EMHD free-convection boundary-layer flow from a Riga-plate

The electro-magnetohydrodynamic (EMHD) free-convection flow of a weakly conducting fluid (e.g. seawater) from an electromagnetic actuator is considered. The actuator is a so called Riga-plate which consists of a spanwise aligned array of alternating electrodes and permanent magnets mounted on a plane surface. This array generates a surface-parallel Lorentz force which decreases exponentially in the direction normal to the (horizontal) plate. The free-convection boundary-layer flow induced by this body force is investigated numerically and analytically. It is shown that a certain length and velocity scale exists on which the flow characteristics are independent of the material properties of the fluid, as well as of the structural and functional parameters of the actuator. These universal velocity profiles are calculated numerically at different distances x from the leading edge and are discussed in some detail, both for the impermeable and the permeable Riga-plate when; in the latter case, a uniform lateral suction or injection of the fluid is applied. For the flow characteristics analytical approximations are reported. The asymptotic suction profiles approached for large values of x are given in exact analytical form. From a mathematical point of view the basic equations of the present boundary-value problem resemble those of the classical Blasius problem with an inhomogeneous forcing instead of an external flow and, accordingly, a homogeneous asymptotic condition.