Similarity solutions for boundary layer flows with prescribed surface temperature

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8 Citations (Scopus)

Abstract

We are concerned with the third-order nonlinear equation f + [(m + 1) / 2] f f - m f ′2 = 0 on (0, ∞), satisfying the boundary conditions f (0) = a ∈ R, f (0) = 1 and f (∞) = 0. The problem arises in the study of similarity solutions in two physically different contexts of fluid mechanics: free convection in a porous medium and flow adjacent to a stretching wall. We shall address two open questions: the first one is the uniqueness of bounded solutions for m ∈ (- 1 / 3, 0) and a < 0, and the second one is the structure of solutions for m ∈ (- 1 / 2, - 1 / 3) and a ≤ 0. Our results complement earlier results in the literature.

Original languageEnglish
Pages (from-to)67-73
Number of pages7
JournalApplied Mathematics Letters
Volume21
Issue number1
DOIs
Publication statusPublished - 2008 Jan 1

Keywords

  • Boundary value problem
  • Initial value problem
  • Phase plane analysis
  • Similarity solution
  • Third-order differential equation

ASJC Scopus subject areas

  • Applied Mathematics

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