On similarity solutions for boundary layer flows with prescribed heat flux

Abstract

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