We pinpoint the limitations in traditional electroviscous analysis for narrow fluidic confinements. We show that because of neglecting the convective transport of ions originated out of the established streaming field itself, the traditional approach may result in physically inconsistent flow rate predictions. We show that the larger the value of an ionic Peclet number and narrower the confinement, the more conspicuous are these erroneous predictions, within threshold limits of the nondimensional zeta potential. We come up with an improved mathematical model to overcome such discrepancies.