A Class of Exact Solutions of Magnetic Hydrodynamics Equations for Describing Convective Flows of Multilayer Fluids

A class of exact solutions of magnetohydrodynamic equations for describing three-dimensional convective flows of multilayer fluids is constructed. For each fluid layer, expressions for hydrodynamic fields with functional arbitrariness are given. The velocity vector and magnetic field are described by linear forms in two horizontal (longitudinal) coordinates with coefficients depending on the third (vertical or transverse) coordinate and time. The pressure field and temperature field are described by quadratic forms. The paper discusses the use of the Stokes approximation for describing slow flows of a conducting continuous medium in a magnetic field. Several cases of integrating the magnetohydrodynamic equations in closed form for polynomial solutions are given.