Similarity solutions for boundary layer flows with prescribed surface temperature

We are concerned with the third-order nonlinear equation f‴+[(m+1)/2]ff″−mf′2=0f‴+[(m+1)/2]ff″−mf′2=0 on (0,∞)(0,∞), satisfying the boundary conditions f(0)=a∈Rf(0)=a∈R, f′(0)=1f′(0)=1 and f′(∞)=0f′(∞)=0. The problem arises in the study of similarity solutions in two physically different contexts of fluid mechanics: free convection in a porous medium and flow adjacent to a stretching wall. We shall address two open questions: the first one is the uniqueness of bounded solutions for m∈(−1/3,0)m∈(−1/3,0) and a<0a<0, and the second one is the structure of solutions for m∈(−1/2,−1/3)m∈(−1/2,−1/3) and a≤0a≤0. Our results complement earlier results in the literature.