Boundary layer velocity distribution of two special ferromagnetic fluid

Poiseuille flow refers to the incompressible viscous laminar flow in a pipe with two fixed plate. Assuming the ferrofluid is flowing along the x axis direction, with external uniform magnetic field B0 along y axis direction and external uniform electric field E0 along z axis direction. The plat plates are fixed in the (x; z) plane and the width between the two plates is 2a. The velocity and magnetic induction of the ferrofluid are given as follows: V=(u(y),0,0), B=Bx(y), By(y),B0+By(y),0). Suppose that ∂p/∂x is irrelevant to y and ∂p/∂y is irrelevant to x, let Fa=a√σ/η(B0+By(y)), then, for poiseuille flow of ferromagnetic fluid we get its boundary layer velocity. Morever, Couette flow of ferromagnetic fluid is also investigated.