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The effect of electro‐convection in a cylindrical flow annulus on heat transfer enhancement has been investigated numerically. Weakly ionized air is considered to be the working fluid throughout this work. The effect of exit boundary condition, considered to be the main hindrance for the numerical solution, has been discussed in detail. The present work shows interesting flow field characteristics, which are in excellent agreement with some other established experiments. The heat transfer enhancement, as reported in this work, appears to be small in view of the low magnitude of the applied voltage but it clearly and surely delineates the trend, i.e. with increase in the strength of the electric field, heat transfer enhances.