Magnetohydrodynamic Rayleigh problem for magnetic prandtl number close to one

Summary In this paper the solutions for indicial motion of an infinite flat plate are discussed. It is assumed that the fluid is incompressible and has constant viscosity and electric conductivity. It is also assumed that both the solid and fluid are semi-infinite or that the solid is thin with fluids on both sides. The conductivity of the wall is assumed in one case to be much greater than the conductivity of the fluid and in a second case to be much less than that of the fluid. In the limit the first case corresponds to a perfectly conducting wall; the second, to a perfectly insulated wall. The distributions of the velocity, magnetic field current, and vorticity are calculated. In the case where the magnetic diffusivity becomes larger than the viscous diffusivity, we show that there is a spreading of the layer in which the magnetic field changes and also a shrinking of the viscous layer. Both layers are very thick in comparison with the non-magneto-hydrodynamic case. This is due to diffusion of the Alfvén wave carrying the vorticity and the current.