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On similarity solutions for boundary layer flows with prescribed heat flux
Author(s) -
Brighi Bernard,
Hoernel JeanDavid
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.578
Subject(s) - mathematics , uniqueness , similarity (geometry) , boundary layer , plane (geometry) , similarity solution , boundary (topology) , mathematical analysis , flux (metallurgy) , boundary value problem , heat flux , geometry , heat transfer , thermodynamics , physics , chemistry , computer science , artificial intelligence , image (mathematics) , organic chemistry
This paper is concerned with existence, uniqueness and behaviour of the solutions of the autonomous third‐order non‐linear differential equation f ‴+( m +2) f f ″−(2 m +1) f ′ 2 =0 on ℝ + with the boundary conditions f (0)=− γ , f ′(∞)=0 and f ″(0)=−1. This problem arises when looking for similarity solutions for boundary layer flows with prescribed heat flux. To study solutions we use some direct approach as well as blowing‐up co‐ordinates to obtain a plane dynamical system. Copyright © 2004 John Wiley & Sons, Ltd.