Magnetohydrodynamic unsteady separated stagnation-point flow of a viscous fluid over a moving plate

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 96; no. 6; pp. 707 - 720
• Main Author: Dholey, S.
• Format: Journal Article
• Language: English
• Published: Weinheim Blackwell Publishing Ltd 01.06.2016; Wiley Subscription Services, Inc
• Subjects: boundary layer; Computational fluid dynamics; Differential equations; dual solutions; Flow characteristics; Fluid flow; Incompressible flow; Magnetic fields; Magnetism; Magnetohydrodynamic; Mathematical models; stagnation-point; Unsteady
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201400218

An analysis has been made for the unsteady separated stagnation‐point (USSP) flow of an incompressible viscous and electrically conducting fluid over a moving surface in the presence of a transverse magnetic field. The unsteadiness in the flow field is caused by the velocity and the magnetic field, both varying continuously with time t. The effects of Hartmann number M and unsteadiness parameter β on the flow characteristics are explored numerically. Following the method of similarity transformation, we show that there exists a definite range of β(<0) for a given M, in which the solution to the governing nonlinear ordinary differential equation divulges two different kinds of solutions: one is the attached flow solution (AFS) and the other is the reverse flow solution (RFS). We also show that below a certain negative value of β dependent on M, only the RFS occurs and is continued up to a certain critical value of β. Beyond this critical value no solution exists. Here, emphasis is given on the point as how long would be the existence of RFS flow for a given value of M. An interesting finding emerges from this analysis is that, after a certain value of M dependent on β(<0), only the AFS exists and the solution becomes unique. Indeed, the magnetic field itself delays the boundary layer separation and finally stabilizes the flow since the reverse flow can be prevented by applying the suitable amount of magnetic field. Further, for a given positive value of β and for any value of M, the governing differential equation yields only the attached flow solution. An analysis has been made for the unsteady separated stagnation‐point (USSP) flow of an incompressible viscous and electrically conducting fluid over a moving surface in the presence of a transverse magnetic field. The unsteadiness in the flow field is caused by the velocity and the magnetic field, both varying continuously with time t. The effects of Hartmann number M and unsteadiness parameter β on the flow characteristics are explored numerically. Following the method of similarity transformation, we show that there exists a definite range of β(< 0) for a given M, in which the solution to the governing nonlinear ordinary differential equation divulges two different kinds of solutions: one is the attached flow solution (AFS) and the other is the reverse flow solution (RFS). The author also shows that below a certain negative value of β dependent on M, only the RFS occurs and is continued up to a certain critical value of β.