Treffer: Unsteady MHD boundary layer on a porous surface

The authors study plane laminar unsteady MHD boundary layers on a porous surface. The outer magnetic field is homogeneous and perpendicular to the porous surface. The external velocity \(U\) is an arbitrary analytic function of the longitudinal coordinate \(x\) and time \(t\). The fluid is incompressible, and its electroconductivity \(\sigma\) is variable being the function of the boundary layer velocities \(u/U\). The fluid of the same properties as the fluid in basic flow is injected (or ejected) through the surface, in perpendicular direction. The described MHD boundary layer is considered in inductionless approximation. Starting from the equations of the observed problem, one can obtain the corresponding mathematical model. It is considered by applying the so-called ``universalization'' method. Namely, the numerical integration of the universal equation, obtained by applying appropriate transformations and by introducing three sets of parameters replacing the coordinates \(x\) and \(t\), is performed, once and forever. These parameters express the influence of the velocity \(U\), the injection (or ejection) velocity, the magnetic induction and the flow history in the boundary layer by means of its characteristic properties. By using these results, general conclusions on the development of the observed boundary layer can be obtained. These results can also be used in the prediction of concrete problems. Special attention is paid to the interesting special cases of universal equations for \(\sigma=0\) and for the so-called Rossow approximation \(\sigma=\sigma_0[1-(u/U)]\). The numerical integration is performed by means of difference schemes and by using three-diagonal algorithm iteratively. A part of the obtained results is analyzed.