A note on similarity solutions for boundary layer flows with prescribed heat flux

Je-Chiang Tsai, Ching An Wang

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We study the third-order nonlinear equation: f″′ + (m + 2) f f″ - (2m + 1) f′2 = 0 on (0, ∞), subject to the boundary conditions f(0) = -γ ∈ ℝ, f′(∞) = 0 f″(0) = -1. The problem arises in the study of similarity solutions for boundary layer flows with prescribed heat flux. We will address the following two open questions which were proposed by Brighi and Hoernel (Math. Methods Appl. Sci. 2005; 28: 479-503): The first one is the uniqueness of bounded solutions for m ∈ (-1, -1/2) and γ>0, and the second one is the structure of solutions for m ∈ (-1, -1/2) and γ>0.

Original languageEnglish
Pages (from-to)1453-1466
Number of pages14
JournalMathematical Methods in the Applied Sciences
Volume30
Issue number12
DOIs
Publication statusPublished - 2007 Aug 1

Keywords

  • Boundary layer theory
  • Initial value problem
  • Nonlinear boundary value problems
  • Phase plane analysis
  • Similarity solution
  • Third-order differential equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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