Numerical Study of Three-dimensional Boundary-layer Flow over ‎a Wedge: Magnetic Field Analysis

The magnetohydrodynamic flow of a viscous fluid over a constant wedge in three- dimensional boundary-layer has been analyzed both numerically and asymptotically. The magnetic field is applied normal to the flow. The mainstream flows aligned with wedge surface are assumed to be proportional to the power of the coordinate distances. The system is described using three-dimensional MHD boundary-layer equations which are converted to couple nonlinear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using the Keller-box method which is second-order accurate and asymptotically for far-field behavior. Both numerical and asymptotic solutions give good agreement in predicting the velocity behaviors and wall shear stresses. The effects of Hartmann number, pressure gradient and shear-to- strain-rate on the velocity fields are studied. Particularly, it is shown that the solutions of three-dimensional boundary-layer for variable pressure gradient exist, its effects are important on the boundary-layer flow. Results show that there are new families of solutions for some range of shear-to-strain-rate and there exists a threshold value of it beyond which no solutions exist. For some range of parameters, there is a reverse flow at which our boundary-layer assumptions are no longer valid. Various results for the velocity profiles, wall-shear stresses and displacement thicknesses are also obtained. The physical mechanisms behind these results are discussed.