Design, Development and Simulations of MHD Equations with its proto type implementations

The equations of motion of conducting fluid in a magnetic field are formulated. These consist of three sets. First is the mass conservation equation, second Navier Stokes equation which is Newton’s second law taking into account the force of magnetic field on moving charges. The electrical field effects are neglected as is usually done in MHD. The third set is Maxwell’s equation especially to monopole condition along with Ampere’s law with the current given by ohm’s law in a moving frame (the frame in which the moving particles of fluid is at rest).The mass conservation equation assuming the fluid to be incompressible leads us to express the velocity field as the curl of a velocity vector potential. The curl of the Navier Stokes equation leads to the elimination of pressure, there by leaving with an equation involving only magnetic field and the fluid velocity field. The curl of the Ampere law equation leads us to another equation relating to the magnetic field to the velocity field. A special case is considered in which the only non vanishing components of the fluid are the x and y components and the only non vanishing component of the magnetic field is z component. In this special case the velocity vector potential only has one non zero component and this is known as stream function. The MHD equation in this reduces to three partial differential equations for the three functions in 2D model. Ψ stream function embeds and components. Application of MHD system prototype has been worked and presented. KeywordsLorentz force, Navier Stokes Equation, Maxwell’s Equation, Iterative Solution, Prototype.