Momentum and Heat Transfer in MHD Stagnation-Point Flow Over a Shrinking Sheet

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
T. Ray Mahapatra ◽  
S. K. Nandy ◽  
A. S. Gupta
Keyword(s):  
Magnetic Field ◽  
Stagnation Point ◽  
Magnetic Parameter ◽  
Reverse Flow ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Electrically Conducting ◽  
Momentum And Heat Transfer ◽  
The Magnetic Field ◽  
Component Parallel

The steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an electrically conducting incompressible viscous fluid toward a shrinking sheet is investigated. The sheet is shrunk in its own plane with a velocity proportional to the distance from the stagnation-point and a uniform magnetic field is applied normal to the sheet. Velocity component parallel to the sheet is found to increase with an increase in the magnetic field parameter M. A region of reverse flow occurs near the surface of the shrinking sheet. It is shown that as M increases, the tendency of this flow reversal decreases. It is also observed that the nonalignment of the stagnation-point flow and the shrinking sheet considerably complicates the flow structure. The effect of the magnetic parameter M on the streamlines is shown for both aligned and nonaligned cases. The temperature distribution in the boundary layer is found when the surface is held at constant temperature. The analysis reveals that the temperature at a point increases with increasing M in a certain neighborhood of the surface but beyond this, the temperature decreases with increasing M. For fixed M, the surface heat flux decreases with increase in the shrinking rate.

Effects of Second-Order Slip and Magnetic Field on Mixed Convection Stagnation-Point Flow of a Maxwellian Fluid: Multiple Solutions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
M. M. Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Reverse Flow ◽  
Second Order ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Variable Surface

In this paper, we investigate the effects of second-order slip and magnetic field on the nonlinear mixed convection stagnation-point flow toward a vertical permeable stretching/shrinking sheet in an upper convected Maxwell (UCM) fluid with variable surface temperature. Numerical results are obtained using the bvp4c function from matlab for the reduced skin-friction coefficient, the rate of heat transfer, the velocity, and the temperature profiles. The results indicate that multiple (dual) solutions exist for a buoyancy opposing flow for certain values of the parameter space irrespective to the types of surfaces whether it is stretched or shrinked. It is found that an applied magnetic field compensates the suction velocity for the existence of the dual solutions. Depending on the parametric conditions; elastic parameter, magnetic field parameter, first- and second-order slip parameters significantly controls the flow and heat transfer characteristics. The illustrated streamlines show that for upper branch solutions, the effects of stretching and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag away from the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions when the mixed convection effect is less significant.

scholarly journals Interaction of Magnetic Field and Nonlinear Convection in the Stagnation Point Flow over a Shrinking Sheet

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Rakesh Kumar ◽  
Shilpa Sood
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Nonlinear Convection ◽  
Keller Box Method ◽  
Reduced Equations ◽  
Dimensional Boundary ◽  
The Magnetic Field

The steady two-dimensional boundary layer stagnation point flow due to a shrinking sheet is analyzed. The combined effects of magnetic field and nonlinear convection are taken into account. The governing equations for the flow are modeled and then simplified using the similarity transformation and boundary layer approach. The numerical solution of the reduced equations is obtained by the second-order finite difference scheme also known as Keller box method. The influence of the pertinent parameters of the problem on velocity and temperature profiles, skin friction, and sheet temperature gradient are presented through the graphs and tables and discussed. The magnetic field and nonlinear convection parameters significantly enhance the solution range.

scholarly journals MHD stagnation point flow of micro nanofluid towards a shrinking sheet with convective and zero mass flux conditions

2017 ◽  
Vol 65 (2) ◽  
pp. 155-162 ◽  
Author(s):  
A. Rauf ◽  
S. A. Shehzad ◽  
T. Hayat ◽  
M. A. Meraj ◽  
A. Alsaedi
Keyword(s):  
Stagnation Point ◽  
Mass Flux ◽  
Numerical Technique ◽  
Convective Boundary Condition ◽  
Momentum Equation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Convective Boundary ◽  
Electrically Conducting ◽  
Zero Mass

AbstractIn this article the stagnation point flow of electrically conducting micro nanofluid towards a shrinking sheet, considering a chemical reaction of first order is investigated. Involvement of magnetic field occurs in the momentum equation, whereas the energy and concentrations equations incorporated the influence of thermophoresis and Brownian motion. Convective boundary condition on temperature and zero mass flux condition on concentration are implemented. Partial differential equations are converted into the ordinary ones using suitable variables. The numerical technique is utilized to discuss the results for velocity, microrotation, temperature, and concentration fields.

scholarly journals MHD stagnation-point flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid with induced magnetic field

2019 ◽  
Vol 30 (3) ◽  
pp. 1345-1364 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Norihan Md Arifin ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Induced Magnetic Field ◽  
Content Type

Purpose The purpose of this paper is to investigate the steady magnetohydrodynamics (MHD) boundary layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking sheet with the effect of induced magnetic field. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via the similarity transformations before they are solved numerically using the “bvp4c” function in MATLAB. Findings It is found that there exist non-unique solutions, namely, dual solutions for a certain range of the stretching/shrinking parameters. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in the heat transfer field such as electronic cooling, engine cooling, generator cooling, welding, nuclear system cooling, lubrication, thermal storage, solar heating, cooling and heating in buildings, biomedical, drug reduction, heat pipe, space aircrafts and ships with better efficiency than that of nanofluids applicability. The results obtained are very useful for researchers to determine which solution is physically stable, whereby, mathematically more than one solution exist. Originality/value The present results are new and original for the problem of MHD stagnation-point flow over a stretching/shrinking sheet in a hybrid nanofluid, with the effect of induced magnetic field.

