Theoretical analyses of immiscible MHD pipe flow

•Effect of magnetic field on flow characteristics was studied.•Immiscible MHD fluid flow was investigated.•Laplace transform was used to estimate local flow velocities.

In this study, effect of normally applied magnetic field on immiscible fluid flow hydrodynamic flow characteristic has been analytically investigated. Flow case modelled for two different flow patterns. The first one is low electrically conductive fluid (gasoline) inner core and higher one (salty water) outer flow regional pattern and the second one is high electrically conductive fluid inner core and lower one is outer regional flow case in a vertical circular pipe. Flow models have been modelled in differential form theoretical equations and solved with Laplace Transform method. Solved equation systems presented the dependent statement of the local flow velocity and flow rates to the magnetic field induction, pipe radius and pressure gradient. It is estimated that high electrically conductive fluid was directly affected by the magnetic forces which is created by the magnetic field, and also low electrically conductive fluid was indirectly affected from the magnetic field because of the interfacial tension between the fluids. As a result, overall velocity of the flow domain was reduced more by the magnetic forces in the event of low conductive fluid inner core and high conductive fluid outer regional flow case.