The phenomenon of convection is investigated in nonequilibrium plasmas where there are substantial nonuniformities in the plasma state. It is shown that a boundary‐value problem can be formulated to solve for the current stream function and the electron temperature including convective effects. The resulting equations are coupled and nonlinear so they are solved by an iteration technique. Two simple examples are chosen to illustrate the procedure. The first consists of a pair of electrodes in a straight channel, and the second is the entrance region of a parallel‐walled solid electrode device. In each case, only an applied electric field was considered. The calculations show the current streamlines and the electron temperature distribution displaced downstream for both uniform and nonuniform flows. It is also shown that as the flow velocity increases the voltage necessary to pass a specified amount of current increases.