Analysis of an hypersonic magnetohydrodynamic shock layer

A plane hypersonic flow collides against a body possessing a magnetic field, creating a bow shock and a shock layer where an enhanced density and temperature generate a positive electrical conductivity; therefore the Lorentz force influences the flow within the layer. A number of approximations of the magnetohydrodynamics equations, appropriate for the hypersonic case, simplify the system enough to allow us to obtain the values of pressure and velocity at any point of the layer, and in particular at the body itself, provided we know the values of these quantities at a section of the layer and at the shock wave. The last ones are provided by the Newtonian approximation. The inverse problem, to find the shape of the shock wave knowing the values of pressure and magnetic field at the body, may also be solved by this procedure.