A comprehensive mathematical model for redox electrochemical systems with magnetohydrodynamics (MHD) and natural convection are presented. The model is based on density changes in isothermal systems that accompany redox reaction at the electrode due to supporting electrolyte ions migrating into and out of the diffusion layer to satisfy electroneutrality. Numerical simulations have been performed for an axisymmetric, milli-electrode electrochemical cell with gravity directed along the axis in both directions to investigate the effect of the electrode orientation with respect to gravity. Results show that natural convection is significant in both cases, with the maximum velocity being an order of magnitude higher when it forms a jet-like flow away from the electrode, compared to the case when the gravity direction is switched causing the fluid to flow toward the electrode. The electrode currents also show similar trend showing a higher current when gravity is directed toward the working electrode.