electroosmotic pressure-driven flow through a slit micro-channel with electric and magnetic transverse field

In the present study, flow through two-dimensional microchannel under an axial electric field, transverse electric and magnetic fields and with axial pressure gradient has been investigated numerically. continuity and momentum equations were solved steadily with respect to the non-slip condition by using discrete finite volume method and a numerical code. the results show that in the presence of the axial electric field, applying transverse magnetic field reduces flow velocity. however, when the transverse electric field and axial electric field exist together, applying the transverse magnetic field increases the flow rate to a certain extent and then reduces the flow rate. hartmann number like this amount of magnetic field is known as critical hartmann number. therefore, with the presence of transverse and axial electric fields and transverse magnetic field, the highest possible flow rate is for critical hartmann number. it was also found that by increasing the pressure gradient within the microchannel, the critical hartmann number decreases. moreover, by increasing the transverse electric field, the sensitivity of critical hartmann number to the pressure gradient decreases and its value tends to a specific number (about 1.5).