Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet

Rajesh Sharma, Anuar Mohd Ishak, Ioan Pop

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

The MHD stagnation point flow of a viscous, incompressible and electrically conducting fluid over a stretching/shrinking permeable semi-infinite flat plate is numerically studied. The governing partial differential equations are transformed into an ordinary differential equation using a similarity transformation, before being solved numerically. Numerical solutions of this equation is obtained using bvp4c package in Matlab software. Dual (first and second or upper and lower branch) solutions are observed in a certain range of the pressure gradient and the stretching/shrinking parameter. A stability analysis is performed to show that the first (upper branch) solution is always stable, while the other (lower branch) solution is always unstable. It is observed that the range of the stretching/shrinking parameter (for which the physically realizable solution exists) increases with an increase of suction, pressure gradient as well as the magnetic parameter. It is also observed that with an increase in the pressure gradient, the first (upper branch) solution becomes more stable while unstable solution becomes more unstable. The variations of velocity inside the boundary layer for some values of the governing parameters, namely, the pressure gradient and the magnetic parameters are presented graphically. Comparison with published results of smallest eigenvalues for several values of suction and stretching/shrinking parameters are presented and it is found to be in excellent agreement.

Original languageEnglish
Pages (from-to)94-98
Number of pages5
JournalComputers and Fluids
Volume102
DOIs
Publication statusPublished - 10 Oct 2014

Fingerprint

Magnetohydrodynamics
Stretching
Pressure gradient
Ordinary differential equations
Partial differential equations
Boundary layers
Fluids

Keywords

  • Dual solutions
  • Numerical solution
  • Permeable flat plate
  • Stability analysis

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)

Cite this

Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet. / Sharma, Rajesh; Mohd Ishak, Anuar; Pop, Ioan.

In: Computers and Fluids, Vol. 102, 10.10.2014, p. 94-98.

Research output: Contribution to journalArticle

@article{296a3d6916a94cdaa7694cbc8aa2ec79,
title = "Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet",
abstract = "The MHD stagnation point flow of a viscous, incompressible and electrically conducting fluid over a stretching/shrinking permeable semi-infinite flat plate is numerically studied. The governing partial differential equations are transformed into an ordinary differential equation using a similarity transformation, before being solved numerically. Numerical solutions of this equation is obtained using bvp4c package in Matlab software. Dual (first and second or upper and lower branch) solutions are observed in a certain range of the pressure gradient and the stretching/shrinking parameter. A stability analysis is performed to show that the first (upper branch) solution is always stable, while the other (lower branch) solution is always unstable. It is observed that the range of the stretching/shrinking parameter (for which the physically realizable solution exists) increases with an increase of suction, pressure gradient as well as the magnetic parameter. It is also observed that with an increase in the pressure gradient, the first (upper branch) solution becomes more stable while unstable solution becomes more unstable. The variations of velocity inside the boundary layer for some values of the governing parameters, namely, the pressure gradient and the magnetic parameters are presented graphically. Comparison with published results of smallest eigenvalues for several values of suction and stretching/shrinking parameters are presented and it is found to be in excellent agreement.",
keywords = "Dual solutions, Numerical solution, Permeable flat plate, Stability analysis",
author = "Rajesh Sharma and {Mohd Ishak}, Anuar and Ioan Pop",
year = "2014",
month = "10",
day = "10",
doi = "10.1016/j.compfluid.2014.06.022",
language = "English",
volume = "102",
pages = "94--98",
journal = "Computers and Fluids",
issn = "0045-7930",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Stability analysis of magnetohydrodynamic stagnation-point flow toward a stretching/shrinking sheet

AU - Sharma, Rajesh

AU - Mohd Ishak, Anuar

AU - Pop, Ioan

PY - 2014/10/10

Y1 - 2014/10/10

N2 - The MHD stagnation point flow of a viscous, incompressible and electrically conducting fluid over a stretching/shrinking permeable semi-infinite flat plate is numerically studied. The governing partial differential equations are transformed into an ordinary differential equation using a similarity transformation, before being solved numerically. Numerical solutions of this equation is obtained using bvp4c package in Matlab software. Dual (first and second or upper and lower branch) solutions are observed in a certain range of the pressure gradient and the stretching/shrinking parameter. A stability analysis is performed to show that the first (upper branch) solution is always stable, while the other (lower branch) solution is always unstable. It is observed that the range of the stretching/shrinking parameter (for which the physically realizable solution exists) increases with an increase of suction, pressure gradient as well as the magnetic parameter. It is also observed that with an increase in the pressure gradient, the first (upper branch) solution becomes more stable while unstable solution becomes more unstable. The variations of velocity inside the boundary layer for some values of the governing parameters, namely, the pressure gradient and the magnetic parameters are presented graphically. Comparison with published results of smallest eigenvalues for several values of suction and stretching/shrinking parameters are presented and it is found to be in excellent agreement.

AB - The MHD stagnation point flow of a viscous, incompressible and electrically conducting fluid over a stretching/shrinking permeable semi-infinite flat plate is numerically studied. The governing partial differential equations are transformed into an ordinary differential equation using a similarity transformation, before being solved numerically. Numerical solutions of this equation is obtained using bvp4c package in Matlab software. Dual (first and second or upper and lower branch) solutions are observed in a certain range of the pressure gradient and the stretching/shrinking parameter. A stability analysis is performed to show that the first (upper branch) solution is always stable, while the other (lower branch) solution is always unstable. It is observed that the range of the stretching/shrinking parameter (for which the physically realizable solution exists) increases with an increase of suction, pressure gradient as well as the magnetic parameter. It is also observed that with an increase in the pressure gradient, the first (upper branch) solution becomes more stable while unstable solution becomes more unstable. The variations of velocity inside the boundary layer for some values of the governing parameters, namely, the pressure gradient and the magnetic parameters are presented graphically. Comparison with published results of smallest eigenvalues for several values of suction and stretching/shrinking parameters are presented and it is found to be in excellent agreement.

KW - Dual solutions

KW - Numerical solution

KW - Permeable flat plate

KW - Stability analysis

UR - http://www.scopus.com/inward/record.url?scp=84904515098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904515098&partnerID=8YFLogxK

U2 - 10.1016/j.compfluid.2014.06.022

DO - 10.1016/j.compfluid.2014.06.022

M3 - Article

AN - SCOPUS:84904515098

VL - 102

SP - 94

EP - 98

JO - Computers and Fluids

JF - Computers and Fluids

SN - 0045-7930

ER -