The hydrodynamics characteristics of buoyancy-driven convection loop containing an electrically-conducting fluid in a transverse magnetic field is investigated analytically using one-dimensional model. The lower portion of the loop is heated and the upper portion is cooled, both isothermally, while the middle portion is insulated. The model was based on the use of Hartmann plane Poiseuille flow solution for estimating loop shear stress. The study covers the range of Grashof number, Gr, from 10(2) to 10(6), the Hartmann number, Ha, from 0 to 20, and the Prandtl number, Pr, from 0.02, to 7. The proposed closed form analytical solution of the magnetohydrodynamic generator predicts the flow velocity and the induced current in terms of the how and geometric parameters. It is shown also that at low Prandtl numbers, Pr << 1, there exist an optimal Hartmann number, Ha(opt) that maximises the induced electric current and Ha(opt) depends weakly on Grashof number. The existence of an optimal Hartmann number is significant in optimising the loop efficiency of conversion from thermal to electrical energy in presence of a transverse magnetic field.