Magneto-fluid dynamic boundary layer on a moving continuous flat surface (Q1095761)

The equations for laminar boundary layer on a moving continuous flat surface, in the presence of a magnetic field, are treated using group analysis and the existence and uniqueness of solutions of the resulting boundary value problem (BVP) \[ f\prime''(\eta)+f(\eta)f''(\eta)-\beta f'(\eta)=0,\quad \beta >0,\quad f(0)=\alpha \geq 0,\quad f'(0)=1,\quad f'(\eta)\to 0\quad as\quad \eta \to \infty, \] where \(\alpha\) is a suction parameter, is established. Further, the numerical solution of the above BVP in the special case \(\alpha =0\) (no suction at the surface) and the effect of the magnetic field on the boundary layer thickness and the skin friction at the surface are discussed. Also, the value of f''(0), which is needed in the numerical solution of the above BVP is estimated in the case \(\alpha =0\) by determining its lower and upper bounds using just the essential qualitative properties of the solution.