scholarly journals CASSON FLUID OF A STAGNATION-POINT FLOW (SPF) TOWARDS A VERTICAL SHRINKING/STRETCHING SHEET

2021 ◽  
Vol 5 (1) ◽  
pp. 16-26
Author(s):  
Winifred N. Mutuku ◽  
Anselm O. Oyem
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Fluid Model ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Integration Scheme ◽  
Shrinking Sheet ◽  
Electrically Conducting ◽  
Casson Fluid Model ◽  
Fluid Behaviour

This study presents a convectively heated hydromagnetic Stagnation-Point Flow (SPF) of an electrically conducting Casson fluid towards a vertically stretching/shrinking sheet. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour and using similarity variables, the governing partial differential equations are transformed into coupled nonlinear ordinary differential equations. The dimensionless nonlinear equations are solved numerically by Runge-Kutta Fehlberg integration scheme with shooting technique. The effects of the thermophysical parameters on velocity and temperature profiles are presented graphically and discussed quantitatively. The result shows that the flow field velocity decreases with increase in magnetic field parameter and Casson fluid parameter .

scholarly journals MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 132 ◽  
Author(s):  
Muhammad Sadiq
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Stagnation Point Flow ◽  
Three Dimensional Flow ◽  
Moving Plate ◽  
Physical Quantities ◽  
The Magnetic Field ◽  
Momentum Boundary Layer

In this article, an axisymmetric three-dimensional stagnation point flow of a nanofluid on a moving plate with different slip constants in two orthogonal directions in the presence of uniform magnetic field has been considered. The magnetic field is considered along the axis of the stagnation point flow. The governing Naiver–Stokes equation, along with the equations of nanofluid for three-dimensional flow, are modified using similarity transform, and reduced nonlinear coupled ordinary differential equations are solved numerically. It is observed that magnetic field M and slip parameter λ 1 increase the velocity and decrease the boundary layer thickness near the stagnation point. Also, a thermal boundary layer is achieved earlier than the momentum boundary layer, with the increase in thermophoresis parameter N t and Brownian motion parameter N b . Important physical quantities, such as skin friction, and Nusselt and Sherwood numbers, are also computed and discussed through graphs and tables.

scholarly journals Magnetohydrodynamics Stagnation-Point Flow of a Nanofluid Past a Stretching/Shrinking Sheet with Induced Magnetic Field: A Revised Model

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1078 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Governing Equations ◽  
Induced Magnetic Field ◽  
The Stability ◽  
Stretching Or Shrinking Sheet

The revised Buongiorno’s nanofluid model with the effect of induced magnetic field on steady magnetohydrodynamics (MHD) stagnation-point flow of nanofluid over a stretching or shrinking sheet is investigated. The effects of zero mass flux and suction are taken into account. A similarity transformation with symmetry variables are introduced in order to alter from the governing nonlinear partial differential equations into a nonlinear ordinary differential equations. These governing equations are numerically solved using the bvp4c function in Matlab solver, a very adequate finite difference method. The influences of considered parameters ( P r , M, χ , L e , N b , N t , S, and λ ) on velocity, induced magnetic, temperature, and concentration profiles together with the reduced skin friction and heat transfer rate are discussed. Results from these criterion exposed the existence of dual solutions when magnetic field and suction are applied for a specific range of λ . The stability of the solutions obtained is carried out by performing a stability analysis.

Erklärung stellarer und planetarer Magnetfelder durch einen turbulenzbedingten Dynamomechanismus

1966 ◽  
Vol 21 (8) ◽  
pp. 1285-1296 ◽  
Author(s):  
M. Steenbeck ◽  
F. Krause
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Magnetic Fields ◽  
Cross Product ◽  
Skin Depth ◽  
Electrically Conducting ◽  
Magnetic Stars ◽  
The Magnetic Field ◽  
Component Parallel ◽  
Good Agreement

In a foregoing paper 1 the effects of a turbulent motion on magnetic fields were investigated. Especially turbulence was treated under the influence of CORIOLiS-forces and gradients of density and/or turbulence intensity. It was shown that on these conditions the average cross-product of velocity and magnetic field has a non-vanishing component parallel to the average magnetic field. Here we give the consequences of this effect for rotating, electrically conducting spheres.At first a sphere rotating with constant angular velocity is investigated. The quadratic effect provides for dynamo maintainance of the magnetic fields. A field of dipol-type has the weakest condition for maintainance. Applications to the magnetic field of the earth show a good agreement with the conceptions of the physical state of the earth’s core.For a second model differential rotation is included. We have also dynamo maintainance. Since we have to assume that generally the angular velocity is a function decreasing with the distance from the centre of the sphere, the calculations show that we have a preferred self-excited build-up of a quadrupol-type field. This model may be applicable to magnetic stars.Finally we look for dynamo maintainance of alternating fields. We consider the skin-depth to be small compared with the radius of the sphere, then we have plane geometry. The existence of periodical solutions is proved. Applications to the general magnetic field of the sun, which has a period of 22 years, are discussed.

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