Analysis of magnetohydrodynamic pressure in conducting fluids

The process of magnetic field influence on the movement of a viscous, conducting liquid was described by using a Maxwell-Navier-Stokes system of equations. By introducing vector potentials Ψ, ζ, A and elements of dimensional analysis, a nonlinear Poisson equation was produced for a function describing pressure distribution in a flat channel. For a Poiseuille flow there was formulated a Neuman boundary condition in a generalised form as an integral identity. To solve the above problem, a finite element approximation method was used. Appropriate numerical experiments were conducted. The calculation results were presented as a family of constant pressure lines and as lines of pressure value on the channel boundaries. All the experiments were performed for different values of criterion numbers: Reynolds (R_e), Reynolds magnetic (R_m ) and Hartman (H_a)