On similarity solutions for boundary layer flows with prescribed heat flux

Details On similarity solutions for boundary layer flows with prescribed heat flux On similarity solutions for boundary layer flows with prescribed heat flux

2006-03-03

arxiv.org/abs/math/0603080v2

Mathematical Methods in the Applied Sciences, vol. 28, 4, 2005, pp. 479-503

Mathematics

Classical Analysis and ODEs

v2: new page-setting

Scientific paper

This paper is concerned with existence, uniqueness and behavior of the solutions of the autonomous third order nonlinear differential equation $f'''+(m+2)ff''-(2m+1)f'^2=0$ on $\mathbb{R}^+$ with the boundary conditions $f(0)=-\gamma$, $f'(\infty)=0$ 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 coordinates to obtain a plane dynamical system.

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