On The Steady Incompressible Laminar Saltwater Flow In Minkowski 2-D Subspace Continuum Through A Rectangular MHD Micro-pump

[Display omitted] •The formation of a uniformly distributed Lorentz force in the electrically conducting NaCl solution flows in a micro pump is investigated under applied DC electric and magnetic fields. The corresponding MHD equations are solved analytically by introducing a new ansatz combining the wave-position characters of the flow in Minkowski 2-D subspace continuum subjected to suitable boundary conditions.•In brief it is found that:•Increasing high ratios of the electrode to channel lengths serves to attain more coverable channel area.•An excess of the applied fields tends to compensate the velocity degradation for deep channel configuration.•Graphics show that the decreased friction force between the channel top and bottom is a preferable factor to improve the process in practice. The problem of a steady, incompressible and fully developed laminar fluid flow is discussed. This study focuses on the predictions of the pumping performance of 1 M NaCl solution. The corresponding Navier-Stokes momentum (MHD) equations are solved analytically by introducing a new ansatz combining the wave-position characters of the flow modelled in Minkowski 2-D subspace continuum subjected to suitable boundary conditions. Solving for the velocity profile of the working fluid across the micro-channel; the obtained solutions which include the dimensional flow velocity, volumetric flow rate, average velocity and pressure gradient are plotted under various operating currents, magnetic flux densities and micro-channel aspect ratio values. Our results provide that increasing high ratios of the electrode to channel lengths serves to attain more coverable channel area. It is also noted that an excess of the applied fields tends to compensate the velocity degradation for deep channel configuration. Graphics show that the decreased friction force between the channel top and bottom is a preferable factor to improve the process in practice. Our results may be useful to shed light on studying the microfluidic systems flow.