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

✍ Scribed by Je-Chiang Tsai; Ching-An Wang

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
261 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We study the third‐order nonlinear equation: fβ€²β€²β€² + (m + 2)ffβ€²β€² βˆ’ (2__m__ + 1)fβ€²^2^ = 0 on (0, ∞), subject to the boundary conditions f(0) = βˆ’ Ξ³ ∈ ℝ, fβ€²(∞) = 0 and fβ€²β€²(0) = βˆ’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 \in (-1, -{1\over2}) $ and Ξ³>0, and the second one is the structure of solutions for $ m \in (-1, -{1\over2}) $ and Ξ³β©Ύ0. Copyright Β© 2007 John Wiley & Sons, Ltd.

πŸ“œ SIMILAR VOLUMES

On similarity solutions for boundary lay
On similarity solutions for boundary layer flows with prescribed heat flux
✍ Bernard Brighi; Jean-David Hoernel πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 207 KB

This paper is concerned with existence, uniqueness and behaviour of the solutions of the autonomous third-order non-linear di erential equation f +(m+2)ff -( 2m+1)f 2 = 0 on R + with the boundary conditions f(0) = -, f (∞) = 0 and f (0) = -1. This problem arises when looking for similarity solutions