Similarity solutions for a model arising from high frequency excitation of liquid metal in an antisymmetric magnetic field (Q2895948)

The paper presents a study on the third-order differential equation NEWLINE\[NEWLINEf'''+\frac{m+1}{2}ff''-mf'{}^{2}=0,NEWLINE\]NEWLINE where \(f\) is defined on \(t\in(0,+\infty)\) and \(m\) is a real parameter. The study is motivated by several physical contexts, e.g., free convection boundary layer flows over a vertical flat plate embedded in a porous medium, boundary layer flows of incompressible viscous fluid over a stretching surface and excitation of liquid metals in a high-frequency magnetic field.NEWLINENEWLINEThe work complements earlier results on the problem subject to the boundary conditions \(f(0)=a\), \(f'(0)=-1\) and \(f'(+\infty)=0\) describing comprehensively the solution structure for the previously unsolved case \(m\in(-1,0)\).