Analysis of stagnation point flow toward a stretching sheet

Joseph Paullet, Patrick Weidman

Research output: Contribution to journalArticle

65 Scopus citations

Abstract

There has been much recent interest in the stagnation point flow of a fluid toward a stretching sheet. Investigations that may include oblique stagnation flow and heat transfer to a horizontal plate all involve the same boundary value problem (BVP):f + ff - (f)2 + b2 = 0,f (0) = 0, f (0) = 1, f (∞) = b .Here b is the ratio of the stagnation flow strain rate to the stretch rate of the sheet. Through numerical analysis of the problem, several authors have conjectured the existence of a solution for all values of b > 0. In this note we present numerical evidence that a second solution exists for 0 < b < bc ≈ 0.16906. Further we present a mathematical proof that for all b > 0 there exists a monotonic solution to the BVP and if b > 1, this solution is unique. If b < 1 it can be shown that any further solutions cannot be monotonic and the second solution found here numerically is non-monotonic. The asymptotic behavior of solutions near b = 0 and 1 is also presented. Finally, a stability analysis is performed to show that solutions on the upper branch of the dual solutions are linearly stable, while those on the lower branch are linearly unstable.

Original languageEnglish (US)
Pages (from-to)1084-1091
Number of pages8
JournalInternational Journal of Non-Linear Mechanics
Volume42
Issue number9
DOIs
StatePublished - Nov 1 2007

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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