The Present work on Computational techniques in transient magneto-hydrodynamic, dusty viscous and run-up flows deals with the Magneto hydrodynamics, the coupling between Navier-Stokes equations and Maxwell equations. The Situations which occur frequently are concerned with the motion of liquid or gas which contains a distribution of solid particles. Such type of motion occurs in the movements of dust, laden air, in fluidization, in the use of dusty gas in cooling systems to enhance heat transfer process by which the rain drops are formed by coalescence of small droplets which might be considered as solid particles for the purpose of examining their movement prior to coalescence. The Run-up flows are wider applications study indifferent technologies. Their applications embrace fields such as petrochemical engineering, Irrigation systems, metropolitan water supply systems and bio fluids mechanics where pressure gradients and suddenly changed from a steady state conditions.