Exact solution of two-dimensional MHD boundary layer flow over a semi-infinite flat plate

In the present paper, an exact solution for the two-dimensional boundary layer viscous flow over a semi-infinite flat plate in the presence of magnetic field is given. Generalized similarity transformations are used to convert the governing boundary layer equations into a third order nonlinear differential equation which is the famous MHD Falkner–Skan equation. This equation contains three flow parameters: the stream-wise pressure gradient (ββ), the magnetic parameter (M  ), and the boundary stretch parameter (λλ). Closed-form analytical solution is obtained for β=-1β=-1 and M=0M=0 in terms of error and exponential functions which is modified to obtain an exact solution for general values of ββ and M  . We also obtain asymptotic analyses of the MHD Falkner–Skan equation in the limit of large ηη and λλ. The results obtained are compared with the direct numerical solution of the full boundary layer equation, and found that results are remarkably in good agreement between the solutions. The derived quantities such as velocity profiles and skin friction coefficient are presented. The physical significance of the flow parameters are also discussed in detail.

► MHD Falkner–Skan equation for 2-d viscous flow over infinite flat plate is derived. ► Obtained exact solution for few parameters has been exploited for other parameters. ► Results thus obtained are compared with direct numerical solution of the problem. ► Asymptotic solutions for large η and ±λ have been obtained for MHD Falkner–Skan equation. ► Dirichlet series is used for asymptotic problem and results agree well with numerics.