MHD stagnation-point flow towards a shrinking sheet

Y. Y. Lok, Anuar Mohd Ishak, I. Pop

Research output: Contribution to journalArticle

93 Citations (Scopus)

Abstract

Purpose The purpose of this paper is to theoretically investigate the steady two-dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied. Design/methodology/approach A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller-box method. Findings The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non-aligned and a reverse flow is formed near the surface due to shrinking effect. Practical implications The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface. Originality/value The present results are original and new for the MHD flow near the stagnation-point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.

Original languageEnglish
Pages (from-to)61-72
Number of pages12
JournalInternational Journal of Numerical Methods for Heat and Fluid Flow
Volume21
Issue number1
DOIs
Publication statusPublished - 2011

Fingerprint

Stagnation Point Flow
Magnetohydrodynamic Flow
Shrinking
Magnetohydrodynamics
Stretching
Stagnation Point
Polymers
Magnetic Field
Magnetic fields
Stretching Surface
Dual Solutions
Manufacturing Industries
Boundary layer flow
Similarity Transformation
Boundary Layer Flow
Extrusion
Chemical engineering
Metallurgy
Nonlinear Ordinary Differential Equations
Filament

Keywords

  • Boundary layers
  • Flow
  • Magnetohydrodynamics
  • Sheets

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Computer Science Applications
  • Applied Mathematics

Cite this

MHD stagnation-point flow towards a shrinking sheet. / Lok, Y. Y.; Mohd Ishak, Anuar; Pop, I.

In: International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 21, No. 1, 2011, p. 61-72.

Research output: Contribution to journalArticle

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