Effect of Induced Magnetic Field on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer on a Stretching Sheet

In this paper, the steady magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous electrically conducting fluid over a stretching sheet has been investigated. Velocity and thermal slip conditions have been incorporated in the study. The effects of induced magnetic field and thermal radiation have also been duly taken into account. The nonlinear partial differential equations arising out of the mathematical analysis of the problem are transformed into a system of nonlinear ordinary differential equations by using similarity transformation and boundary layer approximation. These equations are solved by developing an appropriate numerical method. Considering an illustrative example, numerical results are obtained for velocity, temperature, skin friction, and Nusselt number by considering a chosen set of values of various parameters involved in the study. The results are presented graphically/in tabular form.

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-06-2019-0500 ◽

2019 ◽

Vol 30 (3) ◽

pp. 1345-1364 ◽

Cited By ~ 3

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.

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

Symmetry ◽

10.3390/sym11091078 ◽

2019 ◽

Vol 11 (9) ◽

pp. 1078 ◽

Cited By ~ 1

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.

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MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

Applied Mathematics and Mechanics ◽

10.1007/s10483-011-1426-6 ◽

2011 ◽

Vol 32 (4) ◽

pp. 409-418 ◽

Cited By ~ 55

Author(s):

F. M. Ali ◽

R. Nazar ◽

N. M. Arifin ◽

I. Pop

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Stagnation Point ◽

Stretching Sheet ◽

Stagnation Point Flow ◽

Induced Magnetic Field ◽

Flow And Heat Transfer

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The Effect of Induced Magnetic Field and Convective Boundary Condition on MHD Stagnation Point Flow and Heat Transfer of Nanofluid Past a Stretching Sheet

IEEE Transactions on Nanotechnology ◽

10.1109/tnano.2014.2375912 ◽

2015 ◽

Vol 14 (1) ◽

pp. 178-186 ◽

Cited By ~ 11

Author(s):

Wubshet Ibrahim

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Boundary Condition ◽

Stagnation Point ◽

Stretching Sheet ◽

Convective Boundary Condition ◽

Stagnation Point Flow ◽

Induced Magnetic Field ◽

Convective Boundary ◽

Flow And Heat Transfer

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The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

Propulsion and Power Research ◽

10.1016/j.jppr.2016.05.003 ◽

2016 ◽

Vol 5 (2) ◽

pp. 164-175 ◽

Cited By ~ 26

Author(s):

Wubshet Ibrahim

Keyword(s):

Magnetic Field ◽

Heat Transfer ◽

Boundary Condition ◽

Stagnation Point ◽

Stretching Sheet ◽

Maxwell Fluid ◽

Convective Boundary Condition ◽

Induced Magnetic Field ◽

Convective Boundary ◽

Flow And Heat Transfer

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Stagnation-Point Flow over an Exponentially Shrinking/Stretching Sheet

Zeitschrift für Naturforschung A ◽

10.5560/zna.2011-0037 ◽

2011 ◽

Vol 66 (12) ◽

pp. 705-711 ◽

Cited By ~ 2

Author(s):

Sin Wei Wong ◽

Abu Omar Awang ◽

Anuar Ishak

Keyword(s):

Differential Equations ◽

Stagnation Point ◽

Stretching Sheet ◽

Free Stream ◽

Stagnation Point Flow ◽

Stream Velocity ◽

Heat Transfer Characteristics ◽

Keller Box Method ◽

Flow And Heat Transfer ◽

Box Method

The steady two-dimensional stagnation-point flow of an incompressible viscous fluid over an exponentially shrinking/stretching sheet is studied. The shrinking/stretching velocity, the free stream velocity, and the surface temperature are assumed to vary in a power-law form with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations before being solved numerically by a finite difference scheme known as the Keller-box method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique.

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Unsteady electromagnetic radiative nanofluid stagnation-point flow from a stretching sheet with chemically reactive nanoparticles, Stefan blowing effect and entropy generation

Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanomaterials Nanoengineering and Nanosystems ◽

10.1177/2397791418782030 ◽

2018 ◽

Vol 232 (2-3) ◽

pp. 69-82 ◽

Cited By ~ 5

Author(s):

Puneet Rana ◽

Nisha Shukla ◽

O Anwar Bég ◽

A Kadir ◽

Bani Singh

Keyword(s):

Magnetic Field ◽

Stagnation Point ◽

Entropy Generation ◽

Stretching Sheet ◽

Nonlinear Partial Differential Equations ◽

Stagnation Point Flow ◽

Dimensional System ◽

Electrical Field ◽

Electric Parameter ◽

Entropy Generation Number

This article investigates the combined influence of nonlinear radiation, Stefan blowing and chemical reactions on unsteady electro-magneto-hydrodynamic stagnation-point flow of a nanofluid from a horizontal stretching sheet. Both electrical and magnetic body forces are considered. In addition, the effects of velocity slip, thermal slip and mass slip are considered at the boundaries. An analytical method named as homotopy analysis method is applied to solve the non-dimensional system of nonlinear partial differential equations which are obtained by applying similarity transformations on governing equations. The effects of emerging parameters such as Stefan blowing parameter, electric parameter and magnetic parameter on the important physical quantities are presented graphically. In addition, an entropy generation analysis is provided in this article for thermal optimization. The flow is observed to be accelerated both with increasing magnetic field and electrical field. Entropy generation number is markedly enhanced with greater magnetic field, electrical field and Reynolds number, whereas it is reduced with increasing chemical reaction parameter.

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