scholarly journals MHD mixed convection boundary layer stagnation-point flow on a vertical surface with induced magnetic field

2019 ◽  
Vol 30 (11) ◽  
pp. 4697-4710 ◽  
Author(s):  
Fadzilah Md Ali ◽  
Kohilavani Naganthran ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Stability Analysis ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Convection Boundary Layer ◽  
Induced Magnetic Field ◽  
Content Type ◽  
The Stability

Purpose This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a vertical flat plate. The effect of induced magnetic field is also considered. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings Dual solutions are found to exist for a certain range of the buoyancy parameter for both the assisting and opposing flows. 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 many metallurgical processes, namely, drawing, annealing and tinning of copper wires. The results obtained are very useful for researchers to determine which solution is physically stable, whereby mathematically more than one solution exists for the skin friction coefficient and the heat transfer characteristics. Originality/value The present results of the stability analysis are original and new for the problem of MHD mixed convection stagnation-point flow of viscous conducting fluid over a vertical flat plate, with the effect of induced magnetic field.

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 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.

scholarly journals Mixed Convection Boundary Layers with Prescribed Temperature in the Unsteady Stagnation Point Flow toward a Stretching Vertical Sheet

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Tze Jin Wong ◽  
Melini Suali
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Flow Characteristics ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Convection Boundary Layer ◽  
Shooting Technique ◽  
Boundary Layer Equations ◽  
Convection Boundary

Mixed convection boundary layer caused by time-dependent velocity and the surface temperature in the two-dimensional unsteady stagnation point flow of an in-compressible viscous fluid over a stretching vertical sheet is studied. The transformed nonlinear boundary layer equations are solved numerically using the shooting technique in cooperation with Runge-Kutta-Fehlberg (RKF) method. Different step sizes are used ranging from 0.0001 to 1. Numerical results for the skin friction coefficient and local Nusselt number are presented for both assisting and opposing flows. It is found that the dual solutions exist for the opposing flow, whereas the solution is unique for the assisting flow. Important features of the flow characteristics are displayed graphically. Comparison with the existing results for the steady case show an excellent agreement.

scholarly journals MHD Mixed Convection Boundary Layer Flow Toward a Stagnation Point on a Vertical Surface With Induced Magnetic Field

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
F. M. Ali ◽  
R. Nazar ◽  
N. M. Arifin ◽  
I. Pop
Keyword(s):  
Magnetic Field ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Vertical Surface ◽  
Dual Solutions ◽  
Convection Boundary Layer ◽  
Induced Magnetic Field ◽  
Electrically Conducting ◽  
Implicit Finite Difference Scheme ◽  
Layer Flow

In this paper, the steady magnetohydrodynamic (MHD) mixed convection stagnation point flow of an incompressible, viscous, and electrically conducting fluid over a vertical flat plate is investigated. The effect of induced magnetic field is taken into account. Numerical results are obtained using an implicit finite-difference scheme. Both assisting and opposing flows are considered. The results for skin friction, heat transfer, and induced magnetic field coefficients are obtained and discussed for various parameters. The velocity, temperature, and induced magnetic field profiles are also presented. For the case of the opposing flow, it is found that dual solutions exist for a certain range of the buoyancy parameter. Dual solutions are also obtained for the assisting flow.

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