameters on Hiemenz flow in hydromagnetics is discussed.PACS No.: 46.35

scholarly journals Effects of ohmic heating and viscous dissipation on steady MHD flow near a stagnation point on an isothermal stretching sheet

2009 ◽  
Vol 13 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Pushkar Sharma ◽  
Gurminder Singh
Keyword(s):  
Stagnation Point ◽  
Viscous Dissipation ◽  
Ohmic Heating ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Governing Equations ◽  
Shooting Technique ◽  
Electrically Conducting

Aim of the paper is to investigate effects of ohmic heating and viscous dissipation on steady flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a stretching non-conducting isothermal sheet. The governing equations of continuity, momentum, and energy are transformed into ordinary differential equations and solved numerically using Runge-Kutta fourth order with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed numerically, and their numerical values for various values of physical parameters are compared with earlier results and presented through tables.

Porous exponential slider bearings lubricated with MHD-couple stress fluid

2018 ◽  
Vol 70 (5) ◽  
pp. 838-845 ◽  
Author(s):  
N.B. Naduvinamani ◽  
Shridevi S. Hosmani
Keyword(s):  
Couple Stress ◽  
Numerical Solutions ◽  
Transverse Magnetic ◽  
Operating Conditions ◽  
Couple Stress Fluid ◽  
Content Type ◽  
Electrically Conducting ◽  
Slider Bearings ◽  
Load Carrying ◽  
First Time

Purpose The purpose of this study is to examine the magneto-hydrodynamic (MHD) effect on porous exponential slider bearings lubricated with couple stress fluid and to derive the modified Reynolds’s equation for non-Newtonian fluid under various operating conditions to obtain the optimum bearing parameters. Design/methodology/approach Based upon the MHD theory and Stokes theory for couple stress fluid, the governing equations relevant to the problem under consideration are derived. This paper analyzes the effect on porous exponential slider bearings with an electrically conducting fluid in the presence of a transverse magnetic field. Semi-numerical solutions are obtained and discussed. Findings It is found that there is an increase in the load carrying capacity, frictional force and decrease in the co-efficient of friction in porous bearings due to the presence of magnetic effects with couple stress fluid. Originality/value This study is relatively original and gives the MHD effect on porous exponential slider bearings lubricated with couple stress fluid. The author believes that the paper presents these results for the first time.

scholarly journals Combined effect of conduction and viscous dissipation on magnetohydrodynamic free convection flow along a vertical flat plate

1970 ◽  
Vol 4 (2) ◽  
pp. 87-98 ◽  
Author(s):  
Abdullah Al-Mamun ◽  
Nur Hosain Md Ariful Azim ◽  
Md. Abdul Maleque
Keyword(s):  
Viscous Dissipation ◽  
Numerical Solutions ◽  
Transverse Magnetic ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Temperature Distributions ◽  
Two Dimensional Flow ◽  
Marine Engineering ◽  
Energy Equations ◽  
Conjugate Conduction

This paper concerns the effects of conduction and viscous dissipation on natural convection flow of an incompressible, viscous and electrically conducting fluid in the presence of transverse magnetic field. Numerical solutions for the governing momentum and energy equations are given. A discussion has been provided for the effects of magnetic parameter, Prandtl number, conjugate conduction parameter and viscous dissipation parameter on two-dimensional flow. Results for the details of the velocity, temperature distributions as well as the skin friction and the rate of heat transfer are shown graphically. Also the numerical values of the surface temperature distributions are presented in tabular form.DOI: http://dx.doi.org/10.3329/jname.v4i2.992 Journal of Naval Architecture and Marine Engineering Vol.4(2) 2007 p.87-98

scholarly journals Effect of radiation and porosity parameter on magnetohydrodynamic flow due to stretching sheet in porous media

2011 ◽  
Vol 15 (2) ◽  
pp. 517-526 ◽  
Author(s):  
Phool Singh ◽  
Tomer Singh ◽  
Sandeep Kumar ◽  
Deepa Sinha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Stretching Sheet ◽  
Transverse Magnetic ◽  
Stream Velocity ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Porosity Parameter ◽  
Volumetric Rate ◽  
Two Dimensional Flow

