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

Je Chiang Tsai; Ching An Wang

doi:10.1002/mma.852

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

Je Chiang Tsai^*, Ching An Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	1453-1466
Number of pages	14
Journal	Mathematical Methods in the Applied Sciences
Volume	30
Issue number	12
DOIs	https://doi.org/10.1002/mma.852
Publication status	Published - 2007 Aug
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General Mathematics
General Engineering

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10.1002/mma.852

Cite this

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title = "A note on similarity solutions for boundary layer flows with prescribed heat flux",

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.",

keywords = "Boundary layer theory, Initial value problem, Nonlinear boundary value problems, Phase plane analysis, Similarity solution, Third-order differential equation",

author = "Tsai, {Je Chiang} and Wang, {Ching An}",

year = "2007",

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doi = "10.1002/mma.852",

language = "English",

volume = "30",

pages = "1453--1466",

journal = "Mathematical Methods in the Applied Sciences",

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publisher = "John Wiley and Sons Ltd",

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T1 - A note on similarity solutions for boundary layer flows with prescribed heat flux

AU - Tsai, Je Chiang

AU - Wang, Ching An

PY - 2007/8

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N2 - 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.

AB - 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.

KW - Boundary layer theory

KW - Initial value problem

KW - Nonlinear boundary value problems

KW - Phase plane analysis

KW - Similarity solution

KW - Third-order differential equation

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 12

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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