The fully developed laminar magnetohydrodynamic free convection between two concentric vertical cylinders with Hall currents and heat source/sink, in the presence of the radial magnetic field, are studied. The governing thermal energy and momentum equations are changed into ordinary differential equations whose solutions are determined in closed-form expressions of the Bessel and modified Bessel functions of order zero. A parametric investigation illustrating the impacts of the Hall current, magnetic field, heat source, and radii ratio has been accomplished graphically to examine the changes in temperature as well as velocity while the Nusselt number, mass flux, and skin friction values have been presented in tabular forms. The results ensure that the Hall current has a strong and direct impact on the flow character, such that the influence of the Hall parameter enhances the velocity fields in the appearance of heat source and sink. The velocity remains almost constant as the Hall parameter value is greater than four.Moreover, the velocity and temperature fields have an increasing tendency due to the heat source and inversely for the heat sink. K E Y W O R D S Hall current, heat source/sink, magnetohydrodynamic, natural convection, Nusselt number, skin friction F I G U R E 1 Physical model of system