Multiple solutions of two-dimensional and three-dimensional flows induced by a stretching flat surface

P. D. Weidman, Anuar Mohd Ishak

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

New solutions of flow induced by a biorthogonally stretching surface are reported. The flexible membrane has linear stretching rate a along the x-axis and b along the y-axis. A similarity reduction of the Navier-Stokes equations yields a coupled pair of ordinary differential equations governed the single parameter α=b/a. Dual solutions are found in the region αt<α≤1, where αt=-0.2514. One of the two components of the dual solutions exhibits algebraic decay in the far field. It appears that no self-similar solutions exist for α<αt. It is also shown that the exact solution for flow induced by a unilaterally stretching sheet due to Crane has dual solutions with algebraic decay in the far field.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume25
Issue number1-3
DOIs
Publication statusPublished - 1 Aug 2015

Fingerprint

Dual Solutions
Three-dimensional Flow
Multiple Solutions
Stretching
Far Field
Decay
Stretching Surface
Similarity Reduction
Stretching Sheet
Self-similar Solutions
Cranes
Ordinary differential equations
Navier Stokes equations
Navier-Stokes Equations
Ordinary differential equation
Membrane
Exact Solution
Membranes

Keywords

  • Nonuniqueness
  • Similarity solutions
  • Stretching plates

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

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