MHD boundary layer flow over a non-linear stretching boundary with suction and injection

In this paper, we give an exact solution to the most celebrated magnetohydrodynamic Falkner–Skan equation. The equation governs the two-dimensional laminar boundary layer flow of a viscous, incompressible and electrically conducting fluid over a semi-infinite flat plate in the presence of magnetic field. Similarity transformations are used to convert the governing coupled non-linear partial differential equations into a highly non-linear ordinary differential equation with boundary conditions. An exact analytical solution is obtained for certain parameters which is then modified and generalized to give an exact solution to all other involved parameters. The results thus obtained are compared with that of direct numerical solutions, which agree well up to desired accuracy. The MHD Falkner–Skan equation exhibits the upper and lower branch solutions that reveal a very interesting velocity profiles for a set of parameters. Results are presented in the form of velocity profiles and skin friction for various values of physical parameters and are discussed in detail.

► We have obtained an exact solution to the MHD Falkner–Skan equation for all values of ββ and M   parameters.
► The closed-form solution of the system for β=−1β=−1 and M  =0 in terms of error and exponential functions is obtained.
► This solution is rewritten in convenient form and used to generalize for any values of ββ and M.
► Asymptotic solution to the problem is obtained.
► Physical significance of the problem is discussed.