An analysis is made for the steady two-dimensional flow of a viscous incompressible electrically conducting fluid in the vicinity of a stagnation point on a stretching sheet. Fluid is considered in a porous medium under the influence of (i)transverse magnetic field, (ii)volumetric rate of heat generation/absorption in the presence of radiation effect. Rosseland approximation is used to model the radiative heat transfer. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables. In the present reported work the effect of porosity parameter, radiation parameter, magnetic field parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Variation of above discussed parameters with the ratio of free stream velocity parameter to stretching sheet parameter have been graphically represented.

scholarly journals Numerical Solution of Boundary Layer MHD Flow with Viscous Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
S. R. Mishra ◽  
S. Jena
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Graphical Representation ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Shrinking Sheet ◽  
Shooting Technique ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Runge Kutta Method

The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.

scholarly journals Analytic Treatment for Electrical MHD Non-Newtonian Fluid Flow over a Stretching Sheet through a Porous Medium

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Gossaye Aliy Adem
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Electric Field ◽  
Chemical Reaction ◽  
Internal Heat ◽  
Porous Matrix ◽  
Transverse Magnetic ◽  
Closed Form Solutions ◽  
Electrically Conducting ◽  
Boundary Layer Equations

In this study, an attempt has been made to investigate the mass and heat transfer effects in a BLF through a porous medium of an electrically conducting viscoelastic fluid subject to a transverse magnetic field in the existence of an external electric field, heat source/sink, and chemical reaction. It has been considered the effects of the electric field, viscous and Joule dissipations, radiation, and internal heat generation/absorption. Closed-form solutions for the boundary layer equations of viscoelastic, second-grade, and Walters’ B ′ fluid models are considered. The method of the solution includes similarity transformation. The converted equations of thermal and mass transport are calculated using the optimal homotopy asymptotic method (OHAM). The solutions of the temperature field for both prescribed surface temperature (PST) and prescribed surface heat flux (PHF) are found. It is vital to remark that the interaction of the magnetic field is found to be counterproductive in enhancing velocity and concentration distribution, whereas the presence of chemical reaction, as well as a porous matrix with moderate values of the magnetic parameter, reduces the temperature and concentration fields at all points of the flow domain.

scholarly journals On the existence of solution of the Greenspan-Carrier equation

1973 ◽  
Vol 15 (3) ◽  
pp. 373-384
Author(s):  
H. P. Heinig ◽  
K. Kuen Tam
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Existence Of Solution ◽  
Conducting Fluid ◽  
Rigid Plate ◽  
Different Boundary Conditions ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Electrically Conducting Fluid

We are concerned with the flow of a viscous incompressible electrically conducting fluid of constant properties past a semi-infinite rigid plate. The governing boundary layer equations were derived by Greenspan and Carrier [2] in 1959. Numerical solutions of these equations subject to different boundary conditions have been considered by Stewartson and Wilson [5], Wilson [8], and recently by Bramley [1].

Collapse by ponding of pneumatic elastic spherical caps under distributed loads

1983 ◽  
Vol 10 (4) ◽  
pp. 740-747 ◽  
Author(s):  
G. Ahmadi ◽  
P. G. Glockner
Keyword(s):  
Numerical Solutions ◽  
Graphical Form ◽  
Nonuniform Load ◽  
Spherical Caps ◽  
Load Intensity ◽  
Range Of Values ◽  
Central Load

The problem of collapse by ponding of air-supported elastic spherical caps subjected to a distributed axisymmetric central load is investigated. Cases of uniform and nonuniform load intensity are considered and the expressions for the critical intensities for the onset of collapse are derived. Numerical solutions are obtained for a range of values of the parameters and the results are presented in graphical form. The interpretation of the results in terms of some initial depressions filled with a ponding fluid is also discussed.

On Spectral Relaxation Approach to Radiating Powell-Eyring Fluid Flow over a Stretching Disk with Newtonian Heating

2018 ◽  
Vol 387 ◽  
pp. 461-473 ◽  
Author(s):  
K. Gangadhar ◽  
D. Vijaya Kumar ◽  
S. Mohammed Ibrahim ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Newtonian Heating ◽  
Nonlinear Boundary Value Problems ◽  
Local Skin ◽  
Boundary Layer Equations ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

In this study we use a new spectral relaxation method to investigate an axisymmetric law laminar boundary layer flow of a viscous incompressible non-Newtonian Eyring-Powell fluid and heat transfer over a heated disk with thermal radiation and Newtonian heating. The transformed boundary layer equations are solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significantly improved by using method in conjunction with the successive over-relaxation method. It is observed that CPU time is reduced in SOR method compare with SRM method.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

Sign in / Sign up

Export Citation Format

Share Document