Parametric approach to liquid metal MHD channel studies

Generally, when talking about a parametric approach, it is assumed that the properties of the system considered are studied depending on some values which have neither space nor time distribution. Occasionally, parameter appearance is a natural result of a mathematical model creation, such as hydrodynamic, dimensionless numbers. In some cases, parameters may be introduced in an artificial way to simplify studies. The main simplification for any applied MHD problem is the exclusion of the hydrodynamic or electrodynamic part. In particular, a parametrization of magnetic induction space distribution, under a low magnetic Reynolds number, allows two parts of a general problem to be considered respectively. This means that discretization of continuously distributed magnetic induction should be made and then a set of parameters created, each characterizing a respective continuous field in some limited part of the system. In this paper, a piecewise-constant magnetic field distribution has been introduced and applied to a respective representation of the electric potential and current density in the form of finite